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1010 Student Resources

Chapter 1 1.1 Graph the numbers on a number line.

1. 22, 5 } 3

, 0.2, 2 Ï}

2 , 2 5 } 4

2. 2 4 } 3

, 1, 21.2, Ï}

3 , 1.9 3. 3.7, 2 Ï}

7 , 2 1 } 2

, 4, Ï}

15

1.1 Perform the indicated conversion.

4. 18 feet to inches 5. 20 ounces to pounds 6. 3 years to hours

1.2 Evaluate the expression for the given value of the variable.

7. 22p 1 5 when p 5 25 8. 3x2 2 x 1 7 when x 5 21 9. 8z3 2 6z when z 5 2

1.2 Simplify the expression.

10. 2y2 2 3y 1 5y2 11. 4r2 2 5r 1 2r2 1 12 12. 2w3 1 w2 2 7w2 2 8w3

13. 2(b 1 5) 1 3(2b 2 10) 14. 27(t2 1 2) 1 9(t 2 2) 15. 4(m 2 3) 2 5(m2 2 m)

1.3 Solve the equation. Check your solution.

16. 3a 1 2 5 11 17. 29 5 b 2 14 18. 8 2 0.5c 5 1

19. 23n 2 7 5 2n 1 17 20. 12m 5 15m 2 7.5 21. 6p 1 1 5 21 2 4p

22. 6(x 1 1) 5 2x 2 10 23. 4(y 2 3) 5 2(y 1 8) 24. 11(z 2 5) 5 2(z 1 6) 2 13

1.4 Solve the equation for y. Then find the value of y for the given value of x.

25. 6y 2 x 5 18; x 5 2 26. 2x 1 3y 5 12; x 5 26 27. 4y 2 9x 5 230; x 5 6

28. 3x 2 xy 5 20; x 5 8 29. 4y 1 6xy 5 10; x 5 22 30. 5x 1 8y 1 4xy 5 0; x 5 21

1.5 Look for a pattern in the table. Then write an equation that represents the table.

31. x 0 1 2 3

y 25 22 19 16

32. x 0 1 2 3

y 1.5 4 6.5 9

1.6 Solve the inequality. Then graph the solution.

33. x 1 2 > 9 34. 213 2 3x < 11 35. 4x 2 9 ≤ 2x 1 1

36. 23x 2 8 ≥ 29x 1 10 37. 27 < x 1 3 ≤ 1 38. 24 ≤ 3x 2 7 ≤ 4

39. 29 ≤ 5 2 2x < 7 40. x 1 3 < 22 or x 2 7 > 0 41. 2x 1 9 ≥ 3 or 25x 1 1 ≤ 0

1.7 Solve the equation. Check for extraneous solutions.

42. g 1 5 5 4 43. 1 } 3

q 2 2 } 3

5 1 44. 10 2 3t 5 t 1 4 45. 3z 1 1 5 26z

1.7 Solve the inequality. Then graph the solution.

46. a < 2 47. 2c > 14 48. g 1 11 ≥ 2 49. 4j 2 7 ≤ 9

50. 0.25m 1 3 ≥ 1 51. 10 2 2p > 9 52. 0.6r 1 8 ≤ 17 53. 5t 2 9 1 9 < 10

n2pe-9030.indd 1010n2pe-9030.indd 1010 10/17/05 12:26:30 PM10/17/05 12:26:30 PM

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Extra Practice 1011

Chapter 22.1 Tell whether the relation is a function. Explain.

1.

21

2

3

5

1

2

3

4

Input Output 2.

21

21

0

1

2

Input Output 3.

3

6

9

12

22

Input Output 4.

14

8

28

4

27

4

6

Input Output

2.2 Find the slope of the line passing through the given points. Then tell whether the line rises, falls, is horizontal, or is vertical.

5. (23, 0), (5, 24) 6. (2, 21), (8, 21) 7. (3, 5), (3, 212) 8. (1, 8), (21, 24)

2.2 Tell whether the lines are parallel, perpendicular, or neither.

9. Line 1: through (5, 24) and (24, 2) 10. Line 1: through (0, 24) and (22, 2)Line 2: through (25, 24) and (22, 22) Line 2: through (4, 23) and (5, 26)

2.3 Graph the equation using any method.

11. y 5 2x 2 2 12. y 5 2x 1 2 13. f(x) 5 2 } 3

x 2 1 14. x 1 2y 5 26

15. 24x 1 5y 5 10 16. y 2 2 5 0 17. 22x 5 6y 1 5 18. 2y 1 10 5 22.5x

2.4 Write an equation of the line that satisfies the given conditions.

19. m 5 7, b 5 23 20. m 5 1 } 3

, b 5 4

21. m 5 0, passes through (7, 22) 22. m 5 2 1 } 4

, passes through (3, 6)

23. passes through (21, 23) and (2, 7) 24. passes through (4, 22) and (0, 4)

2.5 The variables x and y vary directly. Write an equation that relates x and y. Then find y when x 5 22.

25. x 5 2, y 5 4 26. x 5 21, y 5 3 27. x 5 228, y 5 27 28. x 5 6, y 5 24

2.6 In Exercises 29 and 30, (a) draw a scatter plot of the data, (b) approximate the best-fitting line, and (c) estimate y when x 5 12.

29. x 1 2 3 4 5

y 8 11 13 16 18

30. x 1 2 3 4 5

y 50 41 37 22 20

2.7 Graph the function. Compare the graph with the graph of y 5 x.

31. y 5 x 1 3 32. y 5 22x 2 5 33. y 5 3x 1 1 2 2 34. y 5 2 1 } 2

x 1 2 1 3

2.8 Graph the inequality in a coordinate plane.

35. x < 4 36. y ≥ 22 37. y ≤ 2x 2 1 38. x 1 2y > 8

39. 2x 2 4y ≤ 6 40. 3x 1 4y > 12 41. y < x 1 1 42. y ≥ 3x 2 2 2 1


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Chapter 33.1 Graph the linear system and estimate the solution. Then check the solution

algebraically.

1. y 5 2x 2 1 2. y 5 2x 1 3 3. x 1 2y 5 6 4. 22x 1 7y 5 27y 5 x 2 4 y 5 24x 25x 1 6y 5 22 4x 2 14y 5 14

3.2 Solve the system using any algebraic method.

5. 25x 2 y 5 23 6. 4x 2 2y 5 26 7. 4x 1 3y 5 25 8. 3x 1 2y 5 4x 2 4y 5 9 23x 1 y 5 23 12x 1 4y 5 10 27x 2 5y 5 27

3.3 Graph the system of inequalities.

9. x > 4 10. x 1 y < 22 11. x ≤ 5 12. x > 23y ≥ 21 x 2 3y > 6 y > 3 x ≤ 2 y > x 2x 1 3y < 10

y > 24x

3.4 Solve the system using any algebraic method.

13. 3x 1 y 2 z 5 26 14. x 1 y 2 z 5 7 15. 2x 1 y 2 2z 5 1.5 16. 26x 1 y 1 9z 5 42x 1 2y 1 3z 5 21 2x 2 3y 1 z 5 2 4x 2 y 1 5z 5 26 2x 2 3y 2 z 5 265x 2 2y 1 6z 5 54 4x 1 2y 2 2z 5 20 2x 1 y 2 2z 5 6 8x 1 5y 2 4z 5 10

3.5 Perform the indicated operation.

17. F 26 7 0 3G 1 F 26 2

28 1G 18. 2 2 } 3 F 29 3

4 21G 19. F 10 17 29 26 4 11G 2 F 26 8 22 24 29 4G

3.6 Find the product. If the product is not defined, state the reason.

20. F 4 1 23 0GF 27 5

7 23G 21. F2162GF 4

15G 22. F 5 21 0 4 22 9GF12

273G

3.7 Evaluate the determinant of the matrix.

23. F 5 8 22 10G 24. F 13 7

211 24G 25. F 1 23 22 7 4 0 27 2 3

G 26. F 6 0 5 24 2 1 1 0 0.5

G 3.7 Use Cramer’s rule to solve the linear system.

27. 2x 1 y 5 28 28. 8x 1 3y 5 1 29. 2x 2 2y 2 3z 5 9 30. 2x 1 y 1 3z 5 425x 2 2y 5 13 7x 1 3y 5 21 3x 1 z 5 10 28x 1 4y 1 z 5 27 x 1 y 5 0 x 1 2y 1 3z 5 21

3.8 Find the inverse of the matrix.

31. F3 73 8G 32. F1 4

0 5G 33. F 22 25 3 8G 34. F 9 2

18 5G 3.8 Use an inverse matrix to solve the linear system.

35. x 1 3y 5 24 36. 2x 1 3y 5 6 37. 3x 2 8y 5 0 38. x 1 y 5 722x 1 y 5 234 2x 2 6y 5 29 2x 1 y 5 219 25x 1 3y 5 23


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Extra Practice 1013

Chapter 44.1 Graph the function. Label the vertex and axis of symmetry.

1. y 5 3x2 1 5 2. y 5 2x2 2 4x 2 4 3. y 5 22x2 1 4x 1 1 4. y 5 2x2 1 5x 1 6

4.2 Graph the function. Label the vertex and axis of symmetry.

5. y 5 4(x 2 2)2 1 1 6. y 5 2(x 1 3)2 2 2 7. y 5 3(x 2 1)(x 2 5) 8. y 5 1 } 2

(x 1 3)(x 1 2)

4.2 Write the quadratic function in standard form.

9. y 5 7(x 1 2)(x 1 4) 10. y 5 2(x 1 5)(x 2 3) 11. y 5 (x 2 7)2 1 7 12. y 5 2(x 1 1)2 2 4

4.3 Factor the expression. If the expression cannot be factored, say so.

13. x2 2 4x 1 4 14. t2 2 11t 2 26 15. x2 1 21x 1 108 16. b2 2 400

4.3 Solve the equation.

17. x2 1 5x 2 14 5 0 18. x2 2 11x 1 24 5 0 19. c2 1 6c 5 55 20. n2 5 5n

4.4 Factor the expression. If the expression cannot be factored, say so.

21. 2x2 1 x 2 15 22. 10a2 2 19a 1 7 23. 3r2 1 9r 2 4 24. 4t 2 1 8t 1 3

4.4 Find the zeros of the function by rewriting the function in intercept form.

25. y 5 81x2 2 16 26. y 5 2x2 2 9x 2 5 27. y 5 4x2 1 18x 1 18 28. y 5 23x2 2 30x 2 27


29. Ï}

56 30. 3 Ï}

2 p Ï}

50 31. Î}

4 } 7

32. 6 } 1 1 Ï

}

2

4.5 Solve the equation.

33. b2 5 8 34. p2 1 6 5 127 35. (x 2 5)2 5 10 36. 3(x 1 2)2 2 4 5 11

4.6 Write the expression as a complex number in standard form.

37. (5 1 2i) 1 (6 2 5i) 38. 23i(7 1 i) 39. 1 1 2i } 3 2 8i

40. (3 2 2i) 1 2i

} (21 1 7i) 2 (2 1 3i)

4.7 Solve the equation by completing the square.

41. x2 1 6x 5 10 42. x2 2 9x 2 2 5 0 43. 2c2 2 12c 1 6 5 0 44. 3z2 2 3z 1 9 5 0

4.8 Use the quadratic formula to solve the equation.

45. x2 1 10x 2 10 5 0 46. x2 2 x 2 1 5 0 47. 4s2 1 3s 5 12 48. 22r2 5 r 1 17

4.9 Solve the inequality using any method.

49. x2 2 10x ≥ 0 50. x2 2 8x 1 12 < 0 51. 2x2 1 7x 1 6 > 1 52. 3x2 1 16x 1 2 ≤ 3x

4.10 Write a quadratic function in standard form for the parabola that passes through the given points.

53. (21, 26), (0, 27), (2, 9) 54. (22, 21), (1, 2), (3, 26) 55. (23, 36), (0, 36), (2, 16)


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Chapter 55.1 Write the answer in scientific notation.

1. (3.4 3 103)(2.8 3 108) 2. (5.8 3 1026)4 3. 4.6 3 1027 }

9.2 3 1029

5.1 Simplify the expression. Tell which properties of exponents you used.

4. 214x23y 5

} 35xy 3

5. (4a5b22)23 6. (2r3s3)(r27s5) 7. xy21

} x2y

p 7x3 }

y24

5.2 Graph the polynomial function.

8. f(x) 5 x4 9. f(x) 5 x3 1 x 1 4 10. f(x) 5 2x3 1 3x 11. f(x) 5 x5 1 2x3

5.3 Perform the indicated operation.

12. (4z3 1 9) 1 (3z2 2 4z 2 2) 13. (x2 1 3x 2 1) 2 (4x2 1 7) 14. (3x 2 4)3

5.4 Factor the polynomial completely using any method.

15. 3x4 1 18x3 1 27x2 16. 343x3 1 1000 17. 2x3 1 x2 2 8x 2 4

5.4 Find the real-number solutions of the equation.

18. 3x3 1 18x2 5 48x 19. x4 1 32 5 14x2 20. 2x3 1 48 5 3x2 1 32x

5.5 Divide using polynomial long division or synthetic division.

21. (2x3 1 4x2 2 5x 1 16) 4 (x 2 3) 22. (x4 1 2x3 2 7x2 2 14) 4 (x 1 2)

5.6 Find all real zeros of the function.

23. f(x) 5 2x3 1 3x2 2 8x 1 3 24. f(x) 5 2x4 1 x3 2 53x2 2 14x 1 20

5.7 Determine the possible numbers of positive real zeros, negative real zeros, and imaginary zeros of the function.

25. f(x) 5 2x3 1 2x2 2 11x 2 1 26. f(x) 5 4x5 1 3x2 2 8x 2 10 27. f(x) 5 x4 2 3x3 2 7x 2 13

5.8 Estimate the coordinates of each turning point and state whether each corresponds to a local maximum or a local minimum. Then estimate all real zeros and determine the least degree the function can have.

28.

x

y

1

1 29.

x

y

1

1 30.

x

y

3

1

5.9 Use finite differences and a system of equations to find a polynomial function that fits the data in the table.

31. x 1 2 3 4 5 6

y 2.5 11 27.5 55 96.5 155

32. x 1 2 3 4 5 6

y 27 26 39 188 525 1158


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Extra Practice 1015

Chapter 66.1 Find the indicated real nth root(s) of a.

1. n 5 4, a 5 81 2. n 5 3, a 5 512 3. n 5 5, a 5 2243

6.1 Evaluate the expression without using a calculator.

4. 3621/2 5. 645/6 6. ( 3 Ï}

216 )22 7. (

5 Ï}

232 )4

6.1 Solve the equation. Round the result to two decimal places when appropriate.

8. x3 5 28 9. x4 1 9 5 90 10. (x 2 3)5 5 60 11. 24x6 5 2400


12. 45/2 p 421/2 13. 173/7 }

174/7 14. (

4 Ï}

5 p Ï}

5 )4 15.

3 Ï}

135 } 3 Ï}

5

16. 5 5 Ï}

7 2 7 5 Ï}

7 17. 3 Ï}

2 1 2 3 Ï}

128 18. 3241/4 }

421/4 19. 4

3 Ï}

108 p 2 3 Ï}

4

6.2 Write the expression in simplest form. Assume all variables are positive.

20. Ï}

20x6y7 21. 5 Ï}

18x3y14z20 22. 4 Î}

x5 }

y16 23.

3 Ï}

16x7y2 p 3 Ï}

6xy5

6.3 Let f(x) 5 2x 1 4, g(x) 5 x3, and h(x) 5 x } 4

. Perform the indicated operation and

state the domain.

24. f(x) 1 g(x) 25. g(x) 2 f(x) 26. g(x) p h(x) 27. f (x)

} g(x)

28. f(g(x)) 29. g(h(x)) 30. h(f(x)) 31. f(f(x))

6.4 Verify that f and g are inverse functions.

32. f(x) 5 2x 2 4, g(x) 5 1 } 2

x 1 2 33. f(x) 5 3x2 1 1, x ≥ 0; g(x) 5 1 x 2 1 } 3

2 1/2

6.4 Find the inverse of the function.

34. f(x) 5 5x 2 3 35. f(x) 5 4 } 3

x 1 2 36. f(x) 5 1 } 2

x2, x ≥ 0

37. f(x) 5 2x6 1 2, x ≤ 0 38. f(x) 5 4x4 2 1 } 18

, x ≥ 0 39. f(x) 5 32x5 1 4

6.5 Graph the function. Then state the domain and range.

40. y 5 2 1 } 3

Ï}

x 41. y 5 2 } 5

3 Ï}

x 42. y 5 5 } 6

Ï}

x 43. y 5 Ï}

x 1 2 2 3

44. y 5 22 3 Ï}

x 2 1 1 2 45. f(x) 5 3 3 Ï}

x 46. g(x) 5 2 1 } 2

Ï}

x 2 2 47. h(x) 5 2 Ï}

x 1 3 1 4

6.6 Solve the equation. Check your solution.

48. Ï}

2x 1 3 5 7 49. 25 Ï}

x 1 1 1 12 5 2 50. 3 Ï}

5x 2 1 1 6 5 10

51. 2 3 Ï}

8x 1 9 5 5 52. 7x4/3 5 175 53. (x 2 2)3/4 5 1

54. x 2 8 5 Ï}

18x 55. x 5 Ï}

4x 2 3 56. Ï}

2x 1 1 1 5 5 Ï}

x 1 12 2 8


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Chapter 77.1 Graph the function. State the domain and range.

1. y 5 1 4 } 3

2 x 2. y 5 22 p 2x 3. y 5 3x 2 3 2 2 4. y 5 1 }

4 p 3x 1 1 1 2

7.2 Graph the function. State the domain and range.

5. y 5 1 3 } 5

2 x 6. y 5 22 1 1 }

4 2

x 7. y 5 (0.8)x 2 3 2 2 8. y 5 2 1 2 }

3 2

x 1 1


9. e23 p e28 10. (2e2x)25 11. Ï}

81e8x 12. 28e3x }

21e2x


13. y 5 0.5e3x 14. y 5 2e2x 2 2 15. y 5 1.5ex 1 1 1 3 16. y 5 e3(x 2 2) 1 1

7.4 Evaluate the logarithm without using a calculator.

17. log4 1 } 16

18. log6 6 19. log5 125 20. log3/4 64 } 27


21. 5log5 x 22. 10log 9 23. log4 16x 24. eln 5


25. y 5 log7 x 26. y 5 log1/2 (x 2 4) 27. y 5 log5 x 1 3 28. y 5 log3 (x 2 2) 1 1

7.5 Expand the expression.

29. log5 2x } 5

30. log 100x 2 } y

31. ln 20x3y2 32. log2 3 Ï}

8x4

7.5 Condense the expression.

33. log4 20 1 4 log4 x 34. log 7 1 2 log x 2 5 log y 35. 0.5 ln 100 2 2 ln x 1 8 ln y

7.5 Use the change-of-base formula to evaluate the logarithm.

36. log2 5 37. log4 80 38. log5 100 39. log7 27


40. 24x 1 2 5 8x 1 2 41. 1 1 } 9

2 x 2 3

5 33x 1 1 42. 79x 5 18

43. ln (3x 1 7) 5 ln (x 2 1) 44. log5 (3x 1 2) 5 3 45. log6 (x 1 9) 1 log6 x 5 2

7.7 Write an exponential function y 5 abx whose graph passes through the given points.

46. (1, 8), (2, 32) 47. (1, 3), (3, 12) 48. (2, 29), (5, 2243) 49. (1, 4), (2, 4)

7.7 Write a power function y 5 axb whose graph passes through the given points.

50. (2, 2), (5, 16) 51. (3, 27), (6, 432) 52. (1, 4), (8, 17) 53. (5, 36), (10, 220)


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Extra Practice 1017

Chapter 88.1 The variables x and y vary inversely. Use the given values to write an equation

relating x and y. Then find y when x 5 25.

1. x 5 2, y 5 210 2. x 5 1 } 3

, y 5 24 3. x 5 23, y 5 25 4. x 5 25, y 5 2 2 } 5

8.1 Determine whether x and y show direct variation, inverse variation, or neither.

5. x y

2.5 32

4 20

5 16

6.4 12.5

8 10

6. x y

1 2.5

3.5 8.75

5 12.5

8 20

9 22.5

7. x y

11 30

14 61

16 85

24 92

27 105

8. x y

1 12

3 4

8 1.5

12 1

15 0.8


9. y 5 6 } x

10. y 5 22 } x

1 3 11. y 5 5 } x 2 1

2 2 12. y 5 4x 1 19 } x 1 3

8.3 Graph the function.

13. y 5 x } x 2 2 4

14. y 5 x 2 1 1 } x 2 1 4x 1 3

15. y 5 x 2 1 2x 2 3 } x 1 2

16. f(x) 5 2x 2 2 8 } x 2 2 2x

8.4 Simplify the rational expression, if possible.

17. x 2 1 x 2 6 } x 2 1 9x 1 18

18. x 3 2 100x } x 4 1 20x 3 1 100x 2

19. x 2 2 5x 2 84 } 2x 2 2 98

20. x 2 1 7x 1 10 } x 2 2 7x 1 10

8.4 Multiply or divide the expressions. Simplify the result.

21. 6x2y

} xy2

p 2y

} 9x3

22. 2x2 2 x 2 6 } 2x2 1 5x 1 3

p x2 1 x }

x2 2 4 23. 3x2 1 15x }

x2 2 12x 1 36 p (x2 2 x 2 30)

24. 12x8y

} 5y5

4 3y2

} x2

25. 6x2 1 x 2 1 } 4x3 1 4x2

4 6x2 2 2x } x2 2 4x 2 5

26. x2 2 4x 2 32 } 2x2 2 13x 2 24

4 x } 4x2 2 9

8.5 Add or subtract the expressions. Simplify the result.

27. x 2 } x 1 1

2 1 } x 1 1

28. x 1 5 } x 1 6

1 1 } x 2 2

29. 5 } x 1 2

1 35 } x 2 2 3x 2 10

8.5 Simplify the complex fraction.

30. x }

2x 1 1 }

5 1 3 } x

31. x } 3

1 2 }

1 } x

1 3 32.

3 } x 2 2 4

}

2 } x 1 2

2 x 1 1 } x 2 2 x 2 6


33. 7 } 3x 2 7

5 14 } x 1 1

34. 1 } 3

1 2 } x

5 2 3 } x 2

35. 2 2 4 } x 1 2

5 2 } x

36. 4 } x 2 2

1 6x 2 } x 2 2 4

5 3x } x 1 2


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Chapter 99.1 Find the distance between the two points. Then find the midpoint of the line

segment joining the two points.

1. (25, 0), (5, 4) 2. (2, 1), (3, 7) 3. (212, 12), (14, 24) 4. (12, 21), (18, 29)

9.2 Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola.

5. y2 5 2x 6. x2 5 24y 7. 14x2 5 221y 8. 12y2 1 3x 5 0

9.3 Graph the equation. Identify the radius of the circle.

9. x2 1 y2 5 4 10. x2 1 y2 5 14 11. 3x2 1 3y2 5 75 12. 16x2 1 16y2 5 4

9.3 Write the standard form of the equation of the circle that passes through the given point and whose center is at the origin.

13. (8, 0) 14. (0, 29) 15. (7, 21) 16. (25, 211)

9.4 Graph the equation. Identify the vertices, co-vertices, and foci of the ellipse.

17. x2 }

81 1

y2

} 16

5 1 18. x2 1 y2

} 9

5 1 19. 9x2 1 4y2 5 576 20. 49x2 1 64y2 5 12,544

9.4 Write an equation of the ellipse with the given characteristics and centerat (0, 0).

21. Vertex: (4, 0) 22. Vertex: (0, 25) 23. Vertex: (9, 0) 24. Co-vertex: (0, 10)Co-vertex: (0, 2) Co-vertex: (4, 0) Focus: (23, 0) Focus: (8, 0)

9.5 Graph the equation. Identify the vertices, foci, and asymptotes of the hyperbola.

25. x2 }

36 2

y2

} 16

5 1 26. x2 2 y2 5 4 27. 49y2 2 81x2 5 3969

9.5 Write an equation of the hyperbola with the given foci and vertices.

28. Foci: (0, 28), (0, 8) 29. Foci: (22, 0), (2, 0) 30. Foci: (0, 25), (0, 5)

Vertices: (0, 26), (0, 6) Vertices: (21, 0), (1, 0) Vertices: (0, 23 Ï}

2 ), (0, 3 Ï}

2 )

9.6 Graph the equation. Identify the important characteristics of the graph.

31. (x 2 3)2

} 25

1 y2

} 9

5 1 32. (x 1 2)2 1 (y 2 1)2 5 4 33. (y 2 4)2 2 (x 1 1)2

} 16

5 1

9.6 Classify the conic section and write its equation in standard form. Then graph the equation.

34. x2 1 y2 1 2x 1 2y 2 7 5 0 35. 9x2 1 4y2 2 72x 1 16y 1 16 5 0

36. 9x2 2 4y2 1 16y 2 52 5 0 37. x2 2 6x 2 4y 1 17 5 0

9.7 Solve the system.

38. x2 1 y2 5 4 39. y 5 x 2 2 40. y2 5 x 2 59x2 2 4y2 5 36 x2 1 y2 2 6x 2 4y 2 12 5 0 9x2 2 25y2 5 225


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Extra Practice 1019

Chapter 1010.1 For the given password configuration, determine how many passwords are

possible if (a) digits and letters can be repeated, and (b) digits and letters cannot be repeated.

1. 8 digits 2. 8 letters

3. 5 letters followed by 1 digit 4. 2 digits followed by 2 letters

10.1 Find the number of permutations.

5. 5P2 6. 6P1 7. 9P9 8. 12P4

10.1 Find the number of distinguishable permutations of the letters in the word.

9. VANILLA 10. CHOCOLATE 11. STRAWBERRY 12. COFFEE

10.2 Find the number of combinations.

13. 7C3 14. 4C1 15. 10C9 16. 15C6

10.2 Use the binomial theorem to write the binomial expansion.

17. (x 2 3)3 18. (2x 1 3y)4 19. (p2 1 4)5 20. (x3 1 y2)6

10.3 You have an equally likely chance of choosing any integer from 1 through 25. Find the probability of the given event.

21. An odd number is chosen. 22. A multiple of 3 is chosen.

10.3 Find the probability that a dart thrown at the given target will hit the shaded region. Assume the dart is equally likely to hit any point inside the target.

23.

8

8

24.

44

25.

20

10

10.4 Events A and B are disjoint. Find P(A or B).

26. P(A) 5 0.4, P(B) 5 0.15 27. P(A) 5 0.3, P(B) 5 0.5 28. P(A) 5 0.7, P(B) 5 0.21

10.4 Find the indicated probability. State whether A and B are disjoint events.

29. P(A) 5 0.25 30. P(A) 5 0.52 31. P(A) 5 0.54 32. P(A) 5 0.5P(B) 5 0.55 P(B) 5 0.15 P(B) 5 0.28 P(B) 5 0.4P(A or B) 5 ? P(A or B) 5 0.67 P(A or B) 5 0.65 P(A or B) 5 ? P(A and B) 5 0.2 P(A and B) 5 ? P(A and B) 5 ? P(A and B) 5 0.3

10.5 Find the probability of drawing the given cards from a standard deck of 52 cards (a) with replacement and (b) without replacement.

33. A jack, then a 3 34. A club, then another club 35. A black ace, then a red card

10.6 Calculate the probability of tossing a coin 15 times and getting the given number of heads.

36. 1 37. 4 38. 7 39. 15


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Chapter 1111.1 Find the mean, median, mode, range, and standard deviation of the data set.

1. 5, 5, 6, 9, 11, 12, 14, 16, 16, 16 2. 16, 18, 29, 30, 34, 35, 35, 38, 46

3. 24, 23, 23, 4, 1, 0, 0, 23, 22, 10, 11 4. 1.7, 2.2, 1.8, 3.0, 0.4, 1.2, 2.8, 2.9

5. 4.5, 5.7, 4.3, 6.9, 22.1, 5.7, 21.2, 3.8 6. 27.2, 3.9, 2.6, 29.1, 2.5, 27.2, 3.9, 27.2

11.2 Find the mean, median, mode, range, and standard deviation of the given data set and of the data set obtained by adding the given constant to each data value.

7. 33, 36, 36, 39, 49, 56; constant: 2 8. 10, 12, 14, 16, 16, 18, 19; constant: 21

11.2 Find the mean, median, mode, range, and standard deviation of the given data set and of the data set obtained by multiplying each data value by the given constant.

9. 22, 22, 5, 4, 2, 22, 8, 3; constant: 1.5 10. 52, 52, 76, 56, 67, 89, 70; constant: 3

11.3 A normal distribution has a mean of 2.7 and a standard deviation of 0.3. Find the probability that a randomly selected x-value from the distribution is in the given interval.

11. Between 2.4 and 2.7 12. At least 3.0 13. At most 2.1

11.4 Identify the type of sample described. Then tell if the sample is biased. Explain your reasoning.

14. The owner of a movie rental store wants to know how often her customers rent movies. She asks every tenth customer how many movies the customer rents each month.

15. A school wants to consult parents about updating its attendance policy. Each student is sent home with a survey for a parent to complete. The school uses only surveys that are returned within one week.

11.4 Find the margin of error for a survey that has the given sample size. Round your answer to the nearest tenth of a percent.

16. 100 17. 600 18. 2900 19. 5000

11.4 Find the sample size required to achieve the given margin of error. Round your answer to the nearest whole number.

20. 61% 21. 62% 22. 65.5% 23. 66.2%

11.5 Use a graphing calculator to find a model for the data. Then graph the model and the data in the same coordinate plane.

24. x 0 2 4 6 8 10 12 14

y 210 23 4 10 14 20 21 36

25. x 1 2 3 4 5 6 7 8

y 0.5 0.8 1.1 3 9 30 90 280


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Extra Practice 1021

Chapter 1212.1 For the sequence, describe the pattern, write the next term, and write a rule for

the nth term.

1. 9, 16, 25, 36, . . . 2. 1 } 3

, 2 } 3

, 1, 4 } 3

, . . . 3. 12.5, 7, 1.5, 24, . . .

12.1 Write the series using summation notation.

4. 16 1 32 1 48 1 64 1 . . . 1 144 5. 1 } 6

1 2 } 7

1 3 } 8

1 4 } 9

1 1 } 2

1 . . .

12.1 Find the sum of the series.

6. i 5 1

∑ 5

(3i 1 2) 7. i 5 0

∑ 5

4i2 8. n 5 4

∑ 6

n } n 1 3

9. k 5 6

∑ 8

k3

12.2 Write a rule for the nth term of the arithmetic sequence. Then graph the first six terms of the sequence.

10. a5 5 15, d 5 6 11. a10 5 278, d 5 210 12. a6 5 2 11 } 5

, d 5 2 2 } 5

12.2 Write a rule for the nth term of the arithmetic sequence. Then find a15.

13. 11, 20, 29, 38, . . . 14. 28, 215, 222, 229, . . . 15. 3, 7 } 3

, 5 } 3

, 1, . . .

12.2 Write a rule for the nth term of the arithmetic sequence that has the two given terms.

16. a2 5 9, a7 5 37 17. a8 5 10.5, a16 5 18.5 18. a3 5 2 14 } 5

, a10 5 2 42 } 5

12.3 Write a rule for the nth term of the geometric sequence. Then find a10.

19. 1 } 27

, 1 } 9

, 1 } 3

, 1, . . . 20. 5, 4, 3.2, 2.56, . . . 21. 4, 16 } 3

, 64 } 9

, 256 } 27

, . . .

12.3 Find the sum of the geometric series.

22. i 5 1

∑ 4

3(4)i 2 1 23. i 5 1

∑ 7

0.5(23)i 2 1 24. i 5 1

∑ 5

10 1 3 } 5

2 i 2 1

25. i 5 1

∑ 7

2(1.2)i 2 1

12.4 Find the sum of the infinite geometric series, if it exists.

26. 8 1 4 1 2 1 1 1 . . . 27. 2 2 4 1 8 2 16 1 . . . 28. 26.75 1 4.5 2 3 1 2 2 . . .

12.4 Write the repeating decimal as a fraction in lowest terms.

29. 0.333. . . 30. 0.898989. . . 31. 0.212121. . . 32. 1.50150150. . .

12.5 Write a recursive rule for the sequence. The sequence may be arithmetic, geometric, or neither.

33. 2.5, 5, 10, 20, . . . 34. 2, 22, 26, 210, . . . 35. 1, 2, 2, 4, 8, 32, . . .

12.5 Find the first three iterates of the function for the given initial value.

36. f(x) 5 2x 2 5, x0 5 3 37. f(x) 5 4 } 5

x 2 2, x0 5 210 38. f(x) 5 3x2 1 x, x0 5 21


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Chapter 1313.1 Let u be an acute angle of a right triangle. Find the values of the other five

trigonometric functions of u.

1. sin u 5 3 } 5

2. tan u 5 8 } 15

3. sec u 5 2 4. cos u 5 Ï}

7 } 4

13.1 Solve n ABC using the diagram and the given measurements.

5. A 5 218, c 5 8 6. B 5 668, a 5 14

7. B 5 608, c 5 20 8. A 5 298, b 5 6

9. A 5 188, c 5 18 10. B 5 568, c 5 7

13.2 Convert the degree measure to radians or the radian measure to degrees.

11. 1008 12. 268 13. 3p }

4 14. 2 p }

6

13.2 Find the arc length and area of a sector with the given radius r and central angle u.

15. r 5 5 ft, u 5 908 16. r 5 2 in., u 5 3008 17. r 5 12 cm, u 5 π

13.3 Sketch the angle. Then find its reference angle.

18. 2508 19. 2308 20. 8p }

3 21. 2 11p

} 6

13.3 Evaluate the function without using a calculator.

22. sin (2608) 23. csc 2408 24. tan 7p }

4 25. cos 1 2 5p

} 4

2

13.4 Evaluate the expression without using a calculator. Give your answer in both radians and degrees.

26. sin21 0 27. cos21 1 2 Ï}

3 } 2

2 28. cos21 3 29. tan21 1

13.4 Solve the equation for u.

30. sin u 5 0.25; 908 < u < 1808 31. cos u 5 0.9; 2708 < u < 3608 32. tan u 5 2; 1808 < u < 2708

13.5 Solve n ABC. (Hint: Some of the “triangles” may have no solution and some may have two solutions.)

33. A 5 348, a 5 6, b 5 7 34. A 5 508, C 5 658, b 5 60 35. B 5 868, b 5 13, c 5 11

13.5 Find the area of n ABC with the given side lengths and included angle.

36. A 5 358, b 5 50, c 5 120 37. B 5 358, a 5 7, c 5 12 38. C 5 208, a 5 10, b 5 16

13.6 Solve n ABC.

39. a 5 16, b 5 23, c 5 17 40. C 5 508, a 5 12, b 5 14 41. A 5 808, b 5 7, c 5 5

13.6 Find the area of n ABC with the given side lengths.

42. a 5 6, b 5 3, c 5 4 43. a 5 14, b 5 30, c 5 27 44. a 5 16, b 5 16, c 5 20

b

B

CA

ac


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Extra Practice 1023

Chapter 1414.1 Graph the function.

1. y 5 cos 1 } 4

x 2. y 5 3 sin x 3. y 5 sin 2πx 4. y 5 2 tan 2x

14.2 Graph the sine or cosine function.

5. y 5 sin 2 1 x 2 p } 4

2 1 1 6. y 5 2sin 1 x 1 p } 4

2 7. y 5 2 cos x 1 3

14.2 Graph the tangent function.

8. y 5 2 tan x 1 2 9. y 5 2 1 } 4

tan 2x 10. y 5 tan 1 x 2 p } 2

2 2 1


11. cos2 1 p } 2

2 x 2 1 cos2 (2x) 12. (sec x 2 1)(sec x 1 1)

} tan x

13. tan 1 p } 2

2 x 2 cot x 2 csc2 x

14.3 Verify the identity.

14. cos (2x)

} 1 1 sin (2x)

5 sec x 1 tan x 15. cos2 x 1 sin2 x } tan2 x 1 1

5 cos2 x 16. 2 2 sec2 x 5 1 2 tan2 x

14.4 Find the general solution of the equation.

17. 12 tan2 x 2 4 5 0 18. 3 sin x 5 22 sin x 1 3 19. tan2 x 2 2 tan x 5 21

14.4 Solve the equation in the given interval. Check your solutions.

20. cos2 x sin x 5 5 sin x; 0 ≤ x < 2π 21. 2 2 2 cos2 x 5 3 1 5 sin x; 0 ≤ x < 2π

22. 8 cos x 5 4 sec x; 0 ≤ x < π 23. cos2 x 2 4 cos x 1 1 5 0; 0 ≤ x < π

14.5 Write a function for the sinusoid.

24. y

x

3

ππ4 s , 21d3π

4

s , 3dπ4

25. y

x

1

1

(0, 3.5)

(1, 2.5)

14.6 Find the exact value of the expression.

26. sin (2158) 27. cos 1658 28. tan 11p }

12 29. cos p }

12

14.7 Find the exact values of sin 2a, cos 2a, and tan 2a.

30. tan a 5 2 } 3

, π < a < 3p }

2 31. cos a 5 9 }

10 , 0 < a < p }

2 32. sin a 5 2 3 }

5 , 3p

} 2

< a < 2π

14.7 Find the general solution of the equation.

33. cos 2x 2 cos x 5 0 34. cos x } 2

5 sin x 35. sin 2x 5 21


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