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Selected Answers and Solutions

connectED.mcgraw-hill.com SA1

Preparing for Integrated Math II

CHAPTER 0

CHCHAPAPTETERR 00

Pretest

1. cm 3. 48 5. 0.18 7.

1.13 9. 32 11. 170

13. 87 15.

5 _ 19 or about 26% 17. 12 _ 19 or about 63%

19. -12 21. -1 23. 12 25. 16 27. -13 29. -2

31. -
10 _ 3

33. 8 35. 38 37. {t|t 11} 39. {a|a 5}

41. {w|w > -12 43. {b|b 30} 45. (4, -2) 47. (-3, 5)

49 & 51.

Favorite Instrument

TrumpetPianoGuitarDrums

0

Number of Students

14 12 10 8 6 4 2

Instrument53.

-1, -3 2, 3 1, 1 0, -1 xO y

55. (0, -4) 57. no solution 59. in“ nitely many solutions

61.
5 _ 7 63.

12 + 3 5

_ 11

Lesson 0-1

1. cm 3. kg 5. mL 7. 10 9. 10,000

11. 0.18

13. 2.5 15. 24 17. 0.370 19. 4 21. 5 23. 16

25. 208 27. 9050

Lesson 0-2

1. 20 3. 12.1 5. 16 7. 12 9. 5.4 11.

22.47 13. 1.125 15. 5.4 17. 15 19. 21. 735.8 g

Lesson 0-3

1. 1 _ 3 or 33% 3. 2 _ 3 or 67% 5. 1 _ 3 or 33% 7. 13 _ 28
or about 46% 9. 11 _ 14 or about 79% 11. 9 _ 70
or about 13% 13. 9 _ 28
or about 32% 15. 1 _ 28
or about 3.6% 17. 13 _ 28
or about 46% 19. 13 _ 14 or about 93% 21. 1 _ 10 or 10%; 1 _ 8 or 12.5%

23. Sample answer: Assign each friend a different colored marble:

red, blue, or green. Place all the marbles in a bag and without looking, select a marble from the bag. Whoevers marble is chosen gets to go

“ rst.

Lesson 0-4

1. 3 3. -2 5. -1 7. -26 9. 26 11. 15

Lesson 0-5

1. -8 3. 15 5. -72 7. -

15 _ 2 9. 7 _ 2

11. -15 13. -7 15. -7 17. -1

19. 60 21. -4 23. 4

25. 15 27. 21 29. -2

31. -
29
_ 2

33. -6 35. 1

Lesson 0-6

1. {xx < 13} 3. {yy < 5} 5. {tt > -42} 7. {dd 4}

9. {kk -3} 11. {zz < -2} 13. {mm < 29}

15. {bb -16} 17. {zz > -2} 19. {bb 10}

21. {qq 2} 23.

ww - 7 _ 3

Lesson 0-7

1. {(Š15, 4), (Š18, Š8), (Š16.5, Š2), (Š15.25, 3)}

3. Ox y5. f -1 (x) = - 1 _ 2 x + 7 _ 2

7a. C

-1 (x) = 1 _ 70
x - 60
_ 7

7b. x is Dwaynes total cost, and C

-1 (x) is the number of games

Dwayne attended. 7c. 5

9. {(-49, -4), (35, 8), (-28, -1), (7, 4)}

11. {(7.4, -3), (4, -1), (0.6, 1), (-2.8, 3), (-6.2, 5)}

SA01_SA82_IM2_T_EM_SA_663851.indd SA1SA01_SA82_IM2_T_EM_SA_663851.indd SA111/15/12 5:33 PM11/15/12 5:33 PM

SA2 | Selected Answers

41. Sometimes; sample answer: f (x ) and g (x ) do not need to be

inverse functions for f (a) = b and g(b) = a. For example, if f (x ) = 2x + 10, then f (2) = 14 and if g (x ) = x - 12, then g (14) = 2, but f (x ) and g(x ) are not inverse functions. However, if f (x ) and g (x ) are inverse functions, then f (a) = b and g (b) = a.

43. Sample answer: A situation may require substituting values for

the dependent variable into a function. By “ nding the inverse of the function, the dependent variable becomes the independent variable. This makes the substitution an easier process.

Lesson 0-8

1. (-2, 3) 3. (2, 2) 5. (-3, 1) 7. (4, 1) 9. (-1, -1)

11. (3, 0) 13. (2, -4) 15. (-4, 2) 17. none 19. IV

21. I 23. III

x 1- 3 5 y 25.
x 1, -1 4, 2 1, 5 -2, 2 y 27.
x -1, -2 2, 4 0, 0 1, 2 y 29.
x 2, 5 1, 2 -1, -4 0, -1 y

Lesson 0-9

1. (2, 0) 3. no solution 5. (2, -5) 7.

4 _ 3 , 3

9. (4, 1)

11. elimination, no solution 13. elimination or substitution,

(3, 0) 15. elimination or substitution, (-6, 4) 13. Ox y

15. f

-1 (x) = -3x + 51 17. f -1 (x) = - 1 _ 6 x + 2

19. f

-1 (x) = - 3 _ 4 x - 12

21a. C

-1 (x) = 1 _ 35
x Š 2 _ 7

21b. x is the total amount collected from the Fosters, and C

-1 (x) is the number of times Chuck mowed the Fosters lawn. 21c. 22

23. f

-1 (x) = 15 - 5x

25. f

-1 (x) = 3 _ 2 x + 12

27. f

-1 (x) = 3x - 3 29. B 31. A

33. f

-1 (x) = 3 _ 2 x - 12 35. f -1 (x) = 1 _ 4 x + 3 _ 4

37a. A(x) = 8(x Š 3) or A(x) = 8x Š 24

37b.
Ox A x 32
16

Š16

2468
A x Sample answer: The domain represents possible values of x. The range represents the area of the rectangle and must be positive. This means that the domain of A(x) is all real numbers greater than 3, and the range of A(x) is all positive real numbers.

37c. A

-1 (x) = 1 _ 8 x + 3; x is the area of the rectangle and A -1 (x) is the value of x in the expression for the length of the side of the rectangle x Š 3. 37d.
Ox A -1 x -16 2 4 6 8 16 32 A -1 x Sample answer: The domain represents the area of the rectangle and must be positive. The range represents possible values for x in the expression x - 3. This means that the domain of A -1 (x ) is all positive real numbers, and the range of A -1 (x ) is all real numbers greater than 3.

37e. Sample answer: The domain of A(x) is the range of A

Š1 (x), and the range of A(x) is the domain of A Š1 (x).

39. a = 2; b = 14

Selected Answers and Solutions

SA01_SA82_IM2_T_EM_SA_663851.indd SA2SA01_SA82_IM2_T_EM_SA_663851.indd SA211/12/12 2:38 PM11/12/12 2:38 PM

SA3 connectED.mcgraw-hill.com

Lesson 0-10

1. 4 2 3. 10 5 5. 6 7. 7x y 3 2x 9. 9 _ 7 11.

3 14

_ 4 13. p 30p _ 9 15.

20 + 8 3

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