Tell whether each table represents a direct variation or an inverse variation. Write an equation to model the data. Then complete the table.

43. x	y
    10	4
    20	□
    8	3.2

44. x	y
    0.4	28
    1.2	84
    □	63

45. x	y
    1.6	30
    4.8	10
    □	96

46. Physics Boyle's Law states that volume V varies inversely with pressure P for any gas at a constant temperature in an enclosed space. Suppose a gas at constant temperature occupies 15.3 L at a pressure of 40 mm of mercury. What equation models this situation?
47. Error Analysis When graphing a certain function, Pedro sees that the value of y decreases by 2 whenever the value of x increases by 1. Pedro says that the graph represents an inverse variation. Is he correct? Explain.

C Challenge

48. Physics The intensity of a sound s varies inversely with the square of the distance d from the sound. This can be modeled by the equation s d 2 = k , s , d squared , equals k comma  where k is a constant. If you decrease your distance from the source of a sound by half, by what factor will the intensity of the sound increase? Explain your reasoning.
49. Write an equation to model each situation.
    1. y varies inversely with the fourth power of x.
    2. y varies inversely with the fourth power of x and directly with z.

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

50. What is the value of 1 ( 64 ) − 1 3 ? fraction 1 , over open 64 close super negative , 1 third end super end fraction . question mark

51. The diagram shows two squares. The area of the nonshaded region is 4 x 2 + 16 x + 16 . 4 , x squared , plus 16 x plus 16 .  The area of the shaded region is 5 x 2 + 14 x + 9 . 5 , x squared , plus 14 x plus 9 .  What is | a + b | ? vertical line eh plus b vertical line question mark

    

52. What is the value of 7 3 ⋅ 2 5 7 ⋅ 2 3 ? fraction 7 cubed , dot , 2 to the fifth , over 7 dot , 2 cubed end fraction . question mark

Mixed Review

See Lesson 11-5.

Solve each equation. If there is no solution, write no solution.

53. 2 d + 5 = 3 d − 5 fraction 2 , over d plus 5 end fraction . equals . fraction 3 , over d minus 5 end fraction
54. − 1 y + 1 y = 1 negative 1 over y , plus , 1 over y , equals 1
55. 3 m − 4 + 2 = 5 m m − 4 fraction 3 , over m minus 4 end fraction . plus 2 equals . fraction 5 m , over m minus 4 end fraction

Get Ready! To prepare for Lesson 11-7, do Exercises 56–59.

See Lessons 4-4, 7-6, and 9-1.

Graph each function.

56. f ( x ) = x − 8 f open x close equals x minus 8
57. g ( x ) = x 2 + 3 g open x close equals , x squared , plus 3
58. y = 3 x y equals , 3 to the x
59. f ( x ) = 2 x + 1 f open x close equals 2 x plus 1

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