Mscc8rb RBC Ans a - birmingham.k12.mi.us

Answers

5.

y

4

3

2

1

-4 -3 -2 O 1

-2 -3 -4

6.

y

16

3 4x

12 10

8 6 4 2

-2 2 4 6 8 10 12 14 x

4.7 Start Thinking!

For use before Lesson 4.7

Sample answer: If you need to write the equation of a line given the slope and a point on the line, you can find the y-intercept (either graphically or algebraically). Then you follow the steps for writing an equation given the slope and y-intercept.

4.7 Warm Up

For use before Lesson 4.7

1. y = 2x - 1

2. y = - x + 1

3.

y

=

-

1 2

x

-

2

4.

y

=

2 3

x

-1

4.7 Practice A 1. y = 3x + 4

2.

y

=

-

2 3

x

+

2

3.

y+

2

=

1 4

(x

-

4)

4.

y-5

=

-

4 3

(

x

+

3)

5. y - 2 = -(x - 2) 6. y + 5 = 4(x + 1)

7.

y

=

1 3

x

-

3

9. y = -2x - 4

8.

y

=

-

5 2

x

+

2

10. y = 5x + 1

11. a. V = -150x + 900 b. $900 c. $150

4.7 Practice B

1.

y

=

5x 4

-

2

3. y - 3 = 13(x + 6)

2. y = -4x + 3

4.

y+7

=

-

3 4

(

x

-

8)

5. y + 5 = 2(x + 1)

6. y - 8 = -3(x + 2)

7. y = 4x - 5

9.

y

=

-

1 3

x

+

2

8.

y

=

4 5

x

-

4

10.

y

=

5 2

x

-1

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11. a. y = - 2x + 24 b. 24 feet c. after 12 seconds

4.7 Enrichment and Extension 1. The slope is the negative of the grade, written as a

fraction or decimal.

2.

Bunny

Slope:

-

1, 25

Medium Trail:

-

3 20

,

Expert Trail:

3 - 10

3. y

=

-

1 25

x

+

58

4. 58; The starting height of the trail is 58 meters.

5. 1450; The length of the trail is 1450 meters.

6.

y

=

-

3x 20

+

1530

7. y = -130 x + 6000

8. no; It has a grade of 8%.

4.7 Puzzle Time THE TEAM SPIRIT

Technology Connection 1. 1.5

2. a. -1.5

b. The sign changed.

c. Sample answer: Visualize the points and determine whether the slope should be positive or negative to check your answer.

3. a. 0.667

b. The are reciprocals.

c. Sample answer: Compare the change in y to the change in x to determine whether the slope is steeper (magnitude greater than 1) or shallower (magnitude less than 1) to check your answer.

4. -0.57 5. 3.33

6. 0

7. 5

Chapter 5

5.1 Start Thinking!

For use before Activity 5.1

The only solution is (3, 2). Methods may vary. Sample answer: Trial and error, to find two numbers where one number is 1 greater than the other and whose sum is 5. Other methods are substitution and graphing.

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5.1 Warm Up

For use before Activity 5.1

1.

y

1

-2 O 1 2 4 x

-3 -4 -5

2.

y

5

4

2 1

x -2 O 1 2 3 4

3.

y

3

1

-2 O -2 -3

2 3 4x

4.

y

-2 O 1

-2 -3 -4 -5 -6

3 4x

5.

y

1

x

O 1234

-2 -3

-5

6.

y

4 3 2 1

O 1 2 3 4 5x

5.1 Start Thinking!

For use before Lesson 5.1

The solution is (?1, ?4). Sample answer: It's easier to see from the graph since you can see where the two lines intersect. With the table, you have to look at all of the values to see the ones in which the y-values are equal. In general, a graph is easier to use than a table because the solution may be excluded from the table.

5.1 Warm Up

For use before Lesson 5.1

1. (2, 130)

2. (5, 80)

3. (4, 180)

4. (3, 45)

5. (6, 72)

6. (4, 50)

5.1 Practice A

1. B

2. A

4. (-2, 2)

5. (2, -5)

7. a. R = 34x b. 6 bracelets

8. a. x + y = 21 x = y+3

b. 12 pens, 9 pencils

5.1 Practice B

1. (3, 15)

2. (-2, -13)

4. a. R = 16x b. 250 tickets

3. C

6. (5, -6)

3. (8, -2)

A26

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5. (4, 7)

6. (1, -2)

7. (-3, 0)

8. x + y = 60 x = 2y

40 one-bedroom apartments, 20 two-bedroom apartments

9. yes; The two lines could be parallel.

10. a. 25 min b. 50 min c. the tortoise

5.1 Enrichment and Extension

The solutions of the systems reading across are:

(0,

0);

(3,

4);

(- 7,

13);

2, 3

13 3

;

(- 2,

2);

(4,

6);

(5,

- 2);

(2,

2);

-

1 7

,

8 7

;

no

solution;

(1,

3);

(3,

0)

5.1 Puzzle Time

THE TEACHER TOLD HIM IT WAS A PIECE OF CAKE

5.2 Start Thinking!

For use before Activity 5.2

A = 3 + (2 + 0.5A)

A = 5 + 0.5A 0.5A = 5

2(0.5A) = 2(5)

A = 10

C = 2 + 0.5(10) = 2 + 5 = 7

Amelia is 10 and Caleb is 7.

5.2 Warm Up

For use before Activity 5.2

1. y = -2x + 5

2. b = a - 3

3. x = 5y - 12

4.

c

=

7d 3

+

4

5.

y

=

-

4 3

x

+

8

6.

x

=

-

3 2

y

+

2

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5.2 Start Thinking!

For use before Lesson 5.2

Check students' solutions. The solutions are (1, 3) and (?4, 1). The second system is easier to solve by graphing because the equations are in a form that is easy to graph. Also solving it by substitution involves fraction operations, which can be tricky. The first system is easier to solve by substitution. Graphing the second equation in the first system can be tough because the y-intercept is 3.6.

5.2 Warm Up

For use before Lesson 5.2

For Exercises 1?6, answers will vary. Sample answers are given.

1. x + y = 2

2. y = x + 1

x= y

2x - 3 = y

3. x = 3y 2x - y = 10

4. y = 2x x+y =6

5. x + y = 11 x - y = -1

6. 2x + y = 7 x = 3y

5.2 Practice A 1. y = 5x - 2; It is already solved for y.

2. 3x - 12 y = 6; Every term is divisible by 3, so you can easily solve for x.

3.

1 5

x

+

y

=

8;

Can easily solve for y.

4. (2, 5)

5. (-3, -10) 6. (17, 3)

7. a. x + y = 25 y = x+7

b. 9 treadmills c. 16 stationary bikes

8. (7, -2)

9. (5, 5)

11. a. x + y = 24 x = 3y

b. 18 spoons c. 6 forks

12. 2x + 2 y = 34 y = 2x + 2 length: 12 cm; width: 5 cm

13. 42 cars; 18 trucks

10.

0,

-

1 3

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5.2 Practice B

1. (-5, 1)

2. (3, -2)

4. a. 208x + 52 y = 5460 y = x + 10

b. $19 c. $29

3.

4,

1 2

5. (7, 8)

6. (-6, 2)

7.

3 2

,

1

8. 83

9. a. x + y = 98 5x = 9y

b. 63 food tents c. 35 retail tents

10. a. 9 two-year-olds b. 18 three-year-olds c. 18 four-year-olds

5.2 Enrichment and Extension 1. Sample answer: y = x, y = 2x

2. y = 2x, x = -2

3. Sample answer: y = x, y = 6

4. y = - x + 12, x = -2

5. Sample answer: y = - x + 6, y = 2x

6. y = x, y = - x + 6

7. x = -2, y = x + 2

8. y = - x + 12, y = x + 2

9. y = x + 2, x = 1

10. y = 2x, y = - x + 12

11. y = 3x + 4, y = 4x + 1

12. Sample answer: y = - x + 6, y = 4x + 1

13. Sample answer: x + 2 y = -16 y = x + 172

5.2 Puzzle Time IN A POLE VAULT

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5.3 Start Thinking!

For use before Activity 5.3

Operation 1: 3 + 7 = 10 2+4= 6 1+ 3= 4

Operation 2: 6 + 14 = 20 2+ 4= 6 8 + 18 = 26

Yes, after completing the operations, the statements are true. You can use the method of adding the equations together to solve the system:

x + y = 10 x-y= 4 2x = 14 x =7

x = 7, so 7 + y = 10, and y = 3.

The solution of the system is (7, 3).

5.3 Warm Up

For use before Activity 5.3

1. y = 15

2. x = -6

3. x = -16

4. y = 19

5. x = - 4

6. y = 7

5.3 Start Thinking!

For use before Lesson 5.3

Both students used elimination to correctly solve the system. Maddie multiplied the second equation by ?2, added the new equation to the first equation, and solved for y. Sophie multiplied the second equation by ?3, added the new equation to the first equation, and solved for x. Each student used substitution to correctly solve for the second variable.

5.3 Warm Up

For use before Lesson 5.3

1. (8.5, 1.5)

2. (-6, 7)

3. (8.5, 1)

4. (1, -8)

5.3 Practice A

1. (3, -1)

2. (2, 1)

3. (3, 5)

4. a. 5x + 2 y = 9 5x + 6 y = 17

b. $1 per pound c. $2 per pound

5. (-4, 2)

6. (1, 0)

7. (-2, -3)

A28

Big Ideas Math Blue Answers

8. a. x + y = 20 3x + 8y = 100

b. 12 multiple choice c. 8 short response d. 4 multiple choice, 11 short response

9. a. yes

b. You added the equations instead of subtracting them.

5.3 Practice B

1. (0, 0)

2. (-5, -2)

3. (8, 3)

4. a. x + y = 42 x = y-8

b. 17 magazine subscriptions c. 25 magazine subscriptions

5. (6, -3)

6. (-1, 1)

7. (-3, -3)

8. a. Sample answer: a = -5 b. Sample answer: b = 4

9. $390 10. a. a = -3 b. b = -1 c. c = 1

5.3 Enrichment and Extension

1. Sample answer: It is best to use graphing when both equations are in a form that is easy to graph and the solution has integer values. It is best to use substitution when one or both of the equations are already solved for one of the variables. It is best to use elimination if it is difficult to solve for one of the variables in one of the equations.

2. Sample answer: The advantage to graphing is that you can visualize the solution and how the lines intersect. The disadvantages are that it can take more time to graph, and if the answer is not at a point where the grid squares cross, you cannot find the solution by graphing.

The advantage to substitution is that you can always find the correct answer. The disadvantage is that sometimes solving for one of the variables is tricky, especially if it involves a lot of fractions.

The advantage to elimination is that you can always use the method. It is quicker than the other methods if the equations are hard to solve for one of the variables. The disadvantage is that there are often more steps, thus more places to make calculation errors.

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Answers

3. Sample answer: I prefer elimination because it works in all situations and I don't have to bother to solve one of the equations for one of the variables.

4. graphing; (-1, 3)

5. elimination; (4, 6)

6. substitution; (-2, 18) 7. graphing; (3, 3)

8. elimination; (-3, 4) 9. elimination; (-3, -7)

10. substitution; (-7, -4) 11. substitution; (0, 1)

5.3 Puzzle Time

SECOND BASE TO THIRD BASE BECAUSE THERE IS A SHORTSTOP

5.4 Start Thinking!

For use before Activity 5.4

Sample answer: No, a pair of numbers cannot add up to two different numbers. The system has no solution. Another system with no solution is: y = 2x - 6

y = 2x + 1

5.4 Warm Up

For use before Activity 5.4

1. parallel

2. coincide

3. intersect at one point 4. coinside

5. intersect at one point 6. parallel

5.4 Start Thinking!

For use before Lesson 5.4

Sample answer: In both instances with no solution, you go through all of the steps of solving and end up with a false statement, such 10 = 6. The two processes are different because solving a system first involves eliminating one of the variables to get an equation in one variable. In solving an equation with a solution of all real numbers or solving a system with infinitely many solutions, you go through all of the steps of solving and end up with a statement that is always true, such as 3 = 3. The two processes are different because solving a system first involves eliminating one of the variables to get an equation in one variable.

5.4 Warm Up

For use before Lesson 5.4

1. no solution

2. x = -0.5, y = 2.5

3. x = 10, y = 0

4. no solution

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5.4 Practice A 1. infinitely many solutions; The lines are identical.

2. no solution; The lines have the same slope and different y-intercepts.

3. one solution; The lines have different slopes.

4. no solution

5. (3, -7)

6. infinitely many solutions

7. no

8. a. yes; If the slopes are different, then the y-intercept is the one solution.

b. no; The y-intercept is a solution to the system.

c. yes; If both equations have the same slope, then they are the same line.

9. There is no such two-digit number. The system has no solution.

10. a = 18, b = 6

5.4 Practice B

1. no solution 2. (-3, 5)

3. no solution

4. infinitely many solutions

5. (0, 0)

6. infinitely many solutions

7. infinitely many solutions

8. Yes, if the y-intercepts are the same. If the y-intercepts are different, then the system has no solution.

9. a. y = 4x + 13 y = 4x

b. no; The system has no solution.

10. Sample answer: x+y =3 2x + 2y = 6

11. Sample answer: 2x - y = 3 x+ y =3

12. Sample answer: y = 3x + 2 y = 3x - 5

13. a = 15, b is any number except 3.

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5.4 Enrichment and Extension

1. a = 1, b = -1

2.

a

=

1, b 2

=

- 2

3. a = -1, b = 6

4. a = 1, b = 2

5. a = 3, b is any number except 1.

6.

a

=

1 3

,

b

=

3

7. a = - 2, b = 11

8. a = 12, b = - 4

9. Check students' work.

5.4 Puzzle Time PAY HIM

Extension 5.4 Start Thinking!

For use before Extension 5.4

Sample answer: The graph shows the linear equations related to each side of the equation. The x-coordinate of the point of intersection is the solution of the equation.

Extension 5.4 Warm Up

For use before Extension 5.4

1. m = -8

2. x = 6

3. p = 3

4. x = 7

5. r = 3

6. x = -5

Extension 5.4 Practice 1. x = 4 2. x = -3 3. x = 1

4. x = -1

5. no; You cannot have -38 CDs.

6. x = 8

7. x = -2.5

8. no; The graph of the system y = 50 - 6x and y = 75 - 6x is a pair of parallel lines.

9. a.

1x 3

=

x

- 20

b. $30 c. $10

d. Sample answer: the cost of the lemonade

Technology Connection

1. (3, 7)

2. (2.5, -3)

3. (-1, 0)

4. (-12, -4)

Chapter 6

6.1 Start Thinking!

For use before Activity 6.1

Answers will vary depending on the cost of milk. For example, if one milk costs $0.25, then the entries in the mapping diagram would be $0.25, $0.50, $0.75, and $1.00. A mapping diagram maps one value to another.

6.1 Warm Up

For use before Activity 6.1

1. x = 11.4

2.

x

=

- 11

1 4

3. x = 7.34

4.

x

=

-

7

1 4

5.

x

=

-

26

1 4

6.

x

=

-

3 5

6.1 Start Thinking!

For use before Lesson 6.1

The output is 15. Observe students playing the Guess the Function Game.

6.1 Warm Up

For use before Lesson 6.1

1. Add 4; missing entries are 8, 9, and 10.

2. Multiply by 5; missing entries are 20, 25, and 30.

6.1 Practice A 1. As each input increases by 1, the output increases

by 3.

Input Output

1

3

2

6

3

9

4

12

5

15

6

18

2. As each input increases by 1, the output increases by 2.

Input Output

1

-2

2

0

3

2

4

4

5

6

6

8

A30

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