Ciaccio Math - About Me



Chapter 1 HomeworkName: ____________________________________1.1.11076325451485001-4.?Carefully place each capitalized letter of the alphabet below into your Venn diagram based on its type of symmetry. 96393037465001-6.?Camille loves guessing games.? She will tell you a fact about her shape to see if you can guess what it is.? (Refer to the Math Notes box in this lesson if you need help with the vocabulary.)? a. “My triangle has only one line of symmetry.? What is it?”b. “My triangle has three lines of symmetry.? What is it?”c. “My quadrilateral has no lines of symmetry, but it does have 180? rotation symmetry.? What is it?”30099004781554667254591051-7.?Solve each equation, then check your solutions. a. b. 2962275293370428625297180 c. d. 1-8.?Angela has a rectangular piece of paper and cuts a rectangle out of a corner as shown at right.? What are the area and perimeter of the resulting shape?? 3777225-2471600432435052070001.1.2 1-16.?Examine the diagram. What is another name for ∠ABC?? 1-17.?If no sides of a triangle have the same length, the triangle is called?scalene?(pronounced SKAY-leen). And, as you might remember, if the triangle has at least two sides that are the same length, the triangle is called isosceles.??Use the markings or description in each diagram below to decide if ?ABC?is isosceles or scalene.? Assume the diagrams are not drawn to scale.? 6762753213100024288753810004562475381000 b. c. 1-18.?Finding and using a pattern is an important problem-solving skill necessary for your study of mathematics.? The patterns in Diamond Problems?are used later in the course to solve other types of algebraic problems. Look for a pattern in the first three diamonds below.? For the fourth diamond, explain how to find the missing numbers (?) if you know the two numbers (#).?Use the pattern you discovered to complete each one.??3998881426071001-20.?Show where each person described below should be represented in the diagram.? If a portion of the Venn diagram remains empty, describe the qualities a person would need to belong there.? Carol: “I rarely study and enjoy braiding my long hair.”Bob: “I never do homework and have a crew cut.”Pedro: “I love joining after school study teams to prepare for tests, and I like being bald!”Toby:?“I really love playing in my heavy metal band, but now that I am enrolled at MIT, I have to study all the time and don’t have much time to play.? My mom really wishes that I would cut my long, messy hair.1.2.11-26.?Solve the equations below for?x, if possible.? Be sure to check your solution.? 357187514986065722573660a. b.542925390525c. 1-27.?Sketch an example of each triangle below, if possible.? If not possible, explain why not.? Refer to the glossary if you need help with the vocabulary.? a. right isosceles triangleb. right obtuse trianglec. scalene equilateral triangled. acute scalene triangle584771516129000left4761251-28.?Copy these Diamond Problems and use the pattern you discovered earlier, shown at right, to complete each problem.? Some of these may be challenging!?? ??4643336242696001-29.?Mei puts the polygons at right into a bucket and asks Brian to pick one.? a. What is the probability that he pulls out a quadrilateral with at least one pair of parallel sides?b. What is the probability that he pulls out a polygon with rotation symmetry??1.2.2.528773635839001-36.?If the perimeter of the rectangle at right is 112 cm, which equation below represents this fact?? Once you have selected the appropriate equation, solve for?x.? (2x???7)?+?(4x?+?3)?=?112b. 4(2x???7)?=?112 c. 2(2x???7)?+?2(4x?+?3)?=?112d. (2x???7)(4x?+?3)?=?1121-37.?Write an expression for the area of each rectangle below.? 742950107950035998159652000?b. 1-40.?Solve each equation below for?x.? Show all work and check each answer by substituting it back into the equation and verifying that it makes the equation true.? 456247510160220980082553619508890a. b. c. 1-41.?Sandy and Robert each have various polygons in their Polygon Buckets (see below).? Sandy randomly selects a polygon from her Polygon Bucket, and Robert randomly selects a polygon from his.? 125095317500a. Who has a greater probability of selecting a quadrilateral?? Justify your conclusion.b. Who has a greater probability of selecting an equilateral polygon?? Justify your conclusion.?c. What is more likely to happen: Sandy selecting a polygon with at least two sides that are parallel or Robert selecting a polygon with at least two sides that are equal???1.2.3 1-50.?For each of the shapes formed by algebra tiles below:? Write an expression that represents the perimeter.323024540386000Simplify your perimeter expression as much as possible.3816353937000a. b. 38195255848353810005848351-51.?For each rectangle below, what is the area of each part and what is the area of the whole??? a. b.1-55.?Simplify the following expression by combining like terms 5x2?+ 6x?? 3 + 4x2?? 8x?+ 2.? A?term?is a single number, variable, or product of numbers and variables.? How many terms are in the original expression?? How many are in the simplified expression?When variable(s) are multiplied by a number, the number is called a?coefficient.? What is the coefficient of?x?in your simplified expression?1.2.441148001219200054673501898651-63.?Write a complete description of the graph shown below.? ? ?1-64.?Match each table of data below with the most appropriate graph and briefly explain why it matches the data.? a. Boiling water cooling down?b. Cost of a phone call ?c. Growth of a baby in the womb ?1-66.?Determine the total area of each rectangle below.? Remember that each number inside the rectangle represents the area of that smaller rectangle, while each number along the side represents the length of that portion of the side.? 3230545144720010750555969000a. b. 6129201248076001-67.?Complete each of the Diamond Problems below.?The pattern used in the Diamond Problems is shown at right.? ????1.3.1 1-75.?Examine the diagrams below.? For each pair of angles marked on the diagram, decide what angle pair relationship(s) the angles have.? You may list more than one relationship for each pair of angles.? 1866900314960114300229235a. b . c.d. 5267325596903562350501651-77.?Examine the diagrams below.? What is the angle pair relationship between the labeled angles? ?Use the relationship to write an equation and solve for?x.? Then confirm your answer by calculating the angle measures of the labeled angles.? 5429251250953943350125095a. b.35753294122961-78.?For the rectangle shown at right, write an equation to show that the area as a?product?of the dimensions is equivalent to the area as a?sum?of the tiles.? Remember to combine like terms whenever possible.? 454687993722001-80.?Graph the line?y?=?x?on graph paper. a) Draw a slope triangle.b) Rotate your slope triangle 90° around the origin to get a new slope triangle.? What is the new slope? ?c) Write an equation of a line perpendicular to?y?=?x. ?1.3.2 5531304537521-87.?Jerry has an idea.? Since he knows that an isosceles trapezoid has reflection symmetry, he reasons,?“That means that it must have two pairs of angles with equal measure.”? He marked this relationship on his diagram at right.152400070548566675781685Similarly, mark?which angles must have equal measure due to reflection symmetry on the shapes below.33197241870115444846238090a.b. c. d.39433505734057429507924801-88.?Determine the total area of each rectangle below.? Each number inside the rectangle represents the area of that smaller rectangle, while each number along the side represents the length of that portion of the side.? ?b.1-90.?Solve the following problem using any method.? Write your solution as a sentence. The length of a rectangle is 5 cm longer than twice the length of the width. If the perimeter of the rectangle is 88 centimeters, what is the width??? 33657795471001-92.?Write a complete description of the graph shown below. ? 1.3.3. 4486352283294001-98.?Using the diagram at right, name the angle pair relationships of the angle pairs listed below. ?d?and?ee?and?ha?and?ec?and?d1-99.?Calculate all the missing angle measures in the diagrams below. 36017202228850035115522288500a. b.4648200241301-101.?Write the area of the rectangle below as a?product?and as a?sum.?? 1.3.4 1-110.?Use the Triangle Angle Sum Theorem to write an equation and solve for?x?in each diagram below.? Show all work.?? 3390900298450057213521082000 b.c. How can you verify that your answer for part (b) is correct?1-111.?Examine each diagram below.? Which diagrams are possible?? Which are impossible?? Justify each conclusion.?? 434467014351000right8288500280850710419600129040310872500-2815577393900 1-112.?Complete each of the Diamond Problems below.?-200972693005721985271780001-113.?Examine the angle pair relationships in the diagram at right.? Then write and solve equations for?x?and?y, if possible.? Justify your work using angle relationships.??? 1-114.?Examine the rectangles formed with tiles below.? For each figure, write an equation showing that its area as a product of the width and length is equal to its area as a sum of its parts.? 37528501333506096009525a.b.Chapter 2 HomeworkName:_________________________________2.1.1 2-6.?The diagrams below are not necessarily drawn to scale. For each pair of triangles:Determine if the two triangles are congruent.If the triangles are congruent, write a congruence statement (such as?ΔPQR?? ΔXYZ) and give the congruence theorem (such as SAS ?).If the triangles are not congruent, or if there is not enough information to?determine congruence, write “cannot be determined” and explain?why not. ? ?71779917153300AC?is a straight segment:1366638462070024618223097800-4276610336700499183259286004951639140795002-11.?Misty is building a triangular planting bed.? Two of the sides have lengths of eight feet and five feet.? What are the possible lengths for the third side?? 2.1.2 2-17.?In an isosceles triangle, the two angles opposite the congruent sides are called the?base angles.? You may have learned in a previous course that the base angles of an isosceles triangle are always congruent.? Now you will prove it!? In the diagram at right, ??SYM?is an isosceles triangle, and point?E?is the midpoint of?SM?.???577215024003000Make a flowchart to prove that the base angles of ??SYM?are congruent, that is, prove that ∠S?? ∠M.Would your proof work for any isosceles triangle??4648780525422002-18.?Determine the area of each of the following figures.? Assume that all angles that look like right angles are right angles.??left5143500? ? 2-21.? Complete each of the Diamond Problems below.?? ? a.b.c.d.432054095440500487045878840002-22.?Use your knowledge of angle pair relationships to write an equation and solve for?x?in the diagrams below.? Then calculate the measures of the labeled angles.? Justify your solutions by naming the theorem.??2.1.3 2-27.?Write a converse for each conditional statement below.? Then, assuming the original statement is true, decide if the converse must be true or not.? If it rains, then the ground is wet.If a polygon is a square, then it is a rectangle.If a polygon is a rectangle, then it has four 90° angles.If a polygon has three angles, it is a triangle.If two lines intersect, then vertical angles are congruent.34048706153151422268579755-456855639012-28.??Solve for?x?in each diagram below. ? ? 849253578594005124450152051002-30? The set of equations at right is an example of a?system of equations.? Solve the system using an algebraic method of your choice (substitution or elimination). 2-31.?Determine whether or not the triangles in each pair below are congruent. Justify?your conclusion with a triangle congruence theorem. ? 33413702603500160274012573000? ? ?-368302514600045580235864123410515712141640073569678center5511802-32.?Complete each of the Diamond Problems below.2.1.42-41.??Solve each equation below.? Show all work and check your answers.? ? ? a. ?b.??c. ?d. ?5048522170592002-42.?? Examine the two triangles at right.??Are the triangles congruent?? Justify your conclusion.? If they are congruent, complete the congruence statement ΔDEF????????.What sequence of transformation(s) will map ΔDEF?onto ΔJKL?56252903020100?2-43.??The dashed line at right represents the line of symmetry of the shaded figure.? Calculate the area and perimeter of the shaded region.? Show all work.?4825002197638002-44.? Examine the figure at right, which is not drawn to scale.? Which is longer,?AB?or?BC?? Explain your answer.??5566898259890002-45.? While waiting for a bus after school, Renae programmed her MP3 player to randomly play two songs from her playlist, at right.? Assume that the MP3 player will not play the same song twice.?a. Are each of the combinations of two songs equally likely?? b. Calculate the probability that Renae will listen to two songs with the name “Mama” in the title.c. What is the probability that at least one of the songs will have the name “Mama” in the titled. Why does it make sense that the probability in part (d) is higher than the probability in part (c)?2.2.13987800498475002-51.??Plot triangle?ABC?with vertices?A(0, 0),?B(3, 4), and?C(3, 0) on graph paper.? Using the origin as the point of dilation, enlarge it by a factor of 2 (imagine using two rubber bands).? Label this new triangle?A'B'C'.?What are the side lengths of the original triangle,?ΔABC?What are the side lengths of the enlarged triangle,?ΔA'B'C'?Calculate the area and the perimeter of ΔA'B'C'.???458498025694500?2-54.?? Examine the triangles at right. Are these triangles congruent??If so, use a flowchart to show how you know.? If they are not congruent, explain how you know.??2-55.?Fill in the missing dimensions and areas.? Then write the area as a product equal to the area as a sum.?? ? ? a.b.4530725471170002-56.??For each triangle below, solve for the variable and answer the questions.?Solve for?x. ?What kind of triangle is ?ABC??Be specific. Solve for?y. ?What kind of triangle is shown in the figure? Be specific.47418218509000right58420002.2.22-61.? If you enlarge the shape at right from the origin by a?scale factor of 4, what are the new coordinates? 2-62.? Look at the similar triangles below.? Which sides correspond?? Write ratios for the corresponding side lengths.Calculate the length of the hypotenuse of each triangle.? Is the ratio of the hypotenuses equal to the ratios you found in part (a)?Describe a sequence of transformations that would map one triangle onto the other.4798060314960002-64.??Examine each diagram below.? Identify the error in each diagram.?? 250126525400045085208280002-65.? Complete each of the Diamond Problems below. ? ? a.b.c.d.2-66.??TOP OF THE CHARTSright4000500Renae’s MP3 player can be programmed to randomly play songs from her playlist without repeating a single song. Currently, Renae’s MP3 player has five songs loaded on it which are listed at right.? At the moment, she only has time to listen to one song. ? Is each song equally likely to be chosen as the first song?What is the probability that her MP3 player will play a country song?What is the probability that Renae will listen to a song with “Mama” in the title?What is the probability that she listens to a duet with Hank Tumbleweed?What is the probability that she listens to a song that is not R & B?2.3.1 2-78.??Decide if each pair of triangles below is similar.? If the triangles are similar, justify your conclusion by stating the similarity condition you used.? Also, describe a possible sequence of transformations that would carry one onto the other.? If the triangles are not similar, explain how you know they are not similar.?? 330263510795000? ?352679063500135255-3175000? 477329588138000295465589662000164338089662000135890956945002-79. Fill in the missing dimensions and areas.? Then write the entire area as a product equivalent to the area as a sum? ? ? ??2-80.? Write a converse for each conditional statement below.? Decide if the converse must be true or not.?If the base angles of a triangle are congruent, then it is isosceles.If a polygon is a triangle, then the sum of the angles in the polygon is 180°.2-82.?Assume that each pair of figures below is similar.? Write a similarity statement to illustrate which parts of each shape correspond.? Remember, letter order is important!??396684586995002162810355600067945361950042498322566102-83.??Plot?ABCDE?with vertices?A(–3, –2),?B(5, –2),?C(5, 3),?D(1, 6), and?E(–3, 3) on graph paper.??Use the method from problem 2-47 to enlarge it from the origin by a factor of 2.? Label the image?A'B'C'D'E'.How are the coordinates of the vertices of?A'B'C'D'E' related to the coordinates of the vertices of?ABCDE?What are the area and the perimeter of both figures?2-84.??Determine which of the following pairs of triangles are similar.? Justify your answer.?? 417449036512500207835521399500266700217170002-85. For the similar triangles below is?.? Write at least three more proportions given that??ABC?~??DEF.????right66619002-87.??Solve the system of equations at right using the method of your choice, then state the solution to the system.? If there is not a solution, explain why.394462027876500311721515875000509333574930002-88.??Based on the measurements provided for each triangle below, determine whether the measure of?x?must be more than, less than, or equal to 45?? ? 2-89.??Simplify the following expression by combining like terms:(3x2?+?x?? 2) ??(4x2?+?x?? 5). 2.3.2 2-94.??Determine which similarity conditions (AA?~, SSS?~, or SAS?~) could be used to establish that the following pairs of triangles are similar.? List as many?as you can.???55880000? ? -454060002148205502400?522514344382-96.??Are the triangles similar?? If so, write a flowchart proof that justifies your conclusion.? If not, explain how you know.?? 2-98.? If two sides of a triangle are 8" and 13" long, what do you know about the length of the third side??? ?2.3.3 right250469002-103. ? Use the triangles at right to answer the following questions. ?Are the triangles at right similar???How do you know if they are similar? ?Show your reasoning in a flowchart.Examine your work from part (a).? Are the triangles also congruent?? Explain why or why not.2-106.? Draw an area model for each expression.? Then write a statement for the area as a product and as a sum.??? ? a. ?(x?+?3)(2x?+?1)b. ?2x(x?+?5) ?? ? c. ?x(2x?+?y)d. ?(2x?+?5)(x?+?y?+?2)475264075191000239283576119002-107.?For each figure below, calculate the area and the perimeter.2-108.??Solve for the missing lengths.? Show all work.??? ?3595056475824-952555372000a. ?ΔGHI?~?ΔPQR ?? ? b. ?ΔABC?~?ΔXYZ ??2.3.4 2-114. ?Which pairs of triangles below are congruent and/or similar?? For each part, explain how you know using an appropriate triangle congruence or similarity condition.? Note: The diagrams are not necessarily drawn to scale. ? ? ? a. ?b. ?? ? c. ?d. ??2-117.??Solve for the missing lengths in the sets of similar figures below.?? 2146935-29083000? ? a. ?ABCD?~?JKLM?159194536258500? ? b. ??NOP?~??XYZ ??2-118.??Which of the following events are independent?? Two events are?independent?if knowing that one event occurred does not affect the probability of the other event occurring.??Flipping five heads in a row and then flipping another head.Drawing two aces from a deck of cards without replacing them and then drawing another ace.Having blue eyes, if you have blonde hair.It rains this weekend, and the debate team from North City High School wins the state championship.Your friend selects a diet soda from a cooler of mixed beverages and then you select a diet soda from the same cooler without looking.2-119.? Sketch an area model with the following dimensions on your paper, label the dimensions, and write an equivalence statement for its area as a product and as a sum.?? ? ? a. ?(2x?+?1)(2x?+?1)b. ?(2x)(4x)? ? c. ?2(3x?+?5)d. ?y(2x?+?y?+?3)Chapter 3 HomeworkName: ____________________________________3.1.13-6? ROLL AND WIN554696948962700You begin the game?Roll and Win?by picking a number.? Then you roll two regular dice, each numbered 1 through 6, and?add?the numbers that come up together.? If the sum is the number you chose, you win a point.? For example, if you choose “11”, and a 6 and a 5 are rolled, you win!?? What is the sample space, which can be thought of as the set of all the possible outcomes, when two dice are rolled and their numbers added?One way to analyze this situation is to make a table of all the possible outcomes like the one at right.? Complete this table of sums on your paper.? Are each of the outcomes in this table equally likely?What is?P(even)???P(10)???P(15)?Which sum is the most likely result?? What is the probability of rolling that sum?3-755108857039500Determine the missing angle measure(s) in each problem at right using the geometric relationships shown in the diagram at right.? Be sure to write down the conjecture that justifies each calculation.? Each part is a separate problem.??a. If?d?= 110° and?k?= 5x?– 20°, write an equation and solve for?x.b. If?b?= 4x?– 11° and?n?=?x?+ 26°, write an equation and solve for?x.? Then determine the measure of?n.327073869500000488019863774300162044475114300265898695207003-8?Complete each of the Diamond Problems below. ?3.1.23-17?Out of the 20 contestants in the state math championships, 10 are girls.? For this round, each contestant gets asked one question.? The first question goes to a randomly chosen contestant.???What is the probability that the first contestant is a girl?If the first contestant is a girl, what is the probability that the second contestant is a girl?Is the probability that the second contestant is a girl independent of the first contestant being a girl?3-19??Eddie is arguing with Tana about the probabilities of different outcomes when flipping three coins.? They decide to flip a penny, nickel, and a dime.?? Which would be better for representing the sample space, a systematic list, a tree diagram, or an area model?? Justify your answer.Determine the sample space of all possible outcomes. ?How many outcomes are there?Calculate the probability of each of the following events occurring.?i.?Three headsii. One head and two tails iii.?At least one tail iv. Exactly two tailsWhich is more likely, flipping at least two heads or at least two tails?? Explain.3-20? WACKY DIAGRAMSAfter drawing some diagrams on his paper, Jason thinks there is something wrong.? Examine each diagram below and decide whether or not the triangle could exist.? If it cannot exist, explain why not. ? ? a. ? b.Multiply and simplify the following expressions using an area model.?? (x?+ 5)(3x?+ 2)(y???6)(2x?+?3y???4)585117720097400-857251322705003-22.??Refer to ?ABC?at right.? Determine if each triangle below is congruent to ?ABC, similar but not congruent to ?ABC, or neither.? Justify each answer.? If you decide that they are congruent, organize your reasoning into a flowchart. ?509174421634700?2600520132743003.1.33-30 Use a probability area model, a tree diagram, or refer to the table you created for the Roll and Win situation (problem 3-6) that represents the sample space for the sum of the numbers when rolling two standard six-sided dice.??In a standard casino dice game the player wins on the first roll if he rolls a sum of 7 or 11.? What is the probability of winning on the first roll?The player loses on the first roll if he rolls a sum of 2, 3, or 12.? What is the probability of losing on the first roll?If the player rolls any other sum, he continues to roll the dice until the first sum he rolled comes up again or until he rolls a 7, whichever happens sooner.? What?is the probability that the game continues after the first roll?4843864159274003-32.??Congratulations!? You are going to be a contestant on a new game show with a chance to win some money.? You will spin the two spinners shown below to see how much money you will win. Make a tree diagram of all the possible outcomes of spinning the two spinners.? At the ends of the branches, on the far right, write the amount you would win for each combination of spins.Are each of the outcomes in the sample space equally likely?What is the probability that you will take home $200?? What is the probability that you will take home more than $500?What is the probability that you will double your winnings?? Does the probability that you will double your winnings depend on the result of the first spinner?What if the amounts on the first spinner were $100, $200, and $1500?? What is the probability that you would take home $200?? Justify your conclusion.453799664560700542925734060003-34??Examine the diagrams below.? For each one, write and solve an equation to calculate the value of?x.? Show all work.?? 47026395550700?3331845102298500?3.1.4 3-41 ?Avery has been learning to play some new card games and is curious about the probabilities of being dealt different cards from a standard 52-card deck.? Help him figure out the probabilities listed below.?? What are?P(king),?P(queen), and?P(club)?What is?P(king or club)?? How does your answer relate to the probabilities you calculated in part?(a)?What is?P(king or queen)?? Again, how does your answer relate to the probabilities you calculated in part (a)?What is the probability of not getting a face card?? Jacks, queens, and kings are face cards.4646930252730003-42 ?The spinners at right are spun and the results are added. ?Assume each of the outcomes on Spinner #2 are equally likely.?? What is?P(sum is 4)?What is?P(sum is 8)?3-43 ?Can a triangle be made with sides of lengths 7, 10, and 20 units??Justify your answer.?? 3-44 ?Multiply each of the following expressions.? Write each expression as a sum(2x?+?5)(x?+?6)(m?–?3)(3m?+?5)(12x?+?1)(x2?–?5)(3?–?5y)(2?+?y)407903067965320194684384923360484132523-45 ?Use the relationships in the diagrams below to write an equation and solve for?x.? 4540885-539750003.1.5 3-55?When he was in first grade, Harvey played games with spinners.? One game he especially liked had two spinners and several markers that you moved around a board.? You were only allowed to move if your color came up on?both spinners.?? Harvey always chose purple because that was his favorite color.? What was the probability that Harvey could move his marker?Is the probability that Harvey moves his marker calculated from a union or an intersection of events?Was purple the best color choice?? Explain.If both spinners are spun, what is the probability that no one gets to move because the two colors are not the same?There are at least two ways to calculate the answer to part (d).? What is another way to solve?3-56 ?Multiply the expressions in parts (a) and (b).? Solve the equations in parts (c) and (d).?? (3x?+?2)(4x?-?5)(4x?-?1)22x(x?+?3)?=?(x?+?1)(2x?-?5)32?+?(x?+?1)2?=?(x?+?2)25041446198183003-57?On graph paper, draw ΔABC?with vertices?A(3,?2),?B(–1,?4), and?C(0, –2).??Calculate the perimeter of ΔABC.Dilate ΔABC?from the origin by a factor of 2 to create ΔA'B'C'.? What is the perimeter of?ΔA'B'C'?right210283003-58?Examine the diagram at right.? If?AC?passes through point?B, then answer the questions below.?? Are the triangles similar?? If so, make a flowchart justifying your answer.Are the triangles congruent?? Explain how you know.3-59 ?In problem?3-19, Eddie and Tana were flipping three coins.? Tana later found out that Eddie was using weighted coins (coins that were not fair), so the probability of getting heads for each coin was??instead of?.?a. Would this change the sample space?b. Recalculate the probabilities for each of the following events for the weighted coins.i.????????? Three headsii.??????? One head and two tailsiii.?????? At least one tailiv.??????? Exactly two tails5552551109108003-61 ?The spinner at right has three regions: $5, $0, and $20.? To play the game, you spin one time and then you win the amount in the region that the spinner lands on.?? What is the expected value for the game?If you have to pay $10 to play, is it a fair game?3-62 Complete each of the Diamond Problems below. ?? ? a.b.c.d.3-63 ?Use the geometric relationships in the diagrams below to solve for?x.? ? a. ?b.3-65 ?Use what you know about a scale factor between similar figures to answer the following Assume a triangle has side lengths 6, 7, and 10 units while another triangle has side lengths 3, 4, and 5 units.? Are these triangles similar?? How do you know?right13970000The pentagons at right are similar.? Use what you have learned about similarity to write equations and solve for the values of?x?and?y.Give a possible sequence of transformations that would map the pentagon on the left onto the pentagon on the right.3-66. ?A player in the casino dice game described in Roll and Win (problem 3-6) rolled a sum of six on his first roll.? He will win if he rolls a sum of six on the second roll but lose if he rolls a sum of seven.? If anything else happens, the result is ignored and he gets to roll again.a. How many ways are there to get a sum of six?b. How many ways are there to get a sum of seven?c. How many possible outcomes are important in this problem?d. What is the probability of getting a sum of six before a sum of seven?3.2.13-72??Use what you know about the angles of a triangle to determine the value of?x?and the angle(s) in each triangle below.? 245554527495500? ? 2476502273300017697452768600078740276860003-73 In a standard deck of 52 playing cards, 13 cards are clubs, and 3 of the clubs are “face” cards (K,?Q,?J).? What is the probability of drawing one card that is: ? A club or a face card?? Is this event a union or an intersection?A club and a face card?? Is this event a union or an intersection?Not a club and not a face card?3-74.?Solve for the missing lengths in the sets of similar figures below.??ΔABC ~?ΔOPQ ? ? ?EFGHI ~ STUVW ? ??JKLM ~ WXYZ ? ??3-75?Multiply each pair of polynomials.? That is, rewrite each product as a sum.??(2x?+?1)(3x?? 2)(2x?+?1)(3x2???2x???5)(3y???8)(?x?+?y)(x???3y)(x?+?3y)53007158150003-76??Looking at the diagram at right, John says that?m∠BCF?=?m∠EFH.?? Do you agree with John? ?Why or why not?Jim says, “You can’t be sure those angles are equal.? An important piece of information is missing from the diagram!”? What is Jim talking about?3.2.23-83??Use your Trig Table Graphic Organizer from problem 3-82 to help you determine the value of each variable below. ? 477266063500023260051974850085090132080005666740294640003-84?The probability of winning $3 on the spinner at right is equal to the chance of winning $5.? Calculate the expected value for one spin.? Is this game fair??? 3-85??Complete each of the Diamond Problems below.? 22267175865? ?2331661415743871814157611458814754871599317773003-86??Multiple Choice:?Which equation below is?not?a correct statement based on the information in the diagram??? A.??????? 3x?+?y?=?180°B.??????? 2x?– 1? = 4? –?xC.??????? 2x?– 1? = 5y?– 10?D.??????? 2x?– 1? + 3x?=?180?E.??????? all of these are correct3-87?Solve each system of equations below.? Then verify that your solution makes each equation true.??y?=?5x?–?2y?=?2x?+10x?=??2y???12x?+?y?=??203-88 For each pair of triangles below, decide whether the triangles are similar and/or congruent.? Justify each conclusion. ? 179070301625003450041190298003756297143921800380047555245003.2.35367234332105003-93??Ben thinks that the slope ratio for this triangle is?Carlissa thinks the ratio is? Who is correct?? 5976943215736003-94?Use your observations from problem 3-92 to answer the following questions:?? Thalia did not have a tool to help her determine the slope angle?θ?in the triangle at right.? However, she claims that the slope angle has to be more than 45°.? Do you agree with Thalia?? Why?58985159334500Lyra was trying to determine the slope ratio for the triangle at right, and she says the answer is??= 2.675.? Isiah claims that cannot be correct.? Who is right? ?How do you know?593788511366500Without determining the actual value, what information do you know about?x?in the diagram at right?3-95 For each pair of triangles below, determine if the triangles are congruent, similar, or if their relationship cannot be determined.? If they are congruent, organize your reasoning into a flowchart.? Triangles may not be drawn to scale. 464756536830002055495889000left11557000Multiply each expression below.? Simplify if possible.??a. 2x(3x?–?4)c. (2x?+?5)(2x?–?5)b. (x?+?3)(2x?–?5)d. x(2x?+?1)(x?–?3)52197008255003-98.??Enlarge the shape at right on graph paper using a scale factor of 2.? Then calculate the perimeter and area of both shapes.? What do you notice when you compare the perimeters?? The areas??? ?3.2.4 3-105.? Calculate the missing side length for each triangle.? Use the tangent button on your calculator to help.?? 9303317672100center2063100478218520002500right3344400Write the equation of the line that has a slope angle of 25° and a?y-intercept of (0, 4).? Sketch a graph of this line.? Assume the slope of the line is positive. ? 4353373216277800 Complete each of the Diamond Problems below.? ? ? a.b.c.d.3-108.?? For the spinner at right, calculate the expected value.?? 345842942588300220976565259003-109? For each diagram, solve for the variable and state the relationship(s) you used.40005025971500? ? 6781805257800058856558357003-110? Rakisha is puzzled.? She is working with the parallelogram drawn at right and wants to make it smaller instead of bigger?What should she do if she wants the sides of her new figure to be?half as long?as the original sides?? What scale factor should she use?? What are the dimensions of her new figure?Rakisha is convinced that every parallelogram with adjacent sides that measure 11 and 16 units will be congruent to the parallelogram above. ?Is she correct?? Justify your answer using a proof or a counterexample.3.2.5 3-113??Leon is standing 60 feet from a telephone pole.? As he looks up, a red-tailed hawk lands on the top of the pole.? Leon’s angle of sight up to the bird is 22° and his eyes are 5.2 feet above the ground.?? Draw a detailed picture of this situation. ?Label it with all of the given information.How tall is the pole?? Show all of your work.4641850259080003-115??Examine the triangles at right.? Are the triangles similar?? If so, show how you know with a flowchart.? If not, explain how you know they cannot be similar.?? 3-116??For each equation below, determine the value of?y?if?x?=?–3.?? y?=?2x2???3x?–?22x???5y?=?4?You help out at the bowling alley on weekends.? One of the arcade games has a bin filled with stuffed animals.? A robotic arm randomly grabs a stuffed animal as a prize for the player.? You are in charge of filling the bin.??a. You are told that the probability of getting a stuffed giraffe today is?.? If there are 28?giraffes in the bin, what is the total number of stuffed animals in the bin?b. The next weekend, you see that the bin contains 22 unicorns, 8?gorillas, 13?striped fish, and 15 elephants.? A shipment of stuffed whales arrives.? What is the probability of getting a sea animal (whale or fish) if you add 17 whales to the bin?? Express the probability as a percent.c. You are told that the probability of selecting a stuffed alligator needs to be 5%.? One weekend you notice there are exactly 3 alligators left.? How many total animals should be in the bin to maintain the probability of 5% for an alligator?3-118.? Two sides of a triangle have lengths 9 and 14 units.? Describe what you know about the length of the third side.??Chapter 4 HomeworkName: _______________________________4.1.14-6 Multiply the expressions below using an area model.? Then verify Casey’s pattern (that the product of one diagonal equals the product of the other diagonal).??(2x?–?3)(4x?+?1)(4x?–?8)24998810276642004-7?Write the area of the rectangle as a sum and as?a product.?? 4-8?? Use the greatest common factor to rewrite each sum as a product.??4x?+?810x?+?25y?+?52x2?–?8x9x2y?+?12x?+?3xyright1270004-9 ?Calculate the perimeter of the shape at right.??4-11 ?At Lara’s school, 25% of the student body is male and 40% of the students walk to school.? Assume that these two events are independent.? If a student from Lara’s school is selected at random, determine the following probabilities.??P(student is female)P(student is male and does not walk to school)P(student walks to school or does not walk to school)Identify the sample space in parts (b) and (c) above as a “union” or an “intersection”.4.1.2 4-18? Use the process you developed in problem 4-13 to factor the following quadratic expressions.?? x2?–?4x?–?122x2?–?9x?–?54x2?+?4x?+?13x2?+?10x?–?8?4-19?When she was younger, Mary had to look up at a 68° angle to see into her father’s eyes whenever she was standing 15 inches away.? How high above the flat ground were her father’s eyes if Mary’s eyes were 32 inches above the ground? ? 4-20 ?Complete the table below for the function?y?=?x2.?? 471237335464200a.b. Sketch the graphx– 4–3–2–1-01234y???????????c. This graph is an example of a?parabola.? The?vertex?is the maximum or minimum point of a parabola.? Where is the vertex of the parabola you graphed in part (a)?38785133201454-21 ?For the spinner below, calculate the expected value.? 4503124170160004-22. ? Examine the triangles in the diagram at right.? Are the triangles similar?? Why or why not?Solve for?x.? Show all work.3794760549910004-23 ?Larry saw Javon’s incomplete Venn diagram below, and he wants to finish it.? However, he does not know the condition that each circle represents.? Determine a possible label for each circle, and place two more shapes into the diagram.??? ?4.1.3 4-28.?Factor the following expressions, if possible.??k2?–?12k?+?206x2?+?17x?–?14x2?–?8x?+?169m2?–?1The expressions in parts (a) through (c) are trinomials while part (d) is a binomial, yet they are all quadratic expressions. ?What makes each of them a quadratic?? 4-29? Salvador has a hotdog stand 58 meters from the base of the Space Needle in Seattle.? He prefers to work in the shade and knows that he can calculate when his hotdog stand will be in the shade if he knows the height of the Space Needle.? To measure its height, Salvador stands at the hotdog stand, gets out his clinometer, and measures the angle to the top of the Space Needle to be 80°.? Salvador’s eyes are 1.5 meters above the ground.? Assuming that the ground is level between the hotdog stand and the Space Needle, how tall is the Space?Needle??? 4-30? Examine the triangles below.? Solve for?x.?? 4-31?You are feeling impulsive, so you are going to have the owner of the pet store randomly pick a fish for your aquarium at home. ? A tank at the pet store contains 9?spotted guppies, 14 red barbs, 10?red tetras, and 7?golden platys.? What is the probability (expressed as a percent) of getting a red fish from this tank?In a different tank that contains only golden platys, the probability of getting a female fish is 30%.? If there are 18 female fish in the tank, how many total fish are in the tank?? ? a.b.c.d.4-32 ?Complete each of the Diamond Problems below.??Simplify the following expression: 3x3???2x2?+?4???(3x3?+?5x2???2).? How many terms are in your answer?What is the coefficient of?x?in your answer?4.1.4 4-39 ?Factor the following expressions, if possible.??2x2?+?3x?–?5x2???x?–?63x2?+?13x?+?42x2?+?5x?+?77x2?–7x?– 426x2?+ 26x?+ 83793875264070004-41??The two polygons at right are similar.?? Determine the value of?x.? Show all workCalculate the area of each polygon240601581597500142875845820004809490429260004-42 ?For each part below, decide if the triangles are similar.? If they are similar,?use the properties of similarity to solve for?x.? If they are not similar, explain why not.?? 4-43 ?Joan and Jim are planning a dinner menu including a main dish and dessert.? They have four main dish choices (steak, vegetable-cheese casserole, turkey burgers, and vegetarian lasagna) and three dessert choices (chocolate brownies, strawberry ice cream, and chocolate chip cookies). ? Joan and Jim would like to know how many different dinner menus they have to choose from. ?How many different menus are there?Assume the main dish choice and the dessert choice are both chosen randomly.? Are all the menus equally likely?What is the probability they pick a menu without meat?? What is the probability they pick a menu with chocolate??4478020487680004-44 ?Complete a table for the function?y?=?x2?+ 2.? Use negative, positive, and zero values for?x.? Then graph the function.? Be sure to label the axes and include the?scale.?? 4.1.54-50 Completely factor each polynomial.??x2?–?64x2???6x?+?94x2?+?4x?+?14x2???49383975590501004-52 ?Calculate the area and the perimeter of the figure.? 4-53 ?For each function below, make a table of?x- and?y-values and then graph the function on graph paper.? Label each graph with its equation.?? y?=?x2 b. y?= ?x22114550157480006667516637000c. Compare the graphs.? What do you notice?For the graph of?y?=?x2, estimate the?x-values corresponding to?y?= 5.For the graph of?y?= ?x2, estimate the?x-values corresponding to?y?= ?10.56965043394.2.14-62.??You now have multiple trig tools to determine missing side lengths of triangles. ?For the triangle, determine the values of?x?and?y.? 4-63??For each triangle below, write a trigonometric equation relating?a,?b, and?θ.?? ? ??a. b.66738517907000 c.4-64? Factor each polynomial completely.? Hint: Look for common factors.?? 6x2?+?5x?–?6c. 2x3?+?2x2?–?112x8x2?–?50d. 9x2???24x?+?165610225-412750004-65 ?Lizzie notices that two angles in ΔDEF, shown at right, have the same measure.?? Based on this information, what statement can you make about the relationship between?ED?and?EF? ?Determine the length of?DF?if?DE?= 9 mm.4-66 To get home, Renae can take one of four buses: #41, #28, #55, or #81.? Once she is on a bus, she will randomly select one of the following activities: listening to her MP3 player, writing a letter, or reading a book.?? Create a tree diagram to show all of the different travel options that Renae could take.Use your tree diagram to determine the following?probabilities:i.???????P(Renae takes an odd-numbered bus)?ii.? ? ??P(Renae does not write a letter)iii.? ? ?P(Renae catches the #28 bus and then reads a book)iv. ? ? P(Renae does not read on the way?home)Does her activity depend on which bus she takes? Explain why or why not. ? ??4.2.24-72? For each triangle below, write an equation relating the reference angle (the given acute angle) with the two side lengths of the right triangle.? Then solve your equation?for?x.???? ? a.?36443161708b.?698672161917c.?For part (c), use the complement of the reference angle to write a different equation.? Solve for?x?to confirm your answer for part (c).?533400010160004-73??Eugene wants to use the cosine ratio to calculate?y?for the triangle.??Which angle should he use to write an equation and solve for?y?using the cosine ratio?? Why?Set up an equation, and solve for?y?using cosine.3373755241935004-74.? **Difficult Problem!!** The shaded figures below are similar.?? ? ? ? ? ? ? ?a. Solve for?m?and?nb. Calculate the area and perimeter of each figure.4-75. ?Factor each of the following expressions.? a. xy?? 6x?? 18 + 3yb. 2xy?– 3y?+ 2x?– 3c. 12y?+ 14x?– 8xy?– 21d. How did you determine where to place the terms in your area models?4619625881380004-76?Complete the table for the function?y?=?x2?+?2x???3.? Then make a complete graph on graph paper.? Fully describe the graph and state the?x and?yintercepts.?? x–4–3–2–1012y???????4-77?Jinning is going to flip a coin.? If the result is “heads,” he wins $4.? If the result is “tails,” he loses $7.?? What is his expected value per flip?If he flips the coin 8 times, about how much should he expect to win?(or lose)?4.2.34-83?While Baljeet is organizing his binder, he finds a conjecture that he wrote for problem 3-81:?If one angle of a right triangle has the slope ratio ?, then the complementary angle has a slope ratio of ? .?? How can Baljeet update the conjecture using the name of the trig ratio?that corresponds to the slope ratio?Write a new conjecture about the sine and cosine of complementary angles.? You might try some examples on your calculator to help you develop your conjecture.right6451004-84?Use two different trig ratios to determine the measure of ∠A. ? 4-85??Factor each expression, if possible. ?Identify any special cases, such as a difference of squares or a perfect square trinomial. ? ? a.???????? 4x2?? 49b.???????? 2x2?+ 11x?+ 12? ? c.???????? 4x2?+ 25d.???????? 9x2?+ 6x?+ 1? ? e.?????????xy?? 4y?+ 2x?? 8f.??????????x4?? 164-86 ??This problem is a checkpoint for solving proportions and similar figures.? ??324802525336500Use the figure at right to solve for?x. 4-87 ?Refrigerators that are produced on an assembly line sometimes contain defects.? The probability that a refrigerator has a paint blemish is 4%.? The probability that it has a dent is ?%.? The probability that it has both a paint blemish and a dent is also %.? What is the probability that a refrigerator has a paint blemish or a dent?? What can you conclude about defects on these refrigerators??? 4.2.4 4-94??An airplane takes off and climbs at an angle of 11°.? If the plane must fly over a 120-foot tower with at least 50 feet of clearance, what is the minimum distance between the point where the plane leaves the ground and the base of the tower? ?Draw and label a diagram for this situation.What is the minimum distance between the point where the plane leaves the ground and the tower?? Explain completely.right333161004-95.??Estelle is trying to solve for?x?in the triangle at right.? She lost her scientific calculator, but luckily her teacher tells her that sin?23??≈?0.391, cos?23??≈?0.921, and tan?23??≈?0.424. ? a. Write an equation that Estelle could use to solve for?x.b. Without a calculator, how could Estelle determine sin?67??? Explain.4-96? Factor each quadratic completely.?? a. 2x2???2x?–?4b. 4x2???24x?+?364933950260350004-97 ?Use a table to make a complete graph of?y?=?x2???2x???8.? a. Write the coordinates of the?y-intercept.? What is the connection between the?yintercept and the equation?y?=?x2???2x???8?b. Write the coordinates of the?x-intercepts.c. What is the lowest point on the graph?4-98 ?When Ms. Shreve randomly selects a student in her class, she has a?probability of selecting a boy. ? a. If her class has 36 students, how many boys are in Ms. Shreve’s class?b. If there are 11 boys in her class, how many girls are in her class?c. What is the probability that she will select a girl?d. Assume that Ms. Shreve’s class has a total of 24 students.? She selected one student (who was a boy) to attend a fieldtrip and then was told she needed to select one more student to attend.? What is the probability that the second randomly selected student will also be a boy?18288020097750043205406153150042945052077085001809756159500021901155359400021888452083435004-99. Complete each Diamond Problem below. ?? ? CHAPTER 5 HOMEWORK5.1.1Name:__________________________________5-4.??Solve each equation.? Check each solution.?? *On c be careful*a. 2x – 10 = 0 b. x + 6 = 0c. (2x-10)(x+6) = 0 5-6.??For each diagram below, set up an equation and solve for?x.?? ? ? a. ? ?Perimeter = 76 units? ? ? ? ??b.? ? c. ? ??d. ? ?51759311104905-7. ? Jackie and Alexa are working on homework together?when Jackie says,?“I got x = 5 as the solution, but it looks like you got something different.”“I think you made a mistake,”?says Alexa.?Has Jackie made a mistake?? Jackie’s work is shown. ? 5-8. ?Examine each pair of polygons below.? Are they similar??Explain how you know.??? ? a. ? ?b.5-10. ?What values of?x?will make the following equations true??? ??a. ? ? ? ??x2?=?16b.?????????x?=?c. ? ? ? ???= 4? ??d.?????????x?+ 3?=?e. ? ? ? ??x2??= –16f. ? ? ? ? ?x2?+ 4 = 05-11. ?Kendra has programmed her cell phone to randomly show one of six photos when she turns it on.? Two of the photos are of her parents, one is of her niece, and three are of her boyfriend, Bruce.? Today she will need to turn her phone on twice: once before school and again after school.??1. Create a model (such as a tree diagram or a probability area model) to represent this situation.2. What is the probability that both photos will be of her boyfriend?3. What is the probability that neither photo will be of her niece?4600575205740005-14.?Determine the measures of ∠ABC?and ∠BAC.?Are these angles acute or obtuse? ?5.1.237097248461005-20.?Graph?y?=?x2???8x?+?7 and fully describe it.?? 5-22.? While shopping at his local home improvement store, Chen notices that the directions for an extension ladder state, “This ladder is most stable when used at a 75° angle with the ground.”? He wants to buy a ladder that will reach a height of 26 feet to paint a two-story house.? How long does his ladder need to be?? Draw a diagram and set up an equation for this situation.? Show all work.?? 5-25. ?A hotel in Las Vegas is famous for its large-scale model of the Eiffel Tower.? The model, built to scale, is 128 meters tall and 41 meters wide at its base.? If the real tower is 324 meters tall, how wide is the base of the real Eiffel Tower??? 5.1.35-32.??Compare the two equations below.?? i.?(x?+?2)(x???1)?=?0 ?????ii.?(x?+?2)?+?(x???1)?=?01. How are the equations similar?? How are they different?2. Solve both equations. 5-33.? Solve each equation below using the Zero Product Property.?? ? ??a.???????? (x???2)(x?+?8)?=?0b.???????? (3x???9)(x???1)?=?0? ??c.???????? (x?+?10)(2x???5)?=?0d.???????? (x???7)2?=?05-34.??The?xintercepts of the graph of?y?=?2x2???16x?+?30 are (3, 0) and (5, 0).?a. What is the?xcoordinate of the vertex?? How do you know?b. Use your answer to part (a) above to calculate the?y-coordinate of the vertex.? Then write the vertex as a point (x,?y).4949611375755-35.??Donnell has a bar graph which shows the probability of a colored section coming up on a spinner that is divided into eight equal sections, but part of the graph has been ripped off.?? a. What is the probability of spinning red?b. What is the probability of spinning yellow?c. What is the probability of spinning blue?d. If there is only one color missing from the graph, namely green, what is the probability of spinning green?? Why?3914775139705-37. ? Solve for?x?in the diagram at right.?? 5.1.45-43.??Based on the tables below, what are the?x- and?y-intercepts of the corresponding graphs?? Use the fact that the relationship shown in the table in part (b) is quadratic to write an equation to represent the relationship.?? ? ? a.xy30016–50–1–862230b.xy7–271010–67.50–2.52.50–7–76c.xy0–16–5113–2801327–6145-44.??Solve the equations.? Check your solutions.?? ? ??a.???????? (6x???18)(3x?+?2)?=?0b.?????????x2???7x?+?10?=?0? ??c.???????? 2x2?+?2x???12?=?0d.???????? 4x2???1?=?0? ??e.?????????x2?= 9f.??????????x2?– 2x?+ 1 = 05-45.??What values of?x?will make the following equations true??? 1. x2?=?642. (x?+?1)2?=?643. (x?+?1)2???64?=?05-46.??To paint a house, Travis leans a ladder against the wall.? If the ladder is 16 feet long and it makes contact with the house 14 feet above ground, what angle does the ladder make with the ground?? 5068702645500 5-47.??Determine the measures of?x,?y, and?z.? 5-48.??A sandwich shop delivers lunches by bicycle to nearby office buildings.? Unfortunately, sometimes the delivery is made later than promised.? A delay can occur either because food preparation takes too long, or because the bicycle rider gets lost.? Last month the food preparation took longer than expected or the rider got lost 11% of the time.? During the same month, the food preparation took longer than expected 18?times and the bicycle rider got lost 12 times.? There were 200 deliveries made during the month.? For a randomly selected delivery last month, what is the probability that both the food preparation took too long and the rider got lost??? 5.1.55-53.??What values of?x?will make the following equations true??? a. x-4=3b. x-4-3=0c. x-4=-3d. (x-4)2 = 9e. (x-4)2 – 9 = 0f. (x-4)2 = -95-55.?QUALITY CONTROL, Part Three?? Lots O’Dough, a wealthy customer, would like to order a variety of parabolas.? However, he is feeling pressed for time and says that he will pay you?lots?of extra money if you complete his order for him.? Of course you agree!? He sends you sketches of each parabola that he would like to receive.? Determine a possible equation for each parabola so that you can pass this information on to the Function Factory.? ? a. ?443164230505b.570865000? ? c.3704581683000? ?d.right13203005-56.? Make a complete graph of?y?=?x2???2x???8.? Then fully describe the graph.?? 5-58.?For each pair of triangles below, determine if the triangles are congruent.?223456528829045872401250952387601155705.2.14714875508005-65.?Determine the exact?xintercepts of?y?=?(x?+?4)2???7. ? What are the approximate?x-intercepts? ?Sketch a graph of the parabola. Are the solutions to the equation 0 = (x?+?4)2?–?7 rational or irrational numbers?? Explain.What are the coordinates of the vertex of the parabola?? Is your answer exact or approximate?4220845179070005-67.?What are the possible lengths for side?ML?in the triangle?? 5-68.?Rewrite the following expressions in simplified radical form.??? ? ?a. ? ??·?b. ? ?2??· ?5c. ? ??5-69.?For each diagram, write and solve an equation to determine the indicated angle measurement.???? ? ?a. ? ?? ? ? ? ?b. ? ?? ? ? ? ??c. ? ?? ? ? ? ? ? ??5.2.25-77.?Suppose you are using algebra tiles to represent each expression below. How many unit tiles would you need to add to build a perfect square? ? x2?+ 10xx2?– 6xx2?+ 22x5-78.?Calculate the value of each expression below.?? a.?b.?c.?52635111958185-79.? Examine the graph of?y?= 2x2?+ 2x?– 1 at right. ?Estimate the?xintercepts of the parabola.What happens if you try to use the Zero Product Property to determine the zeros of 2x2?+ 2x?– 1 = 0? ?5048250-161925005-80.?Does a quadratic equation always have two solutions?? That is, does a parabola always intersect the?x-axis twice? ?? If possible, draw an example of a parabola that only intersects the?x-axis once.503872519113500What does it mean if the quadratic equation has no solution?? Draw a possible parabola that would cause this to happen. ?4372307295626005-81.?In the figure at right, if?PQ???SR?and?PR???SQ?prove that ∠P ? ∠S. Write your proof as a flowchart. ?? 5213821316343005-82.?Marina needs to win ten tickets to get a giant stuffed panda bear.? To win tickets, she throws a dart at the dartboard at right and wins the number of tickets listed in the region where her dart lands.? Unfortunately, she only has enough money to play the game three times.? If she throws the dart randomly, do you predict that she will win enough tickets?? Assume that each dart will land on the dartboard. ? ?5.2.35-89.?Use your generalized process of completing the square to rewrite and solve each quadratic equation below.?? a. ?x2?+ 4x?= ?3b.?x2?? 8x?+ 7 = 0c.?x2?+?5x?–?2 = 05-90.?Solve the equations below for?x. Check your solutions.?? a.?x2?+ 6x?? 40 = 0b.?2x2?+ 13x?? 24 = 0?5-91.?Calculate the value of each expression below.? Then compare your answers to those in problem 5-90.? What do you notice??? a.?b.?c.?d.?4663401224159005-92.?One way to solve absolute value equations is to think about “looking inside” the absolute value. The?expression inside the absolute value symbol can be positive or negative, so you should solve the equation both ways.For example, you can record your steps as shown at right. ?Solve each equation. ?Be sure to determine all?possible answers and check your solutions. a.?|9 + 3x| = 39b.?|2x?+ 1| = 10c.?|?3x?+ 9| = 10d.?|3.2x ??4|?=??5.75.2.45-100.?Solve the following quadratic equations.? Be sure to check your solutions.?? x2?? 13x?+ 42 = 0c. 4x2?+ 8x?? 60 = 00 = 3x2?+ 10x?– 82d. x2?? 10x?= 05-101.While solving (x?? 5)(x?+ 2) = ?6, Kyle decides that?x?must equal 5 or –2.? “Not so fast!” exclaims Stanton. “We need to change the equation first.” ??What is Stanton talking about?How can the equation be rewritten?? Use your algebraic tools to rewrite the equation so that it can be solved.Solve the resulting equation from part?(b) for?x.? Do your solutions?match Kyle’s?5-102. Write an equation for each representation of a quadratic function given below.?? x–4–3–2–101234y1250–3–4–3051240005026162000 b.5-103.?An international charity builds homes for disaster victims.? Often the materials are donated.? The charity recently built 45 homes.? 20% of the houses have granite for the kitchen countertops while the rest have porcelain tile.? Fifteen of the homes have red oak for the wooden kitchen floor, 20 have white oak, and ten have maple.? If a disaster victim is randomly assigned to a home, what is the probability (in percent) of getting a home with an oak floor and granite countertops??? 5.2.55-112.?Solve the quadratic equation below?twice: once using the Quadratic Formula and once by completing the square.? You should get the same result using both methods.? x2?+ 6x?+ 11 = 05-113.?What values of?x?will make the following equations true? a. x2?=?144b. x?=?c. x2???5?=?139d. x?? 1?=?e. x2?=?–144f. x2?+ 5 = 05-114.?Calculate the value of the variable in?each pair of similar figures below. ? 2733675330200ABCD?~?JKLM ??b. ΔNOP?~?ΔXYZ ?1708158255005-116.?Kamillah decides to calculate the height of the Empire State Building.? She walks 1 mile (5280 feet) away from the tower and finds that she has to look up 15.5° to see the top.? Assuming Manhattan is flat, if Kamillah’s eyes are 5 feet above the ground how tall is the Empire State Building? ? 5-117.?Evaluate each expression below without a calculator. ? 5-118.?Solve the following quadratic equations using any method. ? a. 10000x2???64?=?0b. 9x2???8?=??34xc. 2x2???4x?+?7?=?05-120.?Solve these equations.? Each time, be sure you have found all possible solutions.? Check your work and write down the name of the method(s) you used. ? (x?– 13)3?= 83(x?+ 12)2?= 2764?= 365-122.? Solve for the?x-intercepts of the parabolas represented below. a. y?=?3x2???7x?+?4b. (x?+?5)(?2x?+?3)?=?yc. x2?+?6x?=?yd. y?=?3(x???5)(2x?+?3)5.2.65-131.?Rewrite each expression below.?? b. c. (4i)2d. 3i?+ 2i?–?55-132.?Solve each quadratic equation by completing the square.?? 0?=?x2?+?18x?+?32b. –36?=?x2?+?12x5-136?Rewrite each expression using the laws of exponents. ?? (x2)(x2y3)3200400-3810(2x2)(?3x4)(2x)35-133.?Because students complained that there were not enough choices in the cafeteria, the student council decided to collect data about the sandwich choices that were available.? The cafeteria supervisor makes 36 sandwiches each day. ?She makes 12 of the sandwiches with white bread and 24 with whole-grain bread.? Her assistant randomly chooses to make half of the sandwiches with salami and the other half she evenly splits between turkey and ham.? Finally, two-thirds of the sandwiches have mayonnaise and the rest are left plain with no anize the possible sandwich combinations of bread, protein, and condiment by making a tree diagramWade likes any sandwich that has salami or mayonnaise on it.? Which outcomes are sandwiches that Wade likes?? If Wade randomly picks a sandwich, what is the probability he will get a sandwich that he likes?? Madison does not like salami or mayonnaise.? Which outcomes are sandwiches that Madison likes?? If Madison randomly picks a sandwich, what is the probability she will get a sandwich that she likes?If you have not already done so in part (c), show how to use a complement to determine the probability Madison gets a sandwich that she likes.Which outcomes are in the event for the intersection of {salami} and {mayonnaise}?5-134.?For each parabola graphed below, visually estimate the?x-intercepts.? Then use the Quadratic Formula to confirm your estimates. ?? 3714750329565029464000y?=?x2?– 5x?+ 3y?=?x2?+ 2x?– 6Chapter 6 HomeworkName:__________________________________6.1.16-6?For each triangle below, use right triangle patterns to determine the missing side lengths. Then calculate the area and perimeter of each triangle.?46370675639100b.6-7?Lori has written the conjectures below.? For each one, decide if it is true or not.? If you believe it is not true, provide a counterexample?(an example that proves that the statement is false). ?a. If a shape has four equal sides, it cannot be a parallelogram.b. If tan(θ) is more than 1, then?θ?must be more than 45°.c. If two angles formed when two lines are cut by a transversal are corresponding, then the angles are congruent.6-8?Simplify each of the expressions below.? Your final expressions should contain no negative exponents and no parentheses. ?a. (–10a–1)(2a4b)b. (3x4y)2c. 6-9?Solve the quadratic equation below?twice, once using the Zero Product Property and once using the Quadratic Formula.? Verify that the solutions from both methods are the same.??2x2???19x?+?9?=?06-11.?Determine whether or not the two triangles in each pair below are similar.?Explain your reasoning.430530015748000a. b.6.1.26-19.?Use the patterns you have investigated to determine the missing side lengths of each of the triangles below.? Do not use a calculator.?? ?a.b.?c.d.6-20.?Solve each equation by first rewriting the expressions in each part with the same base.?? 8x?= 26 42x?=?6-21.?Rewrite each of the expressions below.? Your final expressions should not contain negative exponents or parentheses.? (5x3)(?3x?2)b. (4p2q)3c. 55911753346456-23.?For each description below, sketch the parabola that matches the given information.?A parabola with?x-intercepts (2, 0) and (7, 0) and?yintercept (0, –8).515302433655519112515240A parabola with only one?x-intercept at (–1, 0) and?y-intercept (0, 3).471424011684045624756350The parabola represented by the equation?y?= (x?+ 5)(x?– 1).413321510795049360532503886-24.?Use the information given for each diagram below to solve for?x.? Show all work.? bisects ∠ABC.? If?m∠ABD?=?5x?–?10? and?m∠ABC?=?65?, solve for?x. 3590925279400Point?M?is a midpoint of?EF.? If?EM?=?4x???2 and?MF?=?3x?+?9, solve for?x.553402512700WXYZ?at right is a parallelogram.?If?m∠W?=?9x?–?3? and?m∠Z?=?3x?+?15?, solve for?x.?6.1.36-30.?In a right triangle, if sin(θ) =?, what is cos(θ)?? Justify your answer.?? 6-31.?Decide if the following statements are true or false.? If a statement is false, provide a diagram of a counterexample.?All squares are rectangles.All quadrilaterals are parallelograms.All squares are rhombi.6-32.??Rewrite each expression without parentheses and using only positive exponents.??a. (3x2y)(5x)b. (x2y3)(x?2y?2)c. d. (2x?1)36-33.?Use the relationships found in each of the diagrams below to solve for?x?and?y. Assume the diagrams are not drawn to scale. State which geometric relationships you used. ? ?a.b.?c.d.6.1.4 6-42.?Rewrite 82/3?in as many different ways as you can. ? 6-43.?Use what you know about Pythagorean Triples to determine the measure of the third side. ? ?a.b.c.right1577196-44.?Calculate the area and perimeter of ΔABC?at right.? Give both exact and approximate (decimal) answers.? 6-46.?Solve each equation.? Identify the solutions as rational or irrational numbers.? x(3x???4)?=?5(3x???2)2?=?6-47.?Examine the information provided in each diagram below.? Decide if each figure is possible or not.? If the figure is not possible, explain why.??a.b.c.7.1.1Name:_____________________________________________43132526127007-9.?For the figure below, create a flow chart to show how the 2 triangles are congruent.? Then, solve for?x.? If the triangles are not congruent, explain why not.?? 7-11.?For each pair of numbers, determine the number that is exactly halfway?between them.??a. 9 and 15b. 3 and 27c. 10 and 217-12.?Identify each sum or product as a rational number or an irrational number. ?a. 6 + ?b. + c. + d. ?7-14.?Kayla brings snacks for herself and her partner on the volleyball team.? She packs flavored water (2 berry and 4 citrus), fruit (5 apricots, 2 apples, and 3?bunches of grapes), and small packages of crackers (2 regular and 2 whole wheat).? Kayla will randomly choose one flavored water, one fruit, and one package of crackers.??Show all the possible combinations of three snacks that Kayla could choose.What is the probability that Kayla will choose a high-fiber snack (any combination that includes both an apple and whole-wheat crackers)?7-15. What are the area and perimeter of the shape below? ?Show all work.?? 7-16.?For each diagram below, determine the value of?x, if possible.? If the triangles are congruent, state which triangle congruence condition you used.? If the triangles are not congruent or if there is not enough information, state, “Cannot be determined”.?? 33712031905360015355018191100a. b. 33712031895660015355018956600c. d. 7-17.?Create a flowchart proof to prove your answer to part (b) of problem 7-16.? That is, prove that?AD???CB?.? Be sure to include a diagram for your proof and reasons for every statement. 7-18.?Factor the following expressions completely. ?Hint: Always look for common factors first.??15x2?+?39x?–?186t2???26t?+?86x2?–?247-19.?Determine the values of?x?and?y?in the diagram below.? 7-20.?Change each expression into radical form and give the value.?No calculator should be?necessary.??1252/3161/216?1/27.1.2Name:_____________________________371076222490007-26.?Remember that a midpoint of a line segment is the point that divides the segment into two segments of equal length.? On graph paper, plot the points?P(0, 3) and?Q(0, 11).? Where is the midpoint?M?such that?PM?=?MQ?? Explain how you found your answer.??7-27.?Use the Zero Product Property or complete the square to solve the following quadratic equations.? a. x2???10x?+?25?=?0b. 0?=?3x2?+?17x?–?6c. 3x2???2x?=?5d. 16x2???9?=?07-28.?Use the Quadratic Formula to solve part (b) of problem 7-27.? Did your solution match the solution you got in part (b) of problem 7-27?? Which solution method do you prefer???7-30.?Earl hates taking out the garbage and he hates washing the dishes, so he decides to make a deal with his parents: He will flip a coin once for each chore and will perform the chore if the coin lands on heads.? What he doesn’t know is that his parents are going to use a weighted coin that lands on heads 80% of the time!??What is the probability that Earl will have to do both chores?What is the probability that Earl will have to take out the garbage but will not need to wash the dishes?7-32.?Calculate the area of an equilateral triangle with side length 12 units. ?Show all work.???7.1.3Name:______________________________51796954445007-39.?Penn started the proof below to show that if?AD?//?EH?and?BF?//?CG, then?a?=?d.? Unfortunately, he did not provide reasons for his proof.? Provide a justification for each statement.??StatementsReasons? 1. ? ?AD?//?EH?? 2. ? ?a?=?b?? 3. ? ?BF?//?CG?? 4. ? ?b?=?c?? 5. ? ?a?=?c?? 6. ? ?c?=?d?? 7. ? ?a?=?d?7-41.? A 100foot long cable is attached 70 feet up the side of a building.? If it is pulled taut (i.e., there is no slack) and staked to the ground as far away from the building as possible, approximately what angle does the cable make with the ground?? right1085857-42.?Complete the square to solve 0 =?x2?– 4x?– 3 and determine the roots.? Then sketch the parabola?y?=?x2?– 4x?– 3 and label the intercepts and vertex.?7-43.??Solve each equation below for?x.?a. 163/4?= 4xb. 81/3?= 4xc. 34x?=?92d. = 47-45.?Examine the geometric relationships in each of the diagrams below.? For each one, write an equation and solve for the value of the variable.? Name all geometric relationships or theorems 15736234205900that you use.??33240781079500a. b. 34109251944870015736219448700c.d. 7.1.4Name:________________________________532003095885007-49.?Carolina compares her proof to Penn’s work in problem 7-39.Like him, she wants to prove that if?AD?//?EH?and?BF?//?CG, then?a?=?d. ?Unfortunately, her statements are in a different order.? Examine her proof below and help her decide if her statements are in a logical sequence to prove that?a?=?d.??StatementsReasons? 1. ? ?AD?//?EHGiven? 2. ? ?a?=?bIf lines are parallel, alternate interior angles are equal.? 3. ? ?BF?//?CGSubstitution? 4. ? ?b?=?cGiven? 5. ? ?a?=?cIf lines are parallel, corresponding angles are equal.? 6. ? ?c?=?dVertical angles are equal.? 7. ? ?a?=?dSubstitution7-50.?Find another valid, logical order for the statements for Penn’s proof from problem 7-39.Explain how you know that changing the order the way you did does not affect the logic.?488253972487-51.?Examine the diagram at right.??a. Are the triangles in this diagram similar?? Justify your answer using similarity transformations.b. What is the relationship between the lengths?HR?and?AK?? c. Between the lengths?SH?and?SA?? Between the lengths?SH?and?HA?d. If?SK?=?20 units and?RH?=?8 units, what is?HA?7-52.?Decide if the following statements are true or false.? If a statement is true, explain how you know it is always true.? If a statement is false, provide a diagram or a description of a counterexample.??If the diagonals of a quadrilateral are congruent, then it is a rectangle.If a quadrilateral has four congruent angles, then it is a rectangle.All rhombi are parallelograms.The diagonals of a parallelogram bisect the angles.7-53.??The temperature in San Antonio, Texas is currently 77°F and is increasing by 3° per hour.? The current temperature in Bombay, India is 92°F and the temperature is dropping by 2° per hour.? If the temperatures continue to change in this same way, when will it be as hot in San Antonio as it is in Bombay?? What will the temperature be??4412975220457-54.?Without making a table, sketch the graph of?y?=?x2?+?3x?+?2 and fully describe it.??7.1.5Name:_______________________________4337362141749007-60.?What else can you prove about quadrilaterals?? Prove that if a pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral must be a parallelogram.For example, for the quadrilateral?ABCD?at right, given that?AB?//?CD?and?AB???CD, show that?BC?//?AD.? Organize your reasoning in a proof (two-column or flowchart).? 7-61.?Consider the quadratic equation 6x2?+?11x???10?=?0.?a. Solve it using the Zero Product Property.b. Solve it using the Quadratic Formula.Do your solutions from parts (a) and (b) match?? If not, why not?7-63.?Earl (from problem 7-30) still hates to wash the dishes and take out the garbage.? He finds his own weighted coin, one that will randomly land on heads 30% of the time.? He will flip a coin once for each chore and will perform the chore if the coin lands on heads.?What is the probability that Earl will get out of doing both chores?What is the probability that Earl will have to take out the garbage but will not need to wash the dishes?7-64.??Bob is hanging a swing so that it can swing a total angle of 120°.? Since there is a bush 5 feet in front of the swing and a shed 5 feet behind the swing, Bob wants to ensure that no one will get hurt when swinging. ?What is the maximum length of chain that Bob can use for the swing??Draw a diagram of this situation.What is the maximum length of chain that Bob can use?468864817145007-65.?Multiple Choice:?Ziva is using a compass and a straightedge to construct the midpoint?M?of line segment?PR.? What is her first step??A. Place the point of the compass on point?P?and draw an arc halfway between points?P?and?R.B. Use a straightedge to measure?PR?and divide that measurement by 2 to calculate?PM.?C. Place the point of the compass on point?P?and draw arcs above and below?PR?using the same compass settingD. Fold the paper so that points?P?and?R?coincide.7-66.??Completely factor the expressions below, if possible.?a. 4x2?? 20x?+ 25b. x2?+ 11x?– 2c. 3x2?? 12xd. 10x2?? 35x?– 20?7.2.1Name:________________________________7-72.?Kendrick is frantic.? He remembers that several years ago he buried his Amazing Electron Ring in his little sister’s sandbox, but he cannot remember where.?542734511938000A few minutes ago he heard that someone is willing to pay $1000 for it.? He has his shovel and is ready to dig.?? The sandbox is rectangular, measuring 4 feet by 5?feet, as shown at right.? If Kendrick only has time to search in the 2 foot-square shaded region,what is the probability that he will find the ring?What is the probability that he will not find the ring?? Explain how you found your answer.479869514668500Kendrick decides instead to dig in the square region shaded at right.? Does this improve his chances for finding the ring?? Why or why not?507492027940007-73.?Suzette started a proof to show that if??BC?//?EF,?AB?//?DE, and AF?=?DC, then??BC???EF.? Examine her work below.? Then complete her missing statements and reasons.??StatementsReasons1. ? ?BC?//?EF1.??2.???m∠BCF?=?m∠EFC2.??3. ? ?AB?//?DE3.??4.??m∠BAC?=?m∠EDF?4.??5.???AF?=?DC5.??6.??6.?? Reflexive Property7.???AF?+?FC?=?FC + DC7.?? Addition Property of Equality (adding the same amount to both sides of an equation keeps the equation true)8.???AC?=?DF8.?? Segment addition9.?? ΔABC???DDEF9.??10.10. ???Δs → ???parts7-75.?The?xintercepts of a quadratic function are given in each part below.?Write a possible equation for each function in standard form.??a. x?=?,?x?= ?2b. x?=??,?x?=?7-76.?Decide if the following statements are true or false.? If they are true, explain how you know.? If they are false, provide a counterexample.??A. If a quadrilateral has two sides that are parallel and two sides that are congruent, then the quadrilateral must be a parallelogram.B. If the interior angles of a polygon add up to 360°, then the polygon must be a quadrilateral.C. If a quadrilateral has three right angles, then the quadrilateral must be a rectangle.D. If the diagonals of a quadrilateral bisect each other, then the quadrilateral must be a rhombus.7-77.?Determine the area and perimeter of each shape below.? Show all work.??a. 153035-1270b. 3370580-12707.2.2Name:______________________________ 7-84.?At University of the Great Plains the following data about engineering majors was collected: What is the conditional probability of living on campus, given that you know a student is an engineering major?What is the probability of living on campus??Are the two events, {living on campus} and {engineering major} associated?? Why?480288989307007-85.?In the diagram at right, ΔABC?~?ΔADE.??Draw each triangle separately on your paper.?Be sure to include all measurements in your diagrams.Calculate the length of?DE. ?7-86.?Multiple Choice:?Which equation below correctly represents the relationship of the side lengths of the trapezoid given in the diagram below??23656864657000A. 3x???2?+?2x?+?17?=?360°B. 3x???2?+?2x?+?17?=?180°C. 3x???2?+?2x?+?17?=?90°D. 3x???2?=?2x?+?177-87.?Factor each polynomial completely.??a. 36x2???a2b. 16x4?? 817-88.?While working on the quadrilateral hotline, Jo Beth gets this call: “I need help identifying the shape of the quadrilateral flowerbed in front of my apartment.? Because a shrub covers one side, I can only see three sides of the flowerbed.? However, of the three sides I can see, two are parallel and all three are congruent.? What are the possible shapes of my flowerbed?”? Help Jo Beth answer the caller’s question.7-89.?Evaluate each expression below without a calculator.?a. 271/3b. 161/4c. 491/2d. 10001/37-90.?Sketch a graph that represents each situation.? Describe the features of the graph completely.a. Rafael walks from his home to the store one mile away in 15 minutes.?He shops for 30 minutes.? Then he waits for a bus outside the store and takes the bus home.? Represent his distance from home over time.b. Sujata works at a gym 15 hours a week.? She makes $9.00/hr, plus a $10 bonus for each new gym membership she sells.? Represent her weekly earnings based on the number of gym memberships she sells.c. Tom has $500 in a savings account.? For balances under $1000, the bank does not pay interest.? For balances over $1000, the bank pays 3% annual interest.? On the last day of each month, Tom deposits $150.? Represent his account balance over time.7-91.?A technology group wants to determine if bringing a laptop on a flight is associated with being on a business trip.? Data for 1000 random passengers at an airport was collected and summarized in the table below.??What is the probability of a passenger bringing a laptop on a flight if the passenger is traveling for business?Does it appear that there is an association between bringing a laptop on a flight and traveling for business?7-92.?This problem is a checkpoint for factoring quadratic expressions.? It will be referred to as Checkpoint 7.??Factor each quadratic expression completely.a. x2?? 8x?+ 7b. y2?? 2y?– 15c. 7x2?– 63d. 3x2?+ 10x?+ 87-93.?Evaluate the expression below when?x?= 27 and?y?= 16.?? 6x2/3y1/4?·?x?1y1/27-94.?For each polygon below, use the geometric relationships to solve for the given variable(s).? Show all work.? Name the geometric relationships you used.?? a. 161925-2540b. 3370580-2540c. 153035-1270d. 3370580-12704045585108437-96.?On graph paper, graph?AB?if?A(1, 6) and?B(5, 2).??Calculate?AB?(the length of?AB).?Leave your answer in exact form.? That is, do not approximate with a decimal.? Explain your method.7-97.?Solve the equations, if possible.? Be sure you have found all possible solutions.? Check your work and write down the name(s) of the method(s) you used.? a. (x?+ 4)2?= 49b. = 12c. + = d. 5(2x?? 1) ? 2 = 13?7.2.3Name:_____________________________7-107.?In a certain small town, 65% of the households subscribe to the daily paper,37% subscribe to the weekly local paper, and 25% subscribe to both papers.Make a twoway table to representthis data.If a household is selected at random, what is the probability that it subscribes to at least one of the two papers?? Shade these areas in your?table.Charlie’s neighbor subscribes to a paper.? What is the probability that he receives the daily paper?7-108.?Dr. G, the principal at Westside High School Academy, is worried that the students who win academic awards might also be more likely to win awards in the Fine Arts.? He would like to spread out the awards.? Out of the 768 students, 128 students have won academic awards of some sort and 48 students have won Fine Arts awards.? Eight students have won both kinds of awards.? Does Dr. G have anything to worry about?? Justify your answer.??411797595257-109.?Complete the square to solve 0 =?x2?+?7x?+?2.? Then sketch a graph of the function?y?=?x2?+?7x?+?2.? State the vertex and?yintercept of the parabola.? Does the vertex represent a minimum or a maximum??5449774338717-110.?Multiple Choice:?Based on the relationships provided in the diagram, which of the equations below is correct?? Justify your solution.??A. 4x?+?2??+?9x?–?3??=?90?B. 4x?+?2??=?9x?–?3?C. 4x?+?2??+?9x?–?3??=?180?D. (4x?+?2?)(9x?–?3?)?=?90?7-111.?Solve for?z?in each equation.? a. 4z?=?8b. 45z?=?8(z?+?2)c. 3z?=?812d. 5(z+1)/3?= 25z7-112.?Describe a sequence of steps to construct an isosceles triangle using a compass and straightedge.? right1438097-113.?On graph paper, graph ΔABC?if?A(3, 0),?B(2, 7), and C(6, 4)What is the most specific name for this triangle?? Prove your answer is correct using both slope and side length. What is?m∠A?? Explain how you found your answer.?Without using your calculator, use ?ABC?to determine the exact value of?tan(45°).7-114.?Parents keep telling their teens to “turn down the music” or “turn off the computer” when studying.? But teens insist that these “distractions” actually help them study better!? In order to put this argument to rest, a psychologist studied whether subjects were able to memorize 20 index cards while listening to loud music or studying in silence.? The sixty subjects had these resultsa. What is the probability that a randomly chosen subject is able to memorize the index cards?b. What is the probability that a music listener memorizes the index cards?c. According to the data from this study, is the ability to memorize independent of listening to loud music?right245147-115.?For the figure at right, determine if the two triangles are congruent.? If so, create a proof (flowchart or twocolumn) to explain why.? Then, solve for x.?If the triangles are not congruent, explain why not.??4894580152407-116.?Multiple Choice:?The measure of ∠ABD?at right is:? A. 27°B. 161°C. 118°D. 153°E. none of theseright1415457-117.?Which quadratic function has the larger maximum value:?y?=??x2?+?5x?+?6 or the quadratic function graphed at right??7-118.?Solve each of the following by completing the square. ?a. 0 =?x2?+ 8x?– 33b. x2?– 2x +?5 = 0c. x2?– 7x?– 3 = 07-120.?Solve the system of equations.? Write your solution as a point in (x,?y) form.? Check your solution.?y?=??3x???22x?+?5y?=?16?right2101858.2.1Name:__________________________________8-26.?Examine the geometric relationships in the diagram below.? Show all of the stepsin your solutions for?x?and?y.? Name the?polygon.?? 5510386140788-27.?Joey uses ten congruent isosceles triangles to create a regular?decagon.??a. What are the three angle measures of one of the triangles? Explain how you know.b. If the area of each triangle is 14.5 square inches, then what is the area of the regular decagon?506640182558-29.??Examine the diagram at right.? Assume that?AD?and?BE?are line segments, and that?BC???DC?and ∠A???∠E.? Prove that??AB???ED.? Use the form of proof that you prefer (such as the flowchart or twocolumn proof format).? Be sure to copy the diagram onto your paper and add any appropriate markings.?? 8-31.?Calculate the area of an equilateral triangle with side length 20.0 mm.?Draw a diagram and show all work.?? 4613910146058-32.?Which of the triangles below are similar to ΔLMN?at right?? How do you know?? Explain.?? a. 144780-1905b. 2439035-1905?c. 135890-1905d. 2439035-19058.2.2Name:__________________________________8-39.?A regular polygon has an interior angle measuring 135°.? How many sides does it have?? Determine the number of sides using?two?different strategies.? Show all work.? Which strategy was most efficient?? 48628062527668-40.?For the triangle at right, write each of the following trigonometric ratios.? The first one is done for you.?? a. tan?C =? b. sin?C = c. tan?A = d. cos?C = e. cos?A = f. sin?A = 8-42.?Examine the diagram at right.? Given that ?ABC????EDF, is ?DBG?is isosceles?? Prove your answer.? 45091474624Use any format of proof that you prefer.? 8-44.??Jamila solves the quadratic equation?x2?+ 3x?– 10 = 8 (see her work below).? When she checks her solutions, they do not make the equation true.? However, Jamila cannot find her mistake.? Explain her error and then solve the quadratic equation correctly.??? ? ? ? ? ? ? x2?+ 3x?– 10 = 8(x?+ 5)(x?– 2) = 8x?+ 5?= 8 or?x?– 2 = 8x?= 3 ? ?or ??x?= 108-45.?One way to look at absolute value is to think of the absolute value of a number as its distance from zero on a number line.? For example, |?6?|?=?6 and |??6?|?=?6 because both 6 and –6 are exactly 6 units from zero on a number line.? You can, therefore, think of the equation such as |?x?|?=?5 as the question,?“What numbers are exactly five units from zero on the number line?”? Thus, the solutions are 5 and –5.? Draw a number line to show the solutions to the following equations.?a. |x| = 3b. |x| = 0c. |x| + 2 = 6d. 3|x| = 15e. |x – 5| = 2f. |x + 3| = 7 right134438-46.?At right is a scale drawing of the floor plan for Nzinga’s dollhouse.? The actual dimensions of the dollhouse are five times the measurements provided in the floor plan at right.??a. Use the measurements provided in the diagram to calculate the area and perimeter of her floor plan.b. Draw a similar figure on your paper.? Label the sides with the actual measurements of Nzinga’s dollhouse.? What is the perimeter and area of the floor of her actual dollhouse?? Show all work.c. What is the ratio of the perimeters of the two figures?? What do you notice?d. What is the ratio of the areas of the two figures?? How does the ratio of the areas seem to be related to the scale factor? Explain.8-47.?Always a romantic, Marris decides to bake his girlfriend a cookie in the shape of a regular dodecagon (12gon) for their 12-day anniversary.??a. If the edge of the dodecagon is 6 cm, what is the area of the top of the cookie?b. His girlfriend decides to divide the cookie into 12 congruent pieces.?After nine of the pieces have been eaten, what area of the cookie is left?433451026035008-48.?On graph paper, plot the points?A(4,?1) and?B(10,?9).??a. What is the distance between points?A?and?B?? That is, what is?AB?8-49.?A survey of local car dealers revealed that 64% of all cars sold last month had a Green Fang system, 28% had alarm systems, and 22% had both Green Fang and alarm systems.?a. What is the probability one of these cars selected at random had neither Green Fang nor an alarm system?b. What is the probability that a car had Green Fang and was not protected by an alarm system?c. Are having Green Fang and an alarm system disjoint (mutually exclusive) events?d. Determine if having Green Fang is associated with having an alarm.8-50.?What is the area of a regular decagon if the length of each side is 20 units??? ?8-51.?Simplify each of the following expressions. Be sure that your answer has no negative or fractional exponents.??a. 641/3b. (4x2y5)–2c. (2x2?·?y–3)(3x–1y5)8-52.?Sketch a graph that could represent each scenario below.? Be sure to label the axes appropriately and then write a description of the graph.??a. The height of a baseball thrown from centerfield to home plate in relation to the distance from the centerfield.b. The number of shoppers at the mall each hour during business hours on a given day.c. The temperature of a cup of coffee?x?minutes after being poured.8.3.1Name:__________________________________8-57.?Examine the shape at right.??right6985a. What is the area and perimeter of the shape?b. If you enlarged the figure so that the linear scale factor is three, what are the area and perimeter of the new shape?c. What is the ratio of the perimeters of the shapes??What is the ratio of the areas?8-58.?The exterior angle of a regular polygon is 20°. ?a. What is the measure of an interior angle of this polygon??Show how you know.b. How many sides does this polygon have?? Show all work.8-59.?A regular hexagon with side length 4 has the same area as a square.?What is the length of the side of the square?? Explain how you know.? 8-60.?Of the students who choose to live on campus at Coastal College, 10% are seniors.? The most desirable dorm rooms are in the newly constructed OceanView dorm, and 60% of the seniors live there while 20% of the rest of the students live there.??a. Represent these probabilities in a two-way table.b. What is the probability that a randomly selected resident of the OceanView dorm is a senior?c. Determine if being a senior is associated with living in the Ocean View dorm.8-61.?As her team is building triangles with linguini, Karen asks for help building a triangle with sides 5, 6, and 1.?“I don’t think that’s possible,”?says her teammate, Kelly.?a. Why is this triangle not possible?b. Change the lengths of one of the sides so that the triangle is possible.8-63.?For each expression below, what real-number value of?x?will yield the lowest possible value of the expression?? For example, in part (a), if?x?=?5, then the value of the expression is 25.? If?x?=?–4, then the value of the expression is 16.? Are there values of?x?that will result in smaller values of the expression?a. x2b. (x – 1)2c. (x + 7)28.3.2Name:__________________________________5227320984258-70.?Assume Figure A and Figure B, at right, are similar.??a. If the ratio of similarity is , then what is the ratio of the perimeters of Figures A and B?8-71.?Beth is creating a wildflower garden, and she is going to build the flowerbed in the shape of a regular hexagon. ?Each side of the flowerbed will be 1 yard long.?a. What will the area of the garden be in square yards?b. A packet of wildflower seeds covers 10 square feet.? How many packets of wildflower seeds will Beth need?8-72.?Determine if all the circles below (not drawn to scale) are similar.? Justify your decision.??8-73.?For each diagram below, write and solve an equation for?x.?? a. 1447800b. 335343505408295152408-74.?Christie has tied a string that is 24 cm long into a closed loop, like the one to the righta. She decides to form an equilateral triangle with her string.? What is the area of the triangle?b. She then forms a square with the same loop of string.? What is the area of the square?? Is it larger or smaller than the area of the equilateral triangle she created in part (a)?443674538108-75.?Your teacher has offered your class extra credit.? She has created two spinners, shown at right.? Your class gets to spin only one of the spinners.? The number that the spinner lands on is the number of extra credit points each member of the class will get.? Study both spinners carefully.??a. Assuming that each spinner is divided into equal portions, which spinner should the class choose?? b. What if the spot labeled “20” were changed to “100”?? Now which spinner should the class choose?8-76.?Think of absolute value as a statement about distance as you answer the questions below.? What values of?x?in parts (a) through (d) make each equation true?? a. | x – 7| = 50b. |x + 7| = 50c. |10 – x| = 12d. |2x + 1| = ?3e. What mathematical operation is best used for calculating the distance between two numbers?? In other words, if you want to know the distance from 42 to 117, what arithmetic expression represents that distance??8.4.1Name:__________________________________8-81.?Use your findings from problem 8-79 to answer the questions below.? Recall that the?diameter?of a circle is a segment with endpoints on the circle that passes through the center.? The length of the segment is also called the diameter.?a. What is the area of a circle with radius 10 units?b. What is the circumference of a circle with diameter 7 units?c. If the area of a circle is 121π?square units, what is its diameter?d. If the circumference of a circle is 20π?units, what is its area?4824095152408-82.? The vertex of the angle in the diagram at right is the center of the circle.? What fraction of the circle is shaded??? 8-83.?Calculate the measure of each interior angle of a regular 30gon.?? 8-84.?An exterior angle of a regular polygon measures 18°.?a. How many sides does the polygon have?b. If the length of a side of the polygon is 2 units, what is the area of the?polygon?5951220334645008-85.??A circle can be named by its center, as in circle?C,?or?⊙C?at right.? Larry started to set up a proof to show that if?AB?⊥?DE?and?DE?is a diameter of ⊙C, then?AF???FB. ?Examine his work below.? Then complete his missing statements and reasons.??StatementsReasons1. ?AB?⊥?DE?and?DE?is a diameter of ⊙C.1.??2.?? ∠AFC?and?∠BFC?are right angles.2.??3. ? ?FC???FC3.??4. ? ?AC???BC4.?? Definition of a circle (radii must be equal)5.??5.?? HL ?6. ? ?AF???FB6. ?162560057158-86.? Approximate?AB.?8-87.?For each expression below, what realnumber value of?x?will yield the maximum possible value of the expression???a. –x2b. –(x?+ 2)2c. –(x?– 5)2?8.4.2Name:__________________________________8-93.?For each circle below, what are the arc length and the area of the shaded sector?? Write your answers in terms of?π.?449226519230a. m∠AOB?=?120°?1102360-3810b. CD?= 6 in8-94.?Solve for?x?in each diagram below.? Show your work.?? 39831646086a. 144780-2540b. 3818890189865c. 1358903810d. 8-95.?The?Isoperimetric Theorem?states that of all the closed figures that can be made on a flat surface with the same perimeter, the circle has the greatest area.? Use this fact to answer the questions below.??a. What is the greatest area that can be enclosed by a loop of string that is 24?cm long?b. What is the greatest area that can be enclosed by a loop of string that is 18π?cm long?8-96.?Use what you know about the area and circumference of circles to answer the questions below. Show all work.? Leave answers in terms of?π.??a. If the radius of a circle is 14 units, what is its circumference?? What is its area?b. If a circle has diameter 10 units, what is its circumference?? What is its area?c. If a circle has circumference 100π?units, what is its area?d. If a circle has circumference C, what is its area in terms of C?8-97.??For a school fair, Donny is going to design a spinner with red, white, and blue regions.? Since he has a certain proportion of three types of prizes, he wants?P(red) = 40% and?P(white)?=?10%.??a. If the spinner only has red, white, and blue regions, then what is?P(blue)?? b. What are the central angles of this spinner if it has only three sections?? Draw a sketch of the spinner.? Be sure to label the regions accurately.c. Is there a different spinner that has the same probabilities?? If so, sketch another spinner that has the same probabilities.? If not, explain why there is no other spinner with the same probabilities.4973955336558-98.??Krista is trying to solve for?x?in the triangle at right.?a. What equation could Krista write?b. Krista does not have a scientific calculator with trig buttons on it, but she does remember something funny her friend Juanisha told her.? Juanisha’s favorite sine ratio is sin 31.5°?≈?0.522 because ?is Juanisha’s birthday!? Without using the trig buttons on your calculator, use Juanisha’s favorite ratio to solve your equation from part (a).8-99.?Jessie looks at the equation (x?– 11)2?+ 4 = 0 and states,?“This equation has no solutions!”??a. Solve (x?– 11)2?+ 4 = 0.?c. Are there really?no solutions?8.4.3Name:__________________________________right2000258-105.?The city of Denver wants you to help with their plan to build a dog park.? The design of the park is a rectangle with two semicircular ends.? (Note: A semicircle is half of a circle.)?a. The entire park needs to be covered with grass.? If grass is sold by the square foot, how much grass should you order?b. The park also needs a fence for its perimeter.? A sturdy chainlink fence is sold by the foot and costs $8 per foot.? How much will a chain-link fence for the entire park cost? c. The local design board has rejected the plan because it is too small.? “Big dogs need lots of room to run,” the president of the board said.? Therefore, you need to increase the size of the park by a linear scale factor of 2.? What is the area of the new design?? What is the perimeter??8-106.?Use the angle relationships in each of the diagrams below to solve for the given variables.? 24395503073880014492430738700Show all work.? a. b. c. 47078906358-107.?This problem is a checkpoint for applying trigonometric ratios and the Pythagorean Theorem.a. Compute the perimeterb. Solve for x.336303219158-17252384337120318978100c. Solve for x.d. Solve for x.-17253726e. Juanito is flying a kite at the park and realizes that all 500 feet of string have been let out.? Margie measures the angle of the string with the ground using her clinometer and determines it is 42°.? How high is Juanito’s kite above the ground?? Draw a diagram and use the appropriate trigonometric ratio.3767898284198-109.??Three spinners are shown at right.? If each spinner is randomly spun and if spinners #2 and #3 are each equally subdivided, calculate the following probabilities.??a. P(A,?C,?and?E)b. P(at least one vowel)8-110.??Write each radian measure in degreesa. 2πb. c. d. ClosureName:__________________________________Solve each problem as completely as you can.? The table at the end of the closure section has answers to these problems.? It also tells you where you can find additional help and practice with problems like these.56135569897CL 8-111.?Mrs. Frank loves the clock in her classroom because it has the school colors, green and purple.? The shape of the clock is a regular dodecagon with a radius of 14 cm.? Centered on the clock’s face is a green circle of radius 9 cm.? If the region outside the circle is purple, which color has more area?? (See problem?8-37?in Lesson 8.2.2 for the definition of the radius of a polygon.)501652410580CL 8-112.?A running track design is composed of two half circles connected by two straight-line segments. ?Garrett is jogging on the inner lane (with radius?r) while Devin is jogging on the outer (with radius?R).? If?r?=?30 meters and?R?=?33 meters, how much longer does Devin have to run to complete one lap?CL 8-113.?Answer the following questions about polygons.? If there is not enough information or the problem is impossible, explain why.a. What is the sum of the interior angles of a dodecagon?b. How many sides does a regular polygon have if its central angle measures 35°?c. If the sum of the interior angles of a regular polygon is 900°, how many sides does the polygon have?d. If the exterior angle of a regular polygon is 15°, what is its central angle?e. What is the measure of an exterior angle of a regular polygon with 10 sides?4872452-8626500CL 8-114.?Use the diagram at right to prove the following statement.? Use the proof format that you prefer, either two-column or flowchart.?If?AB???AD?and?BC???DC, then?AC?⊥?BD.CL 8-115.?After constructing ?ABC, Pricilla decides to try a little experiment.? She chooses a point?V?outside of ΔABC?and then constructs rays , , and .? Her result is shown below. ?Copy this diagram onto your paper.left12700a. Pricilla then uses a compass to mark point?A' so that?VA?=?AA'.? She also constructs points?B' and?C' using the same method.? For the diagram on your paper, locate?A',?B', andC'.b. Now connect the new points to form ΔA'B'C'.? What is the relationship between ΔABC?and ΔA'B'C'?? Explain what happened.c. If the area of ΔABC?is 19 cm2?and its perimeter is 15 cm, what are the area and perimeter of ΔA'B'C'?CL 8-116.?Examine the triangles below.? For each one, solve for?x?and name which relationship(s) you used.? Show all work.?left2397400CL 8-117.?According to a survey, in 2010 pet ownership in the U.S. was distributed as shown in the table below (out of every 1000 households).Number of households with:Household incomeprimarily dogsprimarily catsprimarily birdsprimarily horsesno petsunder $20,00064639370$20,000 to $34,99966597341$35,000 to $54,99977668438$55,000 to $84,99982687431$85,000 and over97779542a. What is the probability that a randomly selected household has no pets?b. What is the probability that a randomly selected household has a pet?c. If a household is selected at random, what is the probability that the household earns under $35,000?and?owns a dog??d. What is the probability that a randomly selected household earns under $35,000?or?owns a dog?e. Use another method for determining the probability of earning under $35,000?or?owning a dog to verify your result for part (d).f. What is the probability that a randomly selected household that earns under $35,000 also owns a dog?54157477357CL 8-118.?Your teacher has constructed a spinner like the one at right.? He has informed you that the class gets one spin.? If the spinner lands on the shaded region, you will have a quiz tomorrow.? What is the probability that you will have a quiz tomorrow?? Explain how you know.CL 8-119.?Check your answers using the table at the end of this section.? Which problems do you feel confident about?? Which problems made you think?? Have you worked on problems like these in math classes you have taken before?? Use the table to make a list of topics you need help on and a list of topics you need to practice more.Chapter 9 Homework9.1.1Name:__________________________________9-5.?For each equation in parts (a) through (d) below, determine the input value that gives the?smallest?possible output. In other words, what is the?xvalue of the?lowest?point on the graph? What is the input value that gives the?largest?possible output (or the?xvalue of the?highest?point on the graph)??? ?a. ??f(x) = (x?– 1)2b. ??f(x) =?x2?– 2?c. ??f(x) = (x?+ 2)2d. ??f(x) = –x2?+ 3?e. ? For each function above, where on its graph is the maximum or minimum point?4457700996959-6.?Sketch?f(x) =?x2,?f(x) = –2x2, and?f(x) = –0.5x2?on the same set of axes.? What does a negative coefficient of?x2?do to the graph? ? 441579035560009-7.?Your results from this problem will be useful in the parabola investigation that you will do in Lesson 9.1.2. ? Make a complete graph of?f(x) = (x?– 2)2. ?How is this graph different from the graph of?f(x) =?x2? ?9-8.?Solve the inequalities below. Show your solutions on a number line.? ?a. ?6x???1?<?11b.??x ≥ 29-9.?How many sides does the regular polygon have if each interior angle has the following measure?? a. 60°156°90°140°9-10.?Solve the system of equations below. y?= ?2x?+ 69442453619500y?=? x?– 99.1.29-16?Use what you learned in the Parabola Lab to write an equation for each of the parabolas described below.? A parabola opening upward, shifted 7 units right, and 4 units down. ?A parabola that is vertically stretched by a factor of 2, sitting with its vertex on the?x-axis at?x?=?–3. ?A downward-opening parabola with vertex (–5, 2) and a vertical compression of 0.5.5185410146685009-17?Carmen made a function machine. The inner workings of the machine are visible in the diagram at right. What will the output be in each of the following cases??? a. If 2 is dropped in?If – 4 is dropped in???If –11.3 is dropped in? ?9-18.? Solve each inequality. Then represent each solution on a number line. ? ?a. 4x?– 3 ≥ 9b. 3(x?+ 4) < 543434001619259-19.?Write the equation of a quadratic function containing the points in the table below. Then make a complete graphx– 4–3–2–101234567y1880–6–10–12–12–10–608189-20.?Solve the following systems of equations algebraically. Then graph each system to confirm your solution.? ?3980815-69278500x + y?= 3 x?= 3y?– 59-21.?One of the giant sequoia trees, in the General Sherman tree in Sequoia National Park, is the largest living thing on Earth. The tree is so gigantic, in fact, that the base has a circumference of 102.6 feet! Assuming that the base of the tree is circular, how wide is the base of the tree? That is, what is its diameter??489585012446000?9-22.?Examine the diagram below. Use the given geometric relationships to solve for?x,?y, and?z. Be sure to justify your work by stating the geometric relationship and applicable theorem.? 9.1.39-29.?Each of the following pictures shows how the same function machine changes the given?xvalue into a corresponding?f(x)-value.? What is the equation for this machine? ?? 9-30.?Your friend goes to a different school and she is not allowed to use a graphing calculator in her math class. ? Explain to her how she can get a good sketch of the graph of the function?f(x)?=?–2(x?– 3)2?+?2 without using a calculator?and?without making an?x?-?y?table.? Be sure to explain how to locate the vertex, whether the parabola opens up or down, and how its shape is related to the shape of the graph of?f(x)?=?x2.Your friend also needs to know the?x and?yintercepts.? Help her determine them without drawing an accurate graph or using a graphing calculator9-31.?Write the equation of a function in graphing form for each parabola described below.?a. A parabola with vertex (0, –5) that passes through the point (–1, 2).???b. A parabola with vertex (1, 4) that passes through the point (5, –4). ?9-32.?Brad says to his granddaughter Kayla, “Even if you squared your age and added one, you still wouldn’t be as old as I am.”? Brad is 65 years old. Write and solve an inequality to determine the possible ages Kayla could be.?9-33. ?Match each regular polygon named on the left with a statement about its qualities listed on the right.?? ?a. regular hexagon(1) central angle of 36°? ?b. regular decagon(2) exterior angle measure of 90°? ?c. equilateral triangle(3) interior angle measure of 120°? ?d. square?(4) exterior angle measure of 120°9-34.?Simplify each of the following expressions.? Be sure that your answer has no negative or fractional exponents.?? ? a. ()?1/4b.?x–1y–3c.?(25x4)1/29-35.?Multiple Choice: What is the solution to the system of equations below??y?=?x ??4x???4y?= 12? ? A. ? (2, 0)B. ? (16, 4)C. ? (?2,??5)? ? D. ? (4,??2)E. ? none of these??9.2.19-54.?Solve each inequality below algebraically. Then represent your solution on a number line.? 5x???7?≥?2x?+?56x???29?>?4x?+?12x2?≤ –4x?+ 59-55.?Determine which type of function—linear, quadratic, or exponential—would be best for modeling each situation below.? You do not need to write an equation for the situation.? Bailey is growing bacteria on a petri dish for science class.? The population of bacteria doubles every 20 minutes, so the initial number of bacteria is 1000, then 2000, then 4000, then 8000, etc.Avery is working on her math homework.? She finished nine problems in class.? She knows that, on average, she can do three problems in five minutes.?Keiton loves catapults.? He is building a small catapult that will launch an apple into the air and over the fence into his friend’s backyard. ?9-56.?Is there a difference between?f(x)?=??and?y?=??in relation to their graphs or tables?? 9-57. ?For each quadratic function below, complete the square to write it in graphing form. Then state the vertex and?yintercept of each parabola. ? ?a.?y?=?x2?+?6x?+ 15b.?y?=?x2???3x?+ 9??9-59.?Solve each system of equations below. Write your solution in the form (x,?y). Check your solution. ?a. 3x?? y?= 14? ? x?= 2y?+ 8b.?x?= 2y?+ 2? ? x?=??y???10c. 16x???y?=??4? ? ? 2x?+?y?= 139.2.29-66.?As you have seen, sometimes the graphs of two equations never intersect.? However, when they do intersect, how many different intersection points can they have? How many intersection points can two lines have? How many intersections can two parabolas have? What about a parabola and a line?? In this problem, you will investigate these questions. Sketch a graph that fits each description below. Not every graph is possible.? A line and a parabola that intersect twiceA line and a parabola that only intersect once.A line and a parabola that intersect more than twice.Two parabolas that intersect twice.Two parabolas that have an infinite number of intersections.Two parabolas that never intersect.Two parabolas that only intersect once.?449580013970009-67.?Solve the system below. Then make a complete graph of the system on graph paper and confirm your solution.? y?=?x?+ 5y?=?x2?+ 5x?+ 89-68. ?Time?(min)Distance (mi)00101.1201.5302.5403.7504.8Eliana is training for a race in San Francisco, so she has a new running route that includes running up and down a steep hill.? Data from her last training run is shown in the table at right.? During which 10-minute interval did Eliana run the fastest? ?The slowest? ?Justify your answers. ?What was Eliana’s average speed during the last 10 minutes of her run? ?Show your work and include units. ??9-69.?For each quadratic function, state the vertex of the parabola.?? a. f(x)?=?(x?+?3.5)2????10.25?f(x)?=?3(x?+?1)2??+?1f(x)?=?(x???2.5)2??+?0.7547840908890009-71.?A sector is attached to the side of a parallelogram, as shown in the?diagram at right. Calculate the area and perimeter of the figure.? ? AgeCracker ACracker BCracker C? Under 201525444? 20 to 391078558? 40 to 597810171? 60 and over34681489-72.?A snack cracker company conducted a taste test for the three different types of crackers it makes. ?It surveyed 250 people in each age group in the table below. ?Participants chose their favorite type of cracker. ?Use the results to answer the questions.? a. What is the probability that a participant chose cracker A or was under 20 years old? What is the probability that a participant did not choose cracker A and was over 20 years old? Use a complement to answer this question.?What is the probability that a participant was 20 years old or older? Use a complement to answer this question.?A randomly-selected participant says he is 15 years old.? What is the probability that he chose cracker A? ?9.3.1Name:________________________________9-82.?Consider the quadratic function?f(x)?=??2(x???2)2?+?6.? a. Without drawing a graph, determine the coordinates of the vertex and state whether the vertex represents the maximum or minimum value of the function.??487680013970Sketch the graph and verify your answer to part (a).?9-83.?Review what you know about the angles of polygons below.? a. If the exterior angle of a polygon is 29°, what is the interior angle???b. If the interior angle of a polygon is 170°, can it be a regular polygon? Why or why not???Determine the sum of the interior angles of a regular 29gon.?5419725-85725009-84.?If the spinner at right spun 80 times, how many times do you predict it will land in each region? Show your work.? 9-86.?Algebraically determine the intersection point(s) of the graph of the system below. How many times do the graphs intersect? y?= 4x?? 7y?=?x2?? 2x?+ 29-87.?Solve each inequality below and graph your solution on a number line.? ?a.?(b?– 4)2?< 12b. ?(x?+ 3)2?> 4c. ?2(x?–?3)?>?49-88.?For each quadratic function below, complete the square to write it in graphing form. Then state the vertex of each parabola.? ?a. ??f(x)?=?x2?+?4x?+?5b. ??f(x)?=?x2???7x9-89.?The United State Department of Defense is located in a building called the Pentagon because it is in the shape of a regular pentagon.? Known as “the largest office building in the world,” its exterior edges measure 921 feet.? a. What is the area of land enclosed by the outer walls of the Pentagon building?b. If 1 mile is equal to 5280 feet, what is that area in square miles?4419600-2571759-90. Determine the area and perimeter of the trapezoid.9.3.29-95.?Mateo is saving money for college. He put $1000 in a nointerest, no fees checking account.? At the end of each year his grandparents give him $200 to add to the account.? Mateo’s friend Marcy has saved $1000, and she put this money into an investment that earns 8% annual interest.? At the end of each year, Marcy pays an investment management fee of $15 and she adds $100 to the account from her babysitting earnings.? Make a table showing how much money Mateo and Marcy will have in their accounts at the end of each year for the first five years.? Start your table with Year 0.?What was the average rate of change of each account from Year 0 to Year?2? ?Show your work and include units in your answers. ?What was the average rate of change from Year 3 to Year 5 in each account??Whose account will have more money in the long-run?? Explain using your results from part (b) and part (c). ?9-96.?Algebraically solve the system of equations below for?x?and?y. (You will need to use the quadratic formula)? y?=?x2?+2.6x?+ 0.45y?= 2x?+ 19-97.?Fireworks for the annual 4th?of July show are launched straight up from a steel platform.? The entire show is computer controlled.? The height of a particular firework in meters above ground level is given by?h?=??4.9t2?+?50t?+?11, where time,?t, is in seconds. ? a. What is the height of the platform?b. How many seconds does it take the firework to hit the ground?c. What is the maximum height of the firework?9-99.?For each geometric relationship represented below, write and solve an equation for?x.? ?a.?b.?9.3.35037159131726009-107.?The absolute value function?f(x)?=??is sometimes written as a piecewise-defined function.? Sketch a graph of?f(x)?=?Write a set of equations to represent?f(x)?as a piecewise-defined function. Be sure to include the domain for each.?5594875365125009-108.?The number 6 is the output for Carmen’s function machine shown at right. What number(s) could have been dropped in?? 9-109.?For the quadratic function?f(x)?=?2(x?+?1)2???5:? a. Identify the vertex and state if it is a maximum or minimum point on the graph.?b. What is the value of the function at that minimum or maximum point?55340259525009-110.?What is the area of the shaded region for the regular pentagon at right if the length of each side of the pentagon is 10 units?? Assume that point?C?is the center of the pentagon.? 9-111.?A particular spinner only has two regions: green and purple.? If the spinner is randomly spun twice, the probability of it landing on green twice is 16%. What is the probability of the spinner landing on purple twice?? 4591050-2286009-112.? The trapezoids at right are similar.? a.What is the ratio of the heights? Hint: It is not pare the areas. What is the ratio of the areas??9-113.?The functions are at it again!? There is another race to infinity.? The functions?g(x)?=?10x2?and?h(x)?=?1.01x?are both in the race.? A third mystery function with the values shown in the table is also in the race.? The mystery function arrives late, so it does not get to the starting line until after the race has already begun.? ? ?x ??m(x)00.0110.0220.0430.0840.1650.32a. Which function will be ahead when?x?=?10? Explain. ??b. How “fast” is each function going during the first two seconds of the race?? That is, what is the average rate of change of each function for the interval 0 ≤?x?≤ 2??c. Write a possible equation for the mystery function. ?d. Which function will eventually win the race?? When will it take the lead? ?9.3.49-118.?If?f(x)?=?x2?+?x???6, then determine: Where the graph of?f(x) intersects the?y-axis. ?Where the graph of?f(x) intersects the?x-axis. If?c(x) = 6, what is?g(x) =?f(x)?+ c(x)?Determine the?x-?and?y-intercepts of?g(x) 9-119.?Write a set of equations for the piecewise-defined function?shown on the graph below. Be sure to include the domain for each part of the function.? 9-120.?Mr. Kyi has placed three red, seven blue, and two yellow beads in a hat.? If a person selects a red bead, they win $3. If that person selects a blue bead, they lose $1.? If the person selects a yellow bead, they win $10. What is the expected value for one draw? Is this game fair? If not, then who has the advantage in this game? Explain. ?? 9-122.?Based on the graph, write an equation for each parabola.? a. ? ? ? ??b. ? ? ? ? ?c. ? ? ? ? ?9-123.? Jill’s car tires are spinning at a rate of 120 revolutions per minute. If her car tires’ radii are each 14 inches, how far does she travel in 5 minutes? ? 9.4.19-134.??331470558800a.? Make an?x?→?y?table and then draw a graph of?y??=?x2???2x???3.?? ? ?b.? Write a possible equation for the given graph.?c.? Without making an?x?→?y?table, what are the?xintercepts of?y??=?x2?+?8x?+?7?? Use them to calculate the coordinates of the vertex and then sketch a graph.???? ? ????????????d.? The height (in feet) of a rocket after?x?seconds is given by the equation?y?=?128x???16x2. ?What is the maximum height reached by the rocket and how long does it take to reach that height?5943600166370009-137.?The diagram at right shows a circle inscribed in a square. What is the area of the shaded region if the side length of the square is 6?units?? 9-140.?Use any algebraic solution method to calculate the point(s) of intersection for the system given below, if any exist. ?Explain what your solution indicates about the graph of the system.?? a.?y?=?x2????4x?+?5? ? y?=??x2??+?4x???1b.?y?=?x2????x???2? ??y?=?x2??+?2x?+?14438650-228600009-143.?Complete the square for?y?=?x2?+ 8x?to determine the vertex.? Then determine the?xintercepts and make a sketch of the parabola.? 9-144.?What is another (more descriptive) name for each polygon described below?? a. A regular polygon with an exterior angle measuring 120°.??b. A quadrilateral with four equal angles. ?c. A polygon with an interior angle sum of 1260°. ?9-145.??Of the 63 drinks at Joe’s Java and Juice Hut, 42 contain coffee and 21 contain dairy products.? If Alexei randomly chooses a drink, what is the probability of getting a drink with both coffee and a dairy product?? What is the probability of getting neither coffee nor a dairy product?? Assume that choosing a coffee drink is independent of choosing a dairy-product drink.? See if you can answer these questions without first making a two-way table. ? Chapter 10 Homework Name:____________________________10.1.148863254994650010-6.?Paul built a tower by stacking six identical layers of the shape at right on top of each other.? What is the volume of his tower? How can you tell without building the shape? ?What is the surface area of his tower?Paul’s tower is an example of a?prism?For each of the prisms below, determine the volume and surface area.?(1)?(2)?4537075787400010-7.?Examine the graph of the circle at right. ? a. What is the equation of the circle?b. Consider the circle?x2?+?y2?=?81. What is the radius?10-plete the square to write?y?=?x2?+?12x???7 in graphing form.?Then determine the vertex and the intercepts of the parabola.? 10-9.?Andres is mailing some presents to his cousins. The rates for sending packages are shown in the table.?Weight not above?(lb)Cost ($) ? ? ? ? ? ? ? ? ?16.7329.64312.78413.38514.33616.08a. What type of function would best represent this situation???b. Andres wants to mail one present that weighs 2.2 pounds and another present that weighs 1.8 pounds.? Should he send them in one?package or two separate packages?10-11 The Mona Lisa, by Leonardo da Vinci, is arguably the most famous painting in existence. ?The rectangular artwork, which hangs in the Musée du Louvre, measures 77 cm by 53 cm. ?When the museum created a billboard with an enlarged version of the portrait for advertisement, they used a linear scale factor of 20. ?What is the area of the billboard? 10-13.?Calculate the area of each figure below. Show all work. a.?b.?c.?10.1.210-18?Rewrite the equation?x2?+?y2???8x? +?6y?+?9?=?0 in graphing form and state the radius and center of the circle.? ?x2?+?y2?= 25y?=?x?+ 110-19.?On graph paper, make a complete graph of the system of equations at right.? Then list all points of intersection in the form (x,?y)4286250609600010-21.?Using a graphing calculator, graph the parabola?y?=?2x2???x?? 15.? a. What are the?xintercepts of the parabola?? Write your points in (x,?y) form.b. How is the graph of?y?=??(2x2???x ??15) the same or different??Can you tell without graphing?10-23.?A cube has an edge length of 16 units. Draw a diagram of the cube and then calculate the volume and surface area.? 10-24.?A spinner is divided into two regions.? One region is red and has a central angle of 60°.? The other region is blue.?? a. On your paper, sketch a picture of this spinner.??b. If the spinner is spun twice, what is the probability that both spins land?on blue? ?c. If the radius of the spinner is 7.0 cm, what is the area of the blue region? ?d. A different spinner has three regions: purple, yellow, and green. If the probability of landing on purple is??and the probability of landing on yellow is?, what is the central angle of the green region? ?10-25.?Factor each of the following expressions completely. Be sure to look for any common factors firsta.?4x2???12xb.?3y2?+?6y?+?3c.?2m3?+?7m2?+?3md.?3x2?+?4x???410.1.310-32.?Solve each of the equations below for the given variable.? Be sure to check your answers. ? a.?4(2x?+?5)???11?=?4x???3b.?c.?3p2?+?10p???8?=?0d.??= 510-34.?In Chapter 8, you encountered the Choose Your Shape Pizza Parlor that sold circular and square pizzas. The area of each slice from the circular pizza is 15.4?in2. The square pizza has slices with area 0.125 ft2.? If each slice costs the same amount, should you order a slice from the circular or square pizza?? 57435751790700010-3 After doing well on a test, Althea’s teacher places a gold star on her paper. When Althea examines the star closely, she realizes that it is really a regular pentagon surrounded by five?isosceles triangles, as shown in the diagram at right. What is the measure of each vertex angle of the star? Show all work.? 10-39.?Multiple Choice:?Which number below could be the length of the third side of a triangle with sides of length 29 and 51? ? A. 10B. 18C. 23D. 8110-41.?Describe each circle by stating the center and radius. ?Complete the square to rewrite the equation in part?(b) in graphing form.? a.?(x???2)2?+?(y?+?3)2?=?25b.?x2?+?2x?+?y2?+?6y???6?=?050367461817170010-44.? The graph and table below represent two different quadratic functions.? x–2–101?2f(x)70–3–23Which function has a smaller minimum value?? Explain how you know.?Determine the roots of?g(x)?=?x2?+?9.? Use your results to write the expression?x2?+?9 as a product.10.2.1539115090805In the diagram,?AD?is a diameter of?⊙B.?Each part is a new problem. Show all work.?? If?m∠A?=?35?, what is?m∠CBD?If?m∠CBD?= 100?, what is?m∠A?If?m∠A?=?x, what is?m∠CBD?10-54.? For each circle, state the center and radius.??a.?????????x2?+?y2?=?4.52b.?????????x2?+?y2?=?75c.???????? (x???3)2?+?y2?=?1 ?d.?????????x2???4x?+?y2???2y?=?14 ?10-55.?Pilar builds a tower by stacking identical layers on top of each other. If her tower uses a total of 312 blocks and if the bottom layer has 13 blocks, how tall is her tower? Explain how you know.? 10-56.?Algebraically determine the points of intersection of the graphs of the two equations below. y?=?xx2?+?y2?= 2510.2.23448050412750010-66.?In?⊙A?at right, m∠C =?64?. What is:? m∠D?mBF?m∠BAF?m?m∠BAF?m∠BAC?10-67. ABCDE?is a regular pentagon inscribed in?⊙O, meaning that each of its five vertices lie on the circle.? Draw a diagram of?ABCDE?and?⊙O?on your paper. ?What is?m∠EDC? How did you determine your answer? ?What is?m∠BOC? What relationship did you use? ?What is?m? 10-68.?Describe each circle by stating the center and radius. Complete the square to rewrite the equation in part?(b) in graphing form.? a.?(x?+?5)2?+?y2?=?10 ?b.?x2???6x?+?y2???2y???5?=?010-69.?Solve the equations below, if possible. ?If there is no solution, explain why.? ?a. ?b. ??2(5x???1)???3?=??10xc. ?x2?+?8x???33?=?0d.??x?? ?12 = 18010-72.?Draw a rectangle with side lengths of 15 units and 9 units.? Reduce the rectangle by using a scale factor of?.? Then determine the area and perimeter of both rectangles.? 10.2.3 5829300209550010-80? Use the diagram of?⊙C?at right to answer the questions below.? Each part is a separate problem.? If?x =?28?, what is?m?If?AD?=?5 and?BD?= 5, what is the area of?⊙C?If the radius of?⊙C?is 8 and if?m?= 100?, what is?BD? ?10-81.?Assume point?B?is the center of the circle below.? Match each item in the left column with the best description for it in the right column.? 3476625210185005143500952500Compute the volume of the figure. ? ?10-84??For each diagram below, write an equation to represent the relationship between?x?and?y.? 10-86.?What are the point(s) of intersection, if any, for the system given below??Use an algebraic solving method of your choice.????????y?=?x2???x???2? ? ? ? y?=?x???6? 5295900-431800010-87.?For the function?f(x) = –(x?+?4)2?+ 1Sketch a graph of the function.Where is the function increasing?What is the maximum value of the function?10.2.442701122825310-94.? In the diagram at right,?⊙M?has a radius of 14 feet and?⊙A?has a radius of 8 feet.??is tangent to both?⊙M?and?⊙A.? If?NC?=?17?feet, what is?ER42335453441700010-95.?On graph paper, sketch a graph of the equation?x2?+?(y???3)2?=?25.? State the?x?and?yintercepts.? 10-96.?Review circle relationships as you answer the questions below.? On your paper, draw a diagram of?⊙B?with?.? If?m?= 80°?and the length of the radius of?⊙B?is 10, what is the length of chord?AC? ?Now draw a diagram of a circle with two chords,?EF?and?GH, that intersect at point?K.? If?EF?=?15,?EK?=?6, and?HK?=?3, what is?GK? ?10-97.? Review what you know about the angles and arcs of circles below.? a. A circle is divided into nine congruent sectors.?What is the measure of each central angle?52205502317b. In the diagram at right, what are?m?and?m∠C?if?m∠B?=?97??c. In?⊙C?at right,?m∠ACB?=?125? and?BC?=?8?units.?d. What are?m?and the length of??? What is the area of the smaller sector?10-98.?Calculate the value of?x?in the triangle at below. Show all work. 10-99.?Match each equation below with its corresponding graph. Can you do this without making any tables? Explain your selections. ? a.?y?=??x2???2b.?y?=?x2???2c.?y?=??x2?+?21.2.3.595312516637010-100.? A cylindrical block of cheese has a 6inch diameter and is 2?inches thick. After a party, only a sector remains that has a central angle?of 45°. What is the volume of the cheese that remains?? Show all work.? 10101.?Determine the value of?x?if the angles in a quadrilateral are 2x, 3x, 4x, and 5x.? 10.2.510-108.?Solve for the variables in each of the diagrams below. Assume point?C?is the center of the circle in part?(b) a.?b.?c.?42192047498710-109.?Sketch a graph of a circle with center (4,?2) and radius 3 units.? Then write its equation in graphing form.? a.?m∠QSOb.??m∠QPOc.??m∠ONSd.?me.?mf.??m∠PQN41176452434360010-110.?If?QS?is a diameter and?PO?is a chord of the circle at right, calculate the measure of the geometric parts listed?below.? 10-111.?In the diagram at right,?AB?is a diameter of?⊙L.? If?BC?=?5 438779223100and?AC?=?12, use the relationships shown in the diagram to solve for the quantities listed below. a.?ABb. length of the radius of?⊙L.c.?m∠ABCd.?mSolve each quadratic equation below using any method you choose.? x2???3x???10?=?0c. x2???8x?+?9?=?0?3x2?+?10?=?4xd. y2???2y?=?1510-114.?What is the area of a regular decagon with perimeter 100 units?? Show all work.? 4388427688930010-115.?In ΔPQR, what is?m∠Q??Explain how you found your answer.?11.1.1Name:__________________________________11-7.?A?regular hexagonal prism has a volume of 2546.13 cm3?and the base has an edge length of 14?cm.? What are the height and surface area of the prism?? 5236210825511-8.?In the diagram at right,?DE?is a midsegment of ΔABC.? If the area of ΔABC?is 96 square units, what is the area of ΔADE? ?Explain how you know.?? 11-10.?The figure at right shows two concentric circles.? 55289456985What is the relationship between??and??? How can??be mapped to??using a transformation??Which has greater measure,??or??? Which has greater length?? Explain.If?m∠P?=?60? and?PD?=?14, what is the length of??? Show all work.11-11.?Solve the system of equations x2?+?y2?=?25(x?+?9)2?+?y2?=?3411-13.?Solve each equation by first rewriting it in a more useful form.? a. 252 = 125x+1b. + = 2c. x2 – 4x + 4 = 25d. 9x = 5240319396511-14.?Hokiri’s ladder has two legs that are each 8 feet long.? When the ladder is opened safely and locked for use, the legs are 4 feet apart on the ground. ?What is the angle that is formed at the top of the ladder where the legs meet??11.1.2Name:__________________________________11-19.?Koy is inflating a spherical balloon for her brother’s birthday party.? She has used three full breaths so far and her balloon is only half the width she needs.? Assuming that she puts the same amount of air into the balloon with each breath, how many more breaths does she need to finish the task?? Explain how you know.??? 11-20.?The radius of a cylinder is 6.0 inches and the height is 9.0 inches.?? What is the surface area of the cylinder??What is the volume of the cylinder??If the cylinder is enlarged by a linear scale factor of 3, what is the volume of the enlarged cylinder?? How do you know?11-21.?What is the surface area of the original cylinder in problem 11-20 in square feet? ?Remember, you are converting from square inches to square feet.??11-22.?West High School has a math building in the shape of a regular polygon.? When Mrs.?Woods measures an interior angle of the polygon (which is inside her classroom), she gets 135°.??How many sides does the math building have?? Show how you got your answer.Mrs. Wood’s ceiling is 10.0 feet high and the length of one side of the building is 25.0 feet. What is the volume of West High School’s math building?11-23.?In the figure at right,?EX?is tangent to?⊙O?at point?X.?OE?=?20.0 cm and?XE?=?15.0 cm.???53714178231What is the area of the circle?What is the area of the sector bounded by OX and ON?What is the area of the region bounded by XE, NE, and ?11-24.?Rewrite?y?=?x2?+?3x?+?4 in graphing form.? 11-25.?Calculate the perimeter of each shape below.? Assume the diagram in part (b) is a parallelogram.a. 144780-635b. 2439035-635c. 4707890317511.1.3Name:__________________________________right1143011-30.?Consider the two similar solids at right.? What is the linear scale factor between the two solids?What is the surface area of each solid?? What is the ratio of the surface areas?? How is this ratio related to the linear scale factor?Now calculate the volume of each solid.? How are the volumes related?? Compare this to the linear scale factor and record your observations.?11-31.?Without using a calculator, what is the sum of the interior angles of a 1002gon?? Show all work. ? 11-32.?Compute the volume of the solid shown below.?? 11-34.?Consider the circle that is centered at the origin and contains the point (0,?3).? Name three other points on the same circle.?470979576200011-35. If the larger cube can hold 27 cubes of edge length 1 unit,then what is the edge length of the larger cube??? 11-36.?Annie remembers the Water Balloon Contest and wants to try her skill at launching a balloon.? Her balloon’s flight can be modeled by the function?y?= –(x?– 1)2?+ 2 where x?is the horizontal distance (yd) the balloon has traveled from the goal line, and?y?is the height (yd) of the balloon above the ground. Sketch a graph of the function and label the?x- and?yintercepts.? What do the intercepts tell 44411904445you about the flight of the balloon?What is the maximum height the balloon reaches?? Justify your answer.11-37.?Jamie teaches ballroom dance at a dance studio.? Each month, she offers a series of group classes fora charge of $45/person.?? Write a function?f?to represent Jamie’s monthly earnings based on the number of participants.? What is an appropriate domain for your function??Jamie rents a large room at the dance studio for $1200/month.? Write a function?p?to represent Jamie’s monthly profits based on the number of participants.? How many participants does Jamie need to make a profit each month??11.2.1Name:__________________________________right310311-45.?THE TRANSAMERICA BUILDINGThe TransAmerica building in San Francisco is built of concrete and is a square-based pyramid.? The building is periodically power-washed using one gallon of cleaning solution for every 250 square meters of surface.? As the new building manager, you need to order the cleaning supplies for this large task.? The problem is that you do not know the height of each triangular face of the building; you only know the vertical height of the building from the base to the top vertex.?? If an edge of the square base is 96 meters and the height of the building is 220?meters, how much cleaning solution is needed to wash the TransAmerica building?? Include a sketch in your solution.?479422617742811-46.?Elliot has a modern fish tank that is in the shape of an oblique prism, shown at right.?? If the slant of the prism makes a 60° angle with the flat surface on which the prism is placed, what is the volume of water the tank can hold?? Assume that each base is a rectangle.?What is the volume of Elliot’s tank in gallons if one cubic foot of water equals 7.48 gallons?? Show your steps and work.?11-47.?A cylinder with volume 500π?cm3?is similar to a smaller cylinder.? If the volume of the smaller cylinder is 4π?cm3, what is the ratio of the heights of the cylinders?? Explain your reasoning.???11-48.?Examine the diagrams below.? For each one, use the geometric relationships to solve for the given variable.? a. is tangent to ⊙C?at?P?and??= 314?.? b. radius = 7 units What is?QR????3674745952500034099563490011-51.?Solve the equations and inequalities below.? Check your solution(s), if possible.?? a. 300x – 1500 = 2400b. x = x + 2c. x2 – 25 ≤ 0d. |3x – 2| > 45682747735611-53.?What are the volume and surface area of a square-based right pyramid if the base edge has length 6?units and the height of the pyramid is 4?units? 11-54.?What is the area of a regular polygon with 100 sides and a perimeter of 100?units????11-55.? The volume of a solid is?V.? If the solid is enlarged proportionally so that its side lengths increase by a factor of 9, what is the volume of the enlarged solid?? ?432131938100011-56.?Compute the volume of the figure below.???11-57.?In problem 11-33, you used the relationship between the segment lengthsformed by intersecting chords to calculate a missing length.? But how are the measures of arcs intercepted by two intersecting chords related?? Examine the diagram at right.? Solve for?a,?b, and?c?using what you know about inscribed angles and the sum of the angles of a triangle.52508155715Compare the result for?c?with 88° and 72°.? Is there a relationship??42983153937011-59.?Sketch a graph of the system below to determine the number of points of intersection. y?= (x +?2)2?– 2y?= x?+ 211.2.2Name:__________________________________1409691708150011-66.?What is the volume and total surface area of each solid below?? Show all work.?? 33508952413000a. b. 11-67.?What is the volume of each solid below??? a. cylinder with a holeb. regular octagonal prism3405709118850017988511802?11-68.?A cube has an edge length of 12 inches. Draw a diagram of the cube and calculate the volume and surface area in cubic and square inches respectively.Now calculate the volume and surface area in cubic and square?feet?respectively.11-69.?A pyramid has a volume of 108 cubic inches and a base area of 27 square inches.? What is its height???? 4665069444511-70.? Use the process from Problem 11-57 to calculate the measure of?x.? Show all work.? ??11-71.?Use the system below to answer each question. ??419417536195y?= –?xx2?+?y2?= 8Algebraically solve the system.To check your answer to part?(a), graph the system.?50440695284911-72.?Prove that when two lines that are tangent to a circle intersect, the distances from the point of intersection to the points of tangency are equal.? That is, in the diagram at right, when??is tangent to?⊙E?at point?D, and??is tangent to?⊙E?at point?F, prove that?AD?=?AF.? Use either a flowchart or a twocolumn proof.? 11-73.?A sixyear old house, now worth $175,000, appreciates at an annual rate of 5%.?? If you want to calculate the value of the house at a given time, what is the multiplier you need to use in this situation??What did the house cost when it was new?Write a function of the form?f(t) =?abt?that represents the value of the house?t?years after it was first built. 11.2.3Name:__________________________________11-80.?As Shannon peels her orange for lunch, she realizes that it is very close to being a sphere.? If her orange has a diameter of 8?centimeters, what is its approximate surface area (the area of the orange peel)?? What is the approximate volume of the orange?? Show all work.?? 11-81.?This problem is a checkpoint for angle measures and areas of regular polygons.?a. What is the measure of each interior angle of a regular 20gon??b. Each angle of a regular polygon measures 157.5?.? How many sides does this polygon have??c. Calculate the area of a regular octagon with side length 5.0 cm11-83.?Cindy’s cylindrical paint bucket has a diameter of 12?inches and a height of?14.5 inches.? If 1?gallon?≈?231?in3, then how many gallons does her paint buckethold?? ?5363570862611-85.?A silo (a structure designed to store grain) has the shape of a cylinder with a cone on top, as shown in the diagram at?right. ?? If a farmer wants to paint the silo, how much surface area must be painted??What is the volume of the silo?? That is, how many cubic meters of grain can the silo hold?41406793387111-86.?Rewrite?y?=?x2??+?8x?+?10 in graphing form and sketch a graph of the function.? Then name the vertex and the?y-intercept. ClosureName:__________________________________Solve each problem as completely as you can.? The table at the end of the closure section has answers to these problems.? It also tells you where you can find additional help and practice with problems like these.CL 11-88.?What is the measure of?x?in each diagram below?? Assume each polygon is regular.a. 1447801270b. 24390351270c. 47078903175528914317672CL 11-89.?A restaurant has a giant fish tank, shown at right, in the shape of an octagonal prism. ?What is the volume and surface area of the fish tank if the base is a regular octagon with side length 0.8 m and the height of the prism is 2 m?5778429186152CL 11-90.?After Myong’s cylindrical birthday cake was sliced, she received the slice at right.? If her birthday cake originally had a diameter of 14?inches and a height of 6?inches, what is the volume of her slice of cake?CL 11-91.?On your paper, draw a diagram of a square-based pyramid.? If the base has side length six units and the height of the pyramid is ten units, what is the total surface area of the pyramid?? What is the volume of the pyramid?? Show all your work.5685850508000CL 11-92.?An ice cream cone is filled with ice cream.? It also has?ice cream on top that is in the shape of a cylinder.? It turns out that the volume of ice cream inside the cone equals the volume of the scoop on top.? If the height of the cone is 6 inches and the radius of the scoop of ice cream is 1.5 inches, what is the height of the extra scoop on top?? Ignore the thickness of the cone.53461138147CL 11-93.?Look at the diagram at right. ?AD?is tangent to ⊙C?at?D.? Assume each part is a separate problem. ?If?AD?=?9?cm and?AB?=?15?cm, what is the area of?⊙C?If the radius of?⊙C?is 10?cm and?m?= 30°, what are?m?and?AD?If?m?=?86°?and?BC?=?7?cm, what is?EB?49923705715CL 11-94.?A circle has two intersecting chords as shown in the diagram below.? What is the value of?x?CL?11-95. For each system below, determine where the graphs intersect.a. y?=??3x?+?5b. y?=?x2???3x???8??? (x???1)2?+?y2?=?4 y = 2right10531CL 11-96.?Assume that the prisms at right are similar.What is the ratio of the corresponding sides of Solid B to Solid A?If the base area of Solid A is 27?square units, what is the base area of Solid B??If the volume of Solid A is 135 cubic units, what is the volume of Solid B?right9525CL 11-97.?Jamie loves to long jump!? The function?y?=?–0.08x(x?–?7.2) where?x?represents horizontal distance and?y?represents vertical distance in meters can be used to model one of Jamie’s jumps.a. Sketch a graph of the function.b. What is an appropriate domain for this model?c. Identify any special points such as the intercepts and vertex.? Explain what each point tells you about Jamie’s jump.4038600134620CL 11-98. Given the function??f(x) =?x2?– 2x?– 8:Identify the domain, range, and any special points such as the intercepts and vertex.Sketch the graph of the function.CL 11-99.?Check your answers using the table at the end of this section.? Which problems do you feel confident about?? Which problems made you think?? Have you worked on problems like these in math classes you have taken before?? Use the table to make a list of topics you need help on and a list of topics you need to practice more. ................
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