Algebra Unit 4 - Lancaster High School



Algebra Unit 5 HW Day 1 SOLVING GRAPHICALLY

Graph the following systems:

1) [pic] 2) [pic]

3) [pic] 4) [pic]

[pic] [pic]

Use your calculator to solve the following systems of equations:

5) [pic] 6) [pic]

[pic] [pic]

Review:

6. Computer monitors are priced according to the length of the diagonal of the screen. To the nearest hundredth of a centimeter, what is the length of the diagonal of the screen shown?

(1) 42.42 cm (2) 59.00 cm (3) 36.87cm (4) 41.87cm

7. At Joe’s Clown Car rental agency, renting a car costs $35 plus $0.75 for every mile driven. What is the equation that can be used to find the number of miles, m, a vehicle was driven, if the total charge was $222.50?

(1) [pic] (3) [pic]

(2) [pic] (4) [pic]

Algebra Unit 5 HW Day 2 SOLVING ALGEBRAICALLY

Solve the following systems algebraically:

1) [pic] 2) [pic]

3) [pic] 4) [pic]

Review:

5. What is the volume of the solid shown:

(1) [pic] (3) [pic]

(2) [pic] (4) [pic]

6. Which of the graphs below shows the solution set of [pic]?

7. Solve for x: [pic]?

Algebra Unit 5 HW DAY 3 MORE SOLVING ALGEBRAICALLY

Solve the following systems algebraically:

1) [pic] 2) [pic]

3) [pic] 4) [pic]

Review:

5. What interval notation represents the data graphed below?

(1) (1, 4] (2) [4, 1) (3) (4, 1) (4) (1, 4)

6. Solve for x: [pic]

7. Solve for x: [pic]

Algebra Unit 5 HW Day 4 APPLICATION WP

1) A baseball manager bought 4 bats and 9 balls for $76.50. On another day, she bought 3 bats and 1 dozen balls at the same prices and paid $81.00. How much did she pay for each bat and each ball?

2) For 30 minutes you do a combination of walking and jogging. At the end of your workout, your pedometer displays a total of 2.5 miles. You know that you walk 0.05 mile per minute and jog 0.1 mile per minute. How much time were you walking? How much time were you jogging?

3) One admission to a roller skating rink costs x dollars and renting a pair of skates costs y dollars. A group pays $243 for admission for 36 people and 21 skate rentals. Another group pays $78 for admission for 11 people and 7 skate rentals. How much does it cost for admission?

4) The measure of the smaller of two supplementary angles is [pic] more than [pic] the measure of the larger angle. Find the degree of the measure of each angle.

REVIEW:

5. Write the equation of a line that has undefined slope and passes through the point (7, -6).

6. Write the equation of a line that has zero slope and passes through the point (-3, 4).

7. State whether the following numbers are rational or irrational:

a. [pic] ________ c. [pic] ________ e. [pic] ________

b. [pic] ________ d. ( ________ f. .47913 ________

8. MATCHING: Match the property to its illustration.

_______ (ab)c = a(bc) A. Multiplicative Identity

_______ x + y = y + x B. Multiplicative Inverse

_______ x + 0 = x C. Additive Identity

_______ x [pic] 1 = x D. Additive Inverse

_______ 7 + (-7) = 0 E. Commutative Property of Addition

_______ [pic] F. Associative Property of Multiplication

_______ 2(x + y) = 2x + 2y G. Distributive Property

Algebra Unit 5 HW DAY 5 SOLVING APPICATONS WP GRAPHICALLY

1)

a) The U-Drive-IT car rental agency rents cars for $50 a day with unlimited free mileage. Write an equation to show the cost of renting a car from U-Drive-IT for one day, y, if the car is driven for x miles.

b) The Safe Travel car rental agency rents cars for $30 a day plus $0.20 a mile. Write an equation to show the cost of renting a car from Safe Travel for one day, y, if the car is driven for x miles.

c) Draw, on the same set of axes, the graphs of the equations written in parts a and b.

d) If Greg drives the car he rents for 200 miles, which agency offers the less expensive car?

e) If Sarah drives the car he rents for 50 miles, which agency offers the less expensive car?

f) If Phillip finds the price that both agencies will be the same, how far is he planning on drive the car?

Algebra Unit 5 HW DAY 6 MONEY/PERCENT WP

1. Mrs. Mayor invested $1400, part at 5% and part at 8%. Her total annual income from her investment was $100. Find the amount she invested in both.

2. Mr. Daniels invested a sum of money in saving bonds yielding 6% a year and in a certificate of deposit (CD) yielding 4% a year. In all, he invested $4000. If his total annual income from his investments was $188, find the amount he invested in each rate.

3. At McDonald’s, four hamburgers and two orders of French fries cost $27.10. Three hamburgers and four orders of fries cost $25.20. If all hamburgers cost the same price and all orders of fries cost the same price, find the price of each.

4. Lisa and George went shopping at Price Buster. George bought 2 rolls of aluminum foil and 3 packages of batteries for a total cost of $21. Lisa bought 5 identical rolls of aluminum foil and 2 identical packages of batteries for a total cost of $25. Find the cost of each item.

5) Bill has 4 times as many quarters as dimes. In all, he has $2.20. How many coins of each type does he have?

ALGEBRA UNIT 5 HW DAY 7 SYSTEMS OF INEQUALITIES

1) [pic] 2) [pic]

3) [pic] 4) [pic]

5. Which equation represents the line that passes through the points (-3, 7) and (3, 3)

(1) [pic] (3) [pic]

(2) [pic] (4) [pic]

6. Which of the following does not represent a rational number?

(1) [pic] (3) [pic]

(2) [pic] (4) [pic]

7. Which equation below illustrates the associative property?

(1) [pic] (3) [pic]

(2) [pic] (4) [pic]

8. Which inequality is represented in the accompanying graph?

[pic]

(1) [pic] (3) [pic]

(2) [pic] (4) [pic]

Algebra Unit 5 HW DAY 8 APPLICATION WP

1) You are planning a cookout. You figure that you will need at least 5 packages of hot dogs and hamburgers. A package of hot dogs costs $1.90 and a package of hamburgers costs $5.20. You can spend a maximum of $20 on the hotdogs and hamburgers.

a) Let x represent the number of packages of hot dogs and let y represent the number of packages of hamburgers. Write a system of linear inequalities for the number of packages of each that can be bought.

b) Graph the system of inequalities.

c)Identify two possible combinations of packages of hot dogs and hamburgers they can buy.

2) Danielle needs at least 4 hours to do her chores, which include cleaning out the garage and weeding the flower beds around her house. It is 1:30 p.m. on Sunday and her friend wants to go to the movies at 7:00 p.m.

a) How much time does Danielle have between now and 7:00 p.m. to do her chores?

b) Let x represent the number of hours spent cleaning out the garage and let y represent the number of hours spent on weeding the flower beds. Write and graph a system of linear equalities that shows the number of hours Danielle can work on each chore if she is to go to the movies.

c) Identify two possible combinations of time she can spend on each chore.

3. Solve for x: [pic]

4. A wall is supported by a brace 10 feet long, as shown in the diagram below. If one end of the brace is placed 6 feet from the base of the wall, how many feet up the wall does the brace reach?

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[pic]

[pic]

[pic]

[pic]

[pic]

(1)

(2)

(3)

(4)

[pic]

(1)

(2)

(3)

(4)

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

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