Chapter 9 Answers

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Chapter 9 Answers

Practice 9-1

1. 1

2. 1.2

3. 50

4.

2 7

5. 4.2

6.

y

5

14 x

7.

y

5

36 x

8. y 5 22x4

9. y 5 23x0

10.

y

5

0.8 x

or y

5

4 5x

11.

y

5

8 x

12.

y

5

3 x

13.

y

5

6.3 x

or

y

5

63 10x

14.

y

5

2

0.3 x

or

y

5

2103x

15. I varies inversely with R.

16. A varies jointly with b and h. 17. h varies directly with V

and inversely with B. 18. V varies directly with the cube of r.

19.

4 3

20. -4

21. 2

22.

y

5

8 x

;

1

23. y 5 2x1 ; 218

24.

y

5

7.2 x

or

y

5

53x6 ; 0.9

25. z = 2xy; 48

26.

z

5

3x y3

;

9 32

27.

inverse; y

5

20 x

28. neither

29. direct; y = 6x 30. direct; y = 125x 31. neither

32.

inverse;

y

5

15 x

12.

y

; x = 2, y = -2

6

4

O

x

2 2 4 6

4 6

13.

y

; x = 0, y = 3

4 3 2

O

x

321 1 2 3

Practice 9-2

1.

y

5

2x

3 2

2

1

1

2.

y

5

2x

3 1

1

1

3

3.

y

5

2x

3 2

4

2

2

4. y 5 2x3 1 6

5.

y

5

2x

3 2

3

6.

y

5

2x

3 2

1

1

2

7.

y

5

2x

3 1

3

2

1

8.

y

5

2x

3 1

2

1

1

9.

y

; x = 1, y = 2

4

2O

x

642 2 2 4 6

4

6

10.

y

; x = -1, y = 0

O

x

6 2 2 4 6

4

11.

y

O

12963 3 6 9 12

; x = -3, y = -3

x

14.

y

; x = -1, y = -2

1O x

4321 1 1 2

2

3

4

5

15.

y

4

3

2

1

1 1 O 2

; x = 2, y = 1

x 2345

16.

y

2

1O

21 1 1 2

2

3

4

; x = 1, y = -1

x

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Algebra 2 Chapter 9

Answers

35

All rights reserved.

Chapter 9 Answers (continued)

17.

y

2

; x = 0, y = 0

2 O 2

2x

22.

y

6

4

2O

642 2 4

4

6

; x = 5, y = 0

x

18.

y

8

6

4

O

42 2 2 4

; x = 3, y = 1

x 68

23.

y

4

; x = 3, y = -2

O

x

2 2 4 6 8 4

6

8

19.

y

; x = -1, y = 2

4

2O

x

642 2 2 4 6

24.

y

; x = 0, y = 0

2

2 O 2

2x

20.

y

3

2

1O

321 1 2

; x = 0, y = 0.5

x

3

21.

y

; x = -3, y = -1

6

4

2O x

8642 2 2 4

4

6

25.

y

4

; x = 1, y = 1

3

2

1O

x

21 1 1 2 3 4

2

26.

y

2

; x = 0, y = 0

2 O 2

2x

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36

Answers

Algebra 2 Chapter 9

All rights reserved.

Chapter 9 Answers (continued)

27.

y

4

; x = 4, y = -2

2O

x

2 4 6 8 10 4 6 8

28.

y

3

2

; x = 2, y = -0.5

O

x

1 1 1 2 3 4 5

2

3

29. 2.25 ft 30. 412.5 Hz 31. 825 Hz 32. 165 Hz 33. $7.50 34. 324 keepsakes 35. $4.50 36. $36.00

Practice 9-3

1. -3, 4 2. 42 3. 2 4. 0, -2 5. -1 6. 0, 43 7. y = 0

8. y = 1

9.

y

5

1 2

10. y = 2

11. y = 0

12. y = 1.5

13.

y

6

4

2O

x

4 2 2 4 6 8

4

6

14.

y

6

4

2O

x

642 2 2 4 6

4

6

15.

y

6

4

2O

x

2 2 2 4 6 8 10

4

6

16.

y

9

6

3O

63 3

6

9

x 6 9 12

17.

y

6

18.

y

9

4

6

2O

3O

x

642 2 2 4 x

63 3 3 6 9 12

4

6

6

9

19.

y

20.

y

2

2 O 2

x 2

2

2 O 2

x 2

21.

y

2

2 O 2

x 2

22. vertical asymptote at x = -2; hole at x = 2

23. vertical asymptote at x = 1; hole at x = 0 24. vertical

asymptotes at x = 1 and x = -1 25. vertical asymptote at

x = -2 26. no vertical asymptotes or holes 27. vertical

asymptote at x = 3; hole at x = -3 28. vertical asymptote

at x = 4 29. vertical asymptotes at x 5 245 and x = 3

30. vertical asymptotes at x = 2 and x = -2

31a.

y

5

0.02x

1 x

3500,

where

x

=

number

of

pages;

31b. at least 2365 pages 31c. 3571 pages 31d. 7292 pages 31e. x = 0; y = 0.02

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Algebra 2 Chapter 9

Answers

37

All rights reserved.

Chapter 9 Answers (continued)

Practice 9-4

1.

2x

1 x

1;

x

2

0

2. 2; x 2 232

3. 3; y 2 1 or -1

4. 43; x 2 -5

5.

x x

1 1

12; x

2

0

or

-2

6. 53; x 2 -2

7.

y

2 1

6;

y

2

0

or

-6

8.

x

x 1

5;

x

2

5

or

-5

9.

x x

2 2

36; x

2

6

or

-6

10.

x x

1 2

87;

x

2

7

or

-5

11.

3x x

2 2

36 ;

x

2

3

or

-2

12.

4x x

2 1

12 7

;

x

2

-3

or

-7

13.

2x 3x

1 1

21;

x

2

-5

or

223

14.

2x x

21 13 ;

x

2

1

or

2 3

15.

x

7 1

4;

x

2

4

or

-4

16.

x

2 2

3; x

2

-3

17. 10; a 2 -1, 0 18. -1; x 2 225, 0, 43 19. x2 - 1; x 2 -4, 2 20. x + 3; x 2 -4, -3, -1

21.

7y 6y

2 1

28 24;

y

2

-5,

-4

22.

3x2 x

1 2

53x;

x

2

0,

45

5y2 1 10y 1 5 23. 36y 1 72 ; y 2 -2, -1

24.

3x 2 14

6; x

2

-1,

2

25.

y

y 2

2;

y

2

2,

49

26. 23; y 2 46

27.

y 5;

y

2

0,

47

28.

x x

1 2

22;

x

2

12,

2,

3, 5

29.

x2 x2

2 2

16 9

;

x

2

41, 43

30. 1; x 2 -3, 0, 5

31.

x2 x2

2 1

5x 5x

1 1

6; 6

x

2

-3,

-2

32. x1; x 2 0, 46 33. x + 8; x 2 -2, 48 34. y4; x, y 2 0

35.

4x

2 3x

16;

x

2

0,

13 ,

5,

44

36. 6xy3; x, y 2 0

37. 3x; x 2 0, -2 38. x3; x 2 -6, -4, 2

39.

x2 2 2x x2 1 14x

1 1

1 ;x 49

2

-7, -3, 4

40.

x2 x2

1 1

2x x

1 2

1; 2

x

2

-2,

41

Practice 9-5

1. 6x(x + 2)(2x - 3) 2. 6(x - 1)(x - 2)2(x + 10)

3. (2x + 3)2(2x - 3) 4. 10x(x + 3)2(x - 3)

6.

x2

1 2x 12

2

2

7.

3 xy3

8.

2 n

2 2

n 4

9. 2x9

5.

2x2 5

7y 1 5 3(3y 2 1) 12y 1 5x 10. 3y 11. y2 2 5 12. 10x2y2

3 2 2x2y2 13. 8x3y3

14.

(x

1

10x 2 26 5)(x 2 5)(x

1

1)

15.

9y 1 4x 21x2y2

16.

x2y x2 2

4

17.

x

3 1

2

18.

(x

2

(5x 1 1)(x 1 3) 3)(x 1 2)(x 1 5)(x

1

1)

19.

2(3x

2

7x 1 5 1)(2x 2 3)(2x

1

3)

2(x 1 2) 20. x(x 2 3)

21.

(x

1

4x 1 1 5)(x 1 1)(x

2

2)

22.

4x2

2 x

36x 29

1

3

23.

3x2 x2

1 1

14 5

24.

5x2 2 25x 1 31 x2 2 5x 1 6

25.

5x 3x

1 2

6 1

26.

5a2 a2

1 2

2a 4

27.

8c2 c2 2

9

28.

2 gh

29.

2t2

6t 2

25

30.

8r2 r2 2

4

x2 1 y2 31. x2 1 xy

32.

2y 3x

33.

x 4x

1 2

2 6

34.

2x2

x 2 3x

2

2

y22 35. 4y

36.

15 4

37. 2x + 3

38.

3x 5x

2 1

3 5

2y 1 6xy 39. x

3y(y 2 2) 40. (y 2 6)(y 1 2)(y 2 4)

41a.

24 17

ohms

41b.

4 3

ohms

Practice 9-6

1. 43

2. 44

3. 2141

4. 2197

5.

9 4

6. -2

7. -0.2

8. -0.5 9. 3 10. -2 11. 0 12. -17 13. 12 14. 6

15.

3 16

16. no solution

17. -9

18. 7

19. 11

20. 41

21. 5

22. -3

23. 0

24. 21295

25. -3

26. 18

27.

60 7

28. -5

29. no solution

30. 12

31. 4

32.

14 3

33. no solution 34. 6 35. -5 36. -1

37. about 13 mi/h tail wind 38. about 14 mi/h head wind

39. about 1.3 days 40. Tom: 125 min, Huck: 500 min

Practice 9-7

1. no 2. yes 3. yes 4. no 5. dependent 6. independent

7. independent 8. dependent 9. 20% 10a. 0.6 10b. 1

10c. 0.7

10d. 0.6

11a.

2 3

11b.

2 3

11c.

2 3

11d.

1 6

12. about 69.6%

13. 12.5%

14.

1 20

15. 0.16

16.

1 20

17.

11 12

18. 55%

19. 38%

Reteaching 9-1

1. 3.5 h 2. 5 h 3. about 28 items 4. 6.75 cm

Reteaching 9-2

1.

y

; x = 0, y = 0

6

4

2O

x

42 2 4 6

4 6

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38

Answers

Algebra 2 Chapter 9

All rights reserved.

Chapter 9 Answers (continued)

2.

y

; x = 0, y = 0

6

4

2O

x

642 2 4 6

4 6

3.

y

; x = 0, y = 0

3

2

1O

x

21 1 2 3

2 3

4.

y

; x = -4, y = 0

6

4

2O

8642 2 4 x

4 6

5. 8 y

; x = 8, y = 0

6

4

2O

x

2 2 4 6 8 10

4

6.

y

10

; x = 0, y = 3

8

6

4

2O

x

642 2 4 6

7.

Oy

x ; x = 0, y = -4

321 1 2 3

2 3

4 5 6

8. 86

y

; x = -3, y = -3

4

2O

2 2 4 x

4 6 8

9.

y

10

; x = 3, y = 4

8

6

4

2O

x

42 2 4 6 8

10.

y

4 O 4

8

; x = 2, y = -4 x 48

11.

y 4

;

x

=

0, y

=

3 2

2

2 O 2

x 2

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Algebra 2 Chapter 9

Answers

39

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