exam · 2017-04-13 · exam name_____ multiple choice. choose the one alternative that best...

Exam

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Plot the given point in a rectangular coordinate system.

1) (5, 4)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

1)

1

2) (-5, 3)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

2)

2

3) (5, -2)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

3)

3

4) (-3, -1)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

4)

4

5) (0, 3)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

5)

5

6) (-5, 0)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

6)

6

7) - 12, - 5

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

7)

7

8) - 92, 0

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

8)

Graph the equation.

8

9) y = x - 2

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

A)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

9)

9

10) y = 2x + 4

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

10)

10

11) y = - 12x + 5

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

11)

11

12) y = x2 - 4

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

12)

12

13) y = x3 + 1

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

A)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

13)

13

14) y = - x - 4

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

14)

14

15) y = -4|x|

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

15)

15

16) y = 1

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

16)

16

17) y = 1x

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

17)

Write the English sentence as an equation in two variables. Then graph the equation.

17

18) The y-value is three more than four times the x-value.

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A) y = 4x + 3

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B) y = 4x - 3

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C) y = -4x - 3

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D) y = -4x + 3

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

18)

18

19) The y-value is two decreased by the square of the x-value.

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

A) y = x2 - 2

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

B) y = 2 - x2

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

C) y = 2 - x

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

D) y = x - 2

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

19)

19

Match the correct viewing rectangle dimensions with the figure.

20)

A) [-5, 5, 5] by [-5, 5, 5] B) [-25, 25, 5] by [-25, 25, 5]

C) [-50, 25, 5] by [-50, 25, 5] D) [-25, 25, 10] by [-25, 25, 10]

20)

21)

A) [-20, 25, 5] by [-5, 40, 5] B) [-5, 40, 5] by [-5, 40, 5]

C) [-50, 25, 5] by [-50, 25, 5] D) [-5, 40, 5] by [-20, 25, 5]

21)

22)

A) [-10, 10, 5] by [-10, 10, 5] B) [-40, 40, 10] by [-10, 10, 5]

C) [-10, 10, 5] by [-200, 200, 20] D) [-50, 50, 5] by [-50, 50, 5]

22)

20

23)

A) [-1, 5, 1] by [-4, 8, 1] B) [-1, 8, 1] by [-1, 8, 1]

C) [-10, 5, 1] by [-10, 5, 1] D) [-10, 30, 10] by [-400, 500, 100]

23)

The table of values was generated by a graphing utility with a TABLE feature. Use the following table to solve.

24) Which equation corresponds to Y2 in the table?

A) y2 = x + 3 B) y2 = 2x + 3 C) y2 = 3 - 2x D) y2 = 3x - 2

24)

25) Does the graph of Y1 pass through the origin?

A) No B) Yes

25)

26) At which points do the graph of Y1 and Y2 intersect?

A) (-1, 1) and (3, 9) B) (-2, 4) and (3, 9)

C) (-1, 1) and (-2, -1) D) (-2, -1) and (-2, 4)

26)

27) For which values of x is Y1 = Y2?

A) 1 and 2 B) -1 and 1 C) 1 and 3 D) -1 and 3

27)

21

Use the graph to determine the x- and y-intercepts.

28)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A) x-intercept: -3; y-intercept: 3 B) x-intercept: -1; y-intercept: 3

C) x-intercept: -1; y-intercept: -3 D) x-intercept: 1; y-intercept: 3

28)

29)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A) y-intercept: -1 B) x-intercepts: -1, 1; y-intercept: -1

C) x-intercepts: -1, 1 D) x-intercepts: -1, 1; y-intercept: 0

29)

22

30)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A) x-intercept: 8; y-intercepts: -2, 4 B) x-intercept: 4; y-intercept: 8

C) x-intercepts: -2, 4; y-intercept: 8 D) x-intercept: -2; y-intercepts: 4, 8

30)

31)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A) x-intercept: -3 B) x-intercept: 3 C) y-intercept: 3 D) y-intercept: -3

31)

23

32)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A) x-intercept: 2; y-intercept: -8 B) x-intercept: 2; y-intercept: 8

C) x-intercept: -2; y-intercept: -8 D) x-intercept: -2; y-intercept: 8

32)

33)

x-10 -5 5

y10

5

-5

-10

x-10 -5 5

y10

5

-5

-10

A) x-intercept: 4; y-intercepts: 4, 1, -5 B) x-intercepts: -4, 1, 5; y-intercept: 4

C) x-intercepts: 4, 1, -5; y-intercept: 4 D) x-intercept: 4; y-intercepts: -4, 1, 5

33)

24

34)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A) x-intercepts: -2, 2 B) x-intercepts: -5, 5; y-intercepts: -2, 2

C) y-intercepts: -5, 5 D) x-intercepts: -2, 2; y-intercepts: -5, 5

34)

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.

35) At what time was the temperature the highest?

A) 11 a.m. B) 1 p.m. C) 2 p.m. D) 5 p.m.

35)

36) At what time was the temperature its lowest?

A) 9 a.m. B) 1 p.m. C) 4 p.m. D) 6 p.m.

36)

37) What temperature was recorded at 4 p.m.?

A) 74 ° F B) 78 ° F C) 77 ° F D) 76 ° F

37)

25

38) During which hour did the temperature increase the most?

A) 9 a.m. to 10 a.m. B) 1 p.m. to 2 p.m.

C) 10 a.m. to 11 a.m. D) 12 p.m. to 1 p.m.

38)

39) At what time was the temperature 77°?

A) 2 p.m. B) 11 a.m. and 12 p.m.

C) 11 a.m. and 12 p.m. and 3 p.m. D) 12 p.m. and 3 p.m.

39)

40) During which two hour period did the temperature increase the most?

A) 9 a.m. to 11 a.m. B) 10 a.m. to 11 a.m.

C) 10 a.m. to 12 p.m. D) 12 p.m. to 2 p.m.

40)

Match the story with the correct figure.

41) The amount of rainfall as a function of time, if the rain fell more and more softly.

A)

x

y

x

y

B)

x

y

x

y

C)

x

y

x

y

D)

x

y

x

y

41)

26

42) The height of an animal as a function of time.

A)

x

y

x

y

B)

x

y

x

y

C)

x

y

x

y

D)

x

y

x

y

42)

27

43) Mark started out by walking up a hill for 5 minutes. For the next 5 minutes he walked down asteep hill to an elevation lower than his starting point. For the next 10 minutes he walked on levelground. For the next 10 minutes he walked uphill. Determine which graph of elevation above sealevel versus time illustrates the story.

A) B)

C) D)

43)

Solve and check the linear equation.

44) 3x - 2 = 13

A) {5} B) {6} C) {16} D) {12}

44)

45) 4x - (2x - 1) = 2

A) 16

B) 12

C) - 12

D) - 16

45)

46) 8x - 3 = 9 + 7x

A) - 112

B) 52

C) 112

D) 12

46)

47) (7x + 9) - 4 = 8(x - 9)

A) {- 77} B) {77} C) {- 14} D) {- 85}

47)

28

48) -6x + 2 - 2(x + 1) = 6x + 6

A) - 53

B) - 1 C) - 37

D) - 57

48)

49) 7[7x - 7 + 4(x + 1)] = -7x - 7

A) - 1 B) 2 C) - 12 D) 16

49)

50) 32 - 2(5 - 2)2 = 45x

A) - 15

B) 75

C) {0} D) {5}

50)

51) -0.05(40) + 0.50x = 0.30(40 + x)

A) {70} B) {60} C) {35} D) {80}

51)

52) 0.80x - 0.40(50 + x) = 0.24(50)

A) {40} B) {80} C) {90} D) {70}

52)

Find all values of x satisfying the given conditions.

53) y1 = 8x + 4(4 + x), y2 = 3(x - 6) + 10x, and y1 = y2

A) {34} B) {10} C) {-10} D) {-34}

53)

Find all values of x such that y = 0.

54) y = 2[3x - (4x - 1)] - 6(x - 1)

A) 12

B) {1} C) {-1} D) - 12

54)

Solve the problem.

55) There is a relationship between the expected number of tickets sold for a raffle and the dollar valueof the prize for the raffle. The equation T - 5P = 300 describes this relationship, where T is theexpected number of tickets sold, and P is the dollar value of the raffle prize. Suppose the expectedticket sales for a certain raffle are 4300. Substitute 4300 into the equation to determine the dollarvalue of the raffle prize.

A) $800 B) $750 C) $21,800 D) $4000

55)

56) The equation V = -2000t + 20,000 describes the value in dollars of a certain model of car after it is tyears old. If a car is worth $12,000, substitute 12,000 into the equation to find the age of the car.

A) 5 years B) 4 years C) 6 years D) 3 years

56)

Solve the equation.

57) x6 = x

7 + 5

A) {42} B) {30} C) 210 D) {35}

57)

29

58) x8 = x

3 + 9

8

A) - 98

B) - 527

C) 0 D) - 275

58)

59) 33 - x2 = x

9

A) {3} B) 3632

C) 1216

D) {54}

59)

60) 2x5 = x

3 + 4

A) {-120} B) {60} C) {120} D) {-60}

60)

61) 8x9 - x = x

36 - 3

4

A) {275} B) {- 9} C) {- 27

5} D) {9}

61)

62) x + 73 = 37

15 - x - 2

5

A) {1} B) {37} C) 16 D) {0}

62)

63) x - 147

+ x + 33 = x + 5

A) 611

B) 4811

C) - 7811

D) - 12611

63)


64) y1 = x + 63

, y2 = x + 86

, and y1 = y2

A) {-12} B) {3} C) {-4} D) {4}

64)

Find all values of x such that y = 0.

65) y = x + 85 + x - 1

3 - 9

5

A) {27} B) {0} C) 10 D) {1}

65)

Solve the problem.

66) A certain store has a fax machine available for use by its customers. The store charges $1.75 to sendthe first page and $0.40 for each subsequent page. The total price, P, for the faxing x pages can bemodeled by the formula P = 0.40(x - 1) + 1.75. Determine the number of pages that can be faxed for$3.75.

A) 9 pages B) 40 pages C) 2 pages D) 6 pages

66)

30

67) A local race for charity has taken place since 1993. Using the actual speeds of the winners from1993 through 1998, mathematicians obtained the formula y = 0.18x + 5, in which x represents thenumber of years after 1993 and y represents the winning speed in miles per hour. In what year isthe winning speed predicted to be 6.8 mph?

A) 2003 B) 2005 C) 2002 D) 2004

67)

68) A car rental agency charges $175 per week plus $0.25 per mile to rent a car. The total cost, C, forthe renting the car for one week and driving it x miles can be modeled by the formulaC = 0.25x + 175. How many miles can you travel in one week for $250?

A) 237.5 miles B) 1000 miles C) 300 miles D) 275 miles

68)

First, write the value(s) that make the denominator(s) zero. Then solve the equation.

69) 7x = 3

2x + 44

A) x ≠ 0; {8} B) x ≠ 0; 18

C) No restrictions; {4} D) x ≠ 0, 2; 5122

69)

70) 5x + 9 = 1

2x + 14

3

A) x ≠ 0; - 2627

B) x ≠ 0; - 2726

C) No restrictions; - 2627

D) x ≠ 0, 2, 3; - 2726

70)

71) x - 63x

+ 2 = x + 8x

A) No restrictions; 73

B) x ≠ 0; 152

C) x ≠ 0, 3; 152

D) x ≠ 0; - 14

71)

72) 3x - 2

+ 3 = 27x - 2

A) x ≠ 2; ∅ B) x ≠ -2; {10} C) x ≠ -2; {12} D) x ≠ 2; {10}

72)

73) 142x - 2

+ 12 = 7

x - 1

A) x ≠ 1; {1} B) x ≠ 1; ∅ C) x ≠ 2; {1} D) x ≠ -1, 2; {1, 2}

73)

31

74) 1x + 3

+ 5x - 3

= 30(x + 3)(x - 3)

A) x ≠ -3, 3; ∅ B) No restrictions; {3}

C) x ≠ -3, 3; {4} D) x ≠ -3; {3}

74)

Solve the equation.

75) x2x + 2

= -2x4x + 4

+ 2x - 3x + 1

A) 32

B) {-3} C) {3} D) - 125

75)

76) 5y + 4

- 8y - 4

= 2y2 - 16

A) {-18} B) {54} C) { 54} D) {18}

76)

77) 1x + 4

+ 2x + 3

= -1x2 + 7x + 12

A) {3} B) {-4} C) {0} D) ∅

77)

78) m + 2m2 - 8m + 15

- 2m2 - 10m + 25

= m - 2m2 - 8m + 15

A) {14 } B) {7 } C) {-2 } D) {-7 }

78)


79) y1 = 1

x + 7, y2 =

2x + 3

, y3 = -4

x2 + 10x + 21, and y1 + y2 = y3

A) {3} B) {0} C) {-7} D) ∅

79)

80) y1 = 7

x + 2, y2 =

9x - 2

, y3 = 14

x2 - 4, and y1 - y2 = y3

A) { 53} B) {46} C) {-23} D) {23}

80)

Solve the problem.

81) The function f(x) = 29,000 + 250xx

models the average cost per unit, f(x), for Electrostuff to

manufacture x units of Electrogadget IV. How many units must the company produce to have anaverage cost per unit of $370?

A) 242 units B) 208 units C) 244 units D) 116 units

81)

82) Suppose a cost-benefit model is given by y = 2845x100 - x

, where y is the cost for removing x percent of

a given pollutant. What percent of pollutant can be removed for $23,000?

A) 89.0% B) 447.0% C) 114.1% D) 8.9%

82)

32

83) The U.S. Maritime Administration estimated that the cost per ton of building an oil tanker could be

represented by the model y = 102,000x + 235

, where y is the cost in dollars per ton and x is the tons (in

thousands). What size of oil tanker (in thousands of tons) can be built for $350 per ton?

A) 56 thousand tons B) 526 thousand tons

C) 6 thousand tons D) 174 thousand tons

83)

Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.

84) 2(4x + 14) = 8x + 28

A) Identity B) Conditional equation C) Inconsistent equation

84)

85) 6x + 9x = 14x


85)

86) -4(x + 6) + 6 = 2x - 6(x + 7)


86)

87) 2x + 5(3x - 4) = 1 - 4x


87)

88) 26x + 7(x + 1) = 33(x + 1) - 26


88)

89) 2x - 3 + 9x - 4 = 3x + 8x - 10


89)

90) 3xx = 3


90)

91) 6xx - 4

= 24x - 4

+ 9


91)

92) -7x + 23

+ 43 = - 7x

2


92)

93) 9y + 5

- 7y - 5

= 12y2 - 25


93)

33

94) 1x + 5

+ 2x + 3

= -2x2 + 8x + 15


94)

Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise.

95) When four times the number is added to 8 times , the result is 48. What is the number?

A) 0.7 B) 6 C) 4 D) -6

95)

96) When 5 times a number is subtracted from 7 times the number, the result is 16. What is thenumber?

A) 2 B) 8 C) 0.3 D) -8

96)

97) When a number is decreased by 30% of itself, the result is 140. What is the number?

A) 60 B) 200 C) 667 D) 15

97)

98) When 50% of a number is added to the number, the result is 180. What is the number?

A) 120 B) 33 C) 150 D) 60

98)

99) 30% of what number is 81?

A) 270 B) 2700 C) 24.3 D) 27

99)

100) One number exceeds another by -4. The sum of the numbers is 10. What are the numbers?

A) -3 and 8 B) 3 and 7 C) 2 and 8 D) No solution

100)


101) y1 = 5x, y2 = (3x - 1), and y1 exceeds y2 by 2.

A) 18

B) 12

C) - 12

D) - 18

101)

102) y1 = x, y2 = 3 + x, y3 = 3(x - 4) + 10x, and the sum of 8 times y1 and 4 times y2 equals y3.

A) {7} B) {24} C) {-7} D) {-24}

102)

103) y1 = 1

x + 5, y2 =

1x + 3

, y3 = -2

x2 + 8x + 15, and the sum of y1 and 2 times y2 is y3.

A) {-5} B) {0} C) {3} D) ∅

103)

104) y1 = 1

x + 4, y2 =

1x - 4

, y3 = 1

x2 - 16, and the difference between 2 times y1 and 8 times y2 is the

product of 14 and y3.

A) {3 2} B) {54} C) {9} D) {-9}

104)

34

Solve the problem.

105) A car rental agency charges $250 per week plus $0.25 per mile to rent a car. How many miles canyou travel in one week for $325?

A) 275 miles B) 331.25 miles C) 1300 miles D) 300 miles

105)

106) A train ticket in a certain city is $1.50. People who use the train also have the option of purchasinga frequent rider pass for $16.50 each month. With the pass, each ticket costs only $0.75. Determinethe number of times in a month the train must be used so that the total monthly cost without thepass is the same as the total monthly cost with the pass.

A) 22 times B) 24 times C) 21 times D) 23 times

106)

107) You inherit $10,000 with the stipulation that for the first year the money must be invested in twostocks paying 6% and 11% annual interest, respectively. How much should be invested at each rateif the total interest earned for the year is to be $700?

A) $7000 invested at 6%; $3000 invested at 11%

B) $8000 invested at 6%; $2000 invested at 11%

C) $2000 invested at 6%; $8000 invested at 11%

D) $9000 invested at 6%; $1000 invested at 11%

107)

108) You inherit $56,000 from a very wealthy grandparent, with the stipulation that for the first year,the money must be invested in two stocks paying 4% and 10% annual interest, respectively. Howmuch should be invested at each rate if the total interest earned for the year is to be $3200?

A) $40,000 invested at 4%; $16,000 invested at 10%

B) $30,000 invested at 4%; $26,000 invested at 10%

C) $16,000 invested at 4%; $40,000 invested at 10%

D) $26,000 invested at 4%; $30,000 invested at 10%

108)

109) A bookcase is to be constructed as shown in the figure below. The height of the bookcase is 2 feetlonger than the length of a shelf. If 22 feet of lumber is available for the entire unit (including theshelves, but NOT the back of the bookcase), find the length and height of the unit.

A) length = 3 feet; height = 5 feet B) length = 4.5 feet; height = 6.5 feet

C) length = 3 feet; height = 6 feet D) length = 10.0 feet; height = 13.5 feet

109)

35

110) An auto repair shop charged a customer $260 to repair a car. The bill listed $80 for parts and theremainder for labor. If the cost of labor is $45 per hour, how many hours of labor did it take torepair the car?

A) 3 hours B) 4 hours C) 4.5 hours D) 5 hours

110)

111) After a 13% price reduction, a boat sold for $26,100. What was the boatʹs price before thereduction? (Round to the nearest cent, if necessary.)

A) $30,000 B) $29,493.00 C) $200,769.23 D) $3393.00

111)

112) Inclusive of a 7.8% sales tax, a diamond ring sold for $1832.60. Find the price of the ring before thetax was added. (Round to the nearest cent, if necessary.)

A) $142.94 B) $1975.54 C) $1689.66 D) $1700

112)

113) The length of a rectangular room is 4 feet longer than twice the width. If the roomʹs perimeter is200 feet, what are the roomʹs dimensions?

A) Width = 37 ft; length = 78 ft B) Width = 32 ft; length = 68 ft

C) Width = 48 ft; length = 52 ft D) Width = 64 ft; length = 136 ft

113)

114) There are 16 more sophomores than juniors in an 8 AM algebra class. If there are 96 students inthis class, find the number of sophomores and the number of juniors in the class.

A) 96 sophomores; 80 juniors B) 40 sophomores; 56 juniors

C) 112 sophomores; 80 juniors D) 56 sophomores; 40 juniors

114)

115) The president of a certain university makes three times as much money as one of the departmentheads. If the total of their salaries is $240,000, find each workerʹs salary.

A) presidentʹs salary = $18,000; department headʹs salary = $6000

B) presidentʹs salary = $120,000; department headʹs salary = $60,000

C) presidentʹs salary = $180,000; department headʹs salary = $60,000

D) presidentʹs salary = $60,000; department headʹs salary = $180,000

115)

116) During a road trip, Tony drove one-third the distance that Lana drove. Mark drives 9 more milesthan Lana drove. The total distance they drove on the trip was 520 miles. How many miles dideach person drive?

A) Tony drove 657 miles, Lana drove 219 miles, and Mark drove 210 miles.

B) Tony drove 70 miles, Lana drove 210 miles, and Mark drove 219 miles.

C) Tony drove 73 miles, Lana drove 219 miles, and Mark drove 228 miles.

D) Tony drove 219 miles, Lana drove 657 miles, and Mark drove 666 miles.

116)

117) The sum of the angles of a triangle is 180°. Find the three angles of the triangle if one angle isfour times the smallest angle and the third angle is 36° greater than the smallest angle.

A) 16°, 64°, 100° B) 0°, 0°, 180° C) 24°, 96°, 60° D) 0°, 36°, 144°

117)

36

118) In a recent International Gymnastics competition, the U.S., China, and Romania were the bigwinners. If the total number of medals won by each team are three consecutive integers whosesum is 36 and the U.S. won more than China who won more than Romania, how many medals dideach team win?

A) U.S.: 14 medals; China: 13 medals; Romania: 12 medals

B) U.S.: 13 medals; China: 12 medals; Romania: 11 medals

C) U.S.: 11 medals; China: 10 medals; Romania: 9 medals

D) U.S.: 38 medals; China: 37 medals; Romania: 36 medals

118)

119) Robin is having her yard landscaped. She obtained an estimate from two landscaping companies.Company A gave an estimate of $190 for materials and equipment rental plus $45 per hour forlabor. Company B gave an estimate of $310 for materials and equipment rental plus $30 per hourfor labor. Determine how many hours of labor will be required for the two companies to cost thesame.

A) 7 hours B) 12 hours C) 8 hours D) 11 hours

119)

120) Sergioʹs internet provider charges its customers $12 per month plus 6¢ per minute of on-lineusage. Sergio received a bill from the provider covering a 4-month period and was charged a totalof $76.80. How many minutes did he spend on-line during that period? (Round to the nearestwhole minute, if necessary.)

A) The number of minutes is 48. B) The number of minutes is 648.

C) The number of minutes is 480. D) The number of minutes is 781.

120)

Solve the formula for the specified variable.

121) A = 12bh for b

A) b = 2Ah

B) b = A2h

C) b = Ah2

D) b = h2A

121)

122) S = 2πrh + 2πr2 for h

A) h = 2π(S - r) B) h = S - r C) h = S - 2πr2

2πrD) h = S

2πr - 1

122)

123) V = 13Bh for h

A) h = V3B

B) h = 3BV

C) h = B3V

D) h = 3VB

123)

124) F = 95C + 32 for C

A) C = 95(F - 32) B) C = 5

9(F - 32) C) C = 5

F - 32D) C = F - 32

9

124)

37

125) A = 12h(a + b) for a

A) a = 2Ab - hh

B) a = 2A - hbh

C) a = hb - 2Ah

D) a = A - hb2h

125)

126) d = rt for t

A) t = d - r B) t = rd

C) t = dr D) t = dr

126)

127) P = 2L + 2W for W

A) W = P - 2L2

B) W = P - 2L C) W = P - L D) W = P - L2

127)

128) A = P(1 + nr) for n

A) n = Ar

B) n = PrA - P

C) n = P - APr

D) n = A - PPr

128)

129) I = Prt for r

A) r = IPt

B) r = P - It C) r = P - 1It

D) r = P - I1 + t

129)

130) 1a + 1

b = 1

cfor c

A) c = a + b B) c = ab(a + b) C) c = aba + b

D) c = a + bab

130)

131) P = A1 + rt

for r

A) r = P - A1 + t

B) r = P - 1At

C) r = A - PPt

D) r = P - At

131)

132) A = 12h(B + b) for B

A) B = A - bhh

B) B = 2A - bhh

C) B = 2A + bhh

D) B = 2A - bh

132)

133) P = s1 + s2 + s3 for s1

A) s1 = P - s2 - s3 B) s1 = P + s2 + s3 C) s1 = P + s2 - s3 D) s1 = s2 + s3 - P

133)

134) I = nEnr + R

for n

A) n = -RIr - E

B) n = IRIr + E

C) n = IR(Ir - E) D) n = -IRIr - E

134)

38

Add or subtract as indicated and write the result in standard form.

135) (2 - 3i) + (4 + 8i)

A) 6 - 5i B) -2 + 11i C) 6 + 5i D) -6 - 5i

135)

136) (6 + 9i) - (-5 + i)

A) -11 - 8i B) 1 + 10i C) 11 - 8i D) 11 + 8i

136)

137) 5i + (-9 - i)

A) -9 + 4i B) 9 - 6i C) -9 + 6i D) 9 - 4i

137)

138) 3i - (-7 - i)

A) 7 - 2i B) -7 + 2i C) -7 - 4i D) 7 + 4i

138)

139) (-5 + 6i) - 2

A) 7 - 6i B) -3 + 6i C) -3 - 6i D) -7 + 6i

139)

140) -2 - (- 3 - 2i) - (- 6 - 2i)

A) 7 - 4i B) 7 + 4i C) 9 - 4i D) 9 + 4i

140)

141) (2 - 7i) + (6 + 5i) + (2 + 5i)

A) 8 - 2i B) 10 + 3i C) 6 - 7i D) -2 - 7i

141)

Find the product and write the result in standard form.

142) -7i(6i - 3)

A) 21i - 42i2 B) -42 + 21i C) 42 + 21i D) 21i + 42i2142)

143) 6i(-7i + 6)

A) 42 + 36i B) 36i - 42i2 C) 36i + 42i2 D) -42 + 36i

143)

144) (9 + 4i)(3 - 2i)

A) 35 + 6i B) -8i2 - 6i + 27 C) 35 - 6i D) 19 + 30i

144)

145) (-8 - 5i)(4 + i)

A) -27 - 28i B) -27 + 12i C) -37 + 12i D) -37 - 28i

145)

146) (7 - 6i)(-3 + 2i)

A) -9 + 32i B) -33 + 32i C) -9 - 4i D) -33 - 4i

146)

39

147) (3 + 9i)(3 - 9i)

A) 90 B) -72 C) 9 - 81i2 D) 9 - 81i

147)

148) (-6 + i)(-6 - i)

A) 37 B) -6 C) -35 D) 36

148)

149) (6 - 9i)2

A) 36 - 108i + 81i2 B) -45 C) 117 - 108i D) -45 - 108i

149)

Perform the indicated operations and write the result in standard form.

150) (5 + 6i)(3 - i) - (1 - i)(1 + i)

A) 19 + 13i B) 23 + 13i C) 19 + 23i D) 21 + 13i

150)

151) (3 + i)2 - (6 - i)2

A) -27 + 18i B) -45 C) 27 + 18i D) -27 - 18i

151)

Complex numbers are used in electronics to describe the current in an electric circuit. Ohmʹs law relates the current in acircuit, I, in amperes, the voltage of the circuit, E, in volts, and the resistance of the circuit, R, in ohms, by the formulaE = IR. Solve the problem using this formula.

152) Find E, the voltage of a circuit, if I = (5 + 2i) amperes and R = (2 + 7i) ohms.

A) (39 + 4i) volts B) (-4 + 39i) volts C) (-4 - 39i) volts D) (39 - 4i) volts

152)

153) Find E, the voltage of a circuit, if I = (16 + i) amperes and R = (2 + 4i) ohms.

A) (-32 - 66i) volts B) (28 - 66i) volts C) (28 + 66i) volts D) (-32 + 66i) volts

153)

Divide and express the result in standard form.

154) 86 - i

A) 4835 + 8

35i B) 48

37 - 8

37i C) 48

35 - 8

35i D) 48

37 + 8

37i

154)

155) 84 + i

A) 3215 + 8

15i B) 32

15 - 8

15i C) 32

17 + 8

17i D) 32

17 - 8

17i

155)

156) 2i1 + i

A) 1 + i B) 1 - i C) 1 + 2i D) -1 + i

156)

40

157) 7i5 - i

A) - 724 + 35

24i B) - 7

26 + 35

26i C) 7

26 + 35

26i D) - 7

26 - 35

26i

157)

158) 3i1 + 7i

A) 350 + 21

50i B) - 7

16 + 1

16i C) 21

50 + 3

50i D) - 1

16 - 7

16i

158)

159) 2 - 3i3 + 2i

A) -i B) 1 C) -1 D) i

159)

160) 6 - 5i8 + 4i

A) 1712 - 1

3i B) 17

5 + 4

5i C) 7

20 - 4

5i D) 7

48 - 1

3i

160)

161) 3 + 2i8 - 2i

A) 517 + 11

34i B) 7

15 + 11

60i C) 1

6 + 11

60i D) 14

17 - 5

17i

161)

162) 4 + 3i5 + 3i

A) 1116 + 3

16i B) 29

16 + 3

16i C) 11

34 - 27

34i D) 29

34 + 3

34i

162)

163) 3 + 3i9 + 2i

A) 37 + 3

11i B) 3

11 + 3

11i C) 21

85 - 33

85i D) 33

85 + 21

85i

163)

164) 4 - 6i5 - 8i

A) 6889 + 2

89i B) - 28

89 + 62

89i C) 28

39 - 2

39i D) - 68

39 - 2

39i

164)

Perform the indicated operations and write the result in standard form.

165) -36 + -64

A) -14 B) -14i C) 48i D) 14i

165)

166) -7 - -100

A) 7i - 10i B) i( 7 + 10) C) i( 7 - 10) D) 7i - 10

166)

41

167) 2 -9 + 5 -4

A) -16 B) -16i C) 16i D) 16

167)

168) 4 -45 + 3 -20

A) 18i 5 B) -18 5 C) -18i 5 D) 18 5

168)

169) (-5 - -100)2

A) -75 + 100i B) 125 - 100i C) 25 - 100i D) 25 + 100i

169)

170) (-5 + -100)2

A) -75 - 100i B) 25 + 100i C) 25 - 100i D) 125 - 100i

170)

171) ( 5 - - 49)( 5 + - 49)

A) 5 - 49i B) 54 C) 5 + 7i D) -44

171)

172) (2 + -5) (3 + -7)

A) (6 - 35 )+ (2 7 + 3 5)i B) 41 + 175i

C) (6 + 35 )- 41i D) -29 - 5 35i

172)

173) -30 + -505

A) -6 + i 2 B) 6 + i 2 C) -6 - i 2 D) -6 + i 5

173)

174) -10 - -505

A) -2 - i 5 B) -2 + i 2 C) -2 - i 2 D) 2 + i 2

174)

175) -81(6 - -81)

A) 54i + 81i2 B) 54i - 81 C) 81 + 54i D) 54i - 81i2175)

176) ( -49)( -49)

A) 49 B) -49 C) -49i D) 49i2176)

Solve the equation by factoring.

177) x2 = x + 12

A) {-3, 4} B) {1, 12} C) {-3, -4} D) {3, 4}

177)

178) x2 + 3x - 40 = 0

A) {-8, 5} B) {-8, 1} C) {8, 5} D) {8, -5}

178)

42

179) 20x2 + 33x + 10 = 0

A) - 25, - 5

4B) 2

5, - 5

4C) - 1

10, - 1

2D) 2

5, 54

179)

180) 6x2 - 11x = 2

A) {-6, 2} B) - 16, 6 C) - 1

6, 2 D) 1

11, - 1

6

180)

181) 9x2 - 9x = 0

A) 1, - 1 B) 0, 1 C) - 1, 0 D) {0}

181)

182) 2x(x - 2) = 5x2 - 5x

A) {0, 3} B) - 13, 0 C) {0} D) 0, 1

3

182)

183) 7 - 7x = (4x + 9)(x - 1)

A) {-1, 4} B) {-4, 1} C) 1 D) 1, - 94

183)

184) -6x - 2 = (3x + 1)2

A) -1, - 13

B) - 13

C) ∅ D) 13, 1

184)

Solve the equation by the square root property.

185) 2x2 = 18

A) {0} B) {-2, 2} C) {-3, 3} D) {-3 2, 3 2}

185)

186) 5x2 = 65

A) {- 13, 13} B) {14} C) {32.5} D) {-13, 13}

186)

187) 4x2 + 4 = 20

A) {-3, 3} B) {2} C) {10} D) {-2, 2}

187)

188) (x - 5)2 = 4

A) {3, 7} B) {-2, 2} C) {9} D) {-7, 3}

188)

189) (2x - 3)2 = 49

A) {-2, 5} B) {-4, 10} C) {-5, 2} D) {-10, 4}

189)

190) (4x + 4)2 = 64

A) {-3, 1} B) {-17, 17} C) {0, 1} D) {1, 3}

190)

43

191) 3(x - 3)2 = 18

A) {-3, 9} B) {-3 ± 6} C) {3 ± 6} D) {-9, 3}

191)

192) (5x + 4)2 = 5

A) 4 - 55

, 4 + 55

B) 5 - 45

, 5 + 45

C) - 95 , 15

D) -4 - 55

, -4 + 55

192)

193) (5x - 12)2 = 8

A) 45, 4 B) -12 - 2 2

5, -12 + 2 2

5

C) 12 - 2 25

, 12 + 2 25

D) {-2 5, 2 5}

193)

194) (x - 3)2 = -16

A) ± 4i3

B) {-3 ± 4i} C) {3i ± 4} D) {3 ± 4i}

194)

195) (x - 2)2 = -3

A) {2 ± 3} B) {-2 ± 3i} C) {-1, 5} D) {2 ± i 3}

195)

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then writeand factor the trinomial.

196) x2 + 16x

A) 8; x2 + 16x + 8 = (x + 64)2 B) 64; x2 + 16x + 64 = (x + 8)2

C) 256; x2 + 16x + 256 = (x + 16)2 D) 16; x2 + 16x + 16 = (x + 256)2

196)

197) x2 - 4x

A) 4; x2 - 4x + 4 = (x - 2) 2 B) -16; x2 - 4x - 16 = (x - 4) 2

C) 16; x2 - 4x + 16 = (x - 4) 2 D) -4; x2 - 4x - 4 = (x - 2) 2

197)

198) x2 - 9x

A) 92; x2 - 9x + 9

2 = x - 9

22

B) - 814; x2 - 9x - 81

4 = x - 9

22

C) 81; x2 - 9x + 81 = (x - 9)2 D) 814; x2 - 9x + 81

4 = x - 9

22

198)

44

199) x2 + 13x

A) 16; x2 + 1

3x + 1

6 = x + 1

32

B) 19; x2 + 1

3x + 1

9 = x + 1

32

C) 36; x2 + 13x + 36 = (x +6) 2 D) 1

36; x2 + 1

3x + 1

36 = x + 1

62

199)

200) x2 + 43x

A) 43; x2 + 4

3x + 4

3 = x + 2

32

B) 89; x2 + 4

3x + 8

9 = x + 4

32

C) 29; x2 + 4

3x + 2

9 = x + 2

32

D) 49; x2 + 4

3x + 4

9 = x + 2

32

200)

201) x2 - 213

x

A) 1169

; x2 - 213

x + 1169

= x + 113

2B) 4

169; x2 - 2

13x + 4

169 = x - 2

132

C) 1169

; x2 - 213

x + 1169

= x - 113

2D) 2

169; x2 - 2

13x + 2

169 = x - 1

132

201)

Solve the equation by completing the square.

202) x2 + 8x = 5

A) {-4 - 2 21, -4 + 2 21} B) {-1 - 21, -1 + 21}

C) {-4 - 21, -4 + 21} D) {4 + 21}

202)

203) x2 - 6x + 5 = 0

A) {- 5, 5} B) {1, 4} C) {-5, -1} D) {1, 5}

203)

204) x2 + 18x + 58 = 0

A) {-18 + 58} B) {-9 - 23 , -9 + 23}

C) {9 + 23} D) {9 - 58 , 9 + 58}

204)

205) x2 + 8x - 3 = 0

A) {-4 - 19 , -4 + 19} B) {-1 - 19 , -1 + 19}

C) {4 + 19} D) {-4 - 2 19 , -4 + 2 19}

205)

206) x2 - 8x - 3 = 0

A) {4 - 19 , 4 + 19} B) {-4 - 19 , -4 + 19}

C) {8 - 67, 8 + 67 } D) {4 - 3 , 4 + 3}

206)

45

207) x2 + 5x - 5 = 0

A) {-5 - 3 5 , -5 + 3 5} B) 5 + 3 52

C) -5 - 3 52

D) -5 - 3 52

, -5 + 3 52

207)

208) x2 + 12x + 61 = 0

A) {-1, -11} B) {-6 ± 25i} C) {-6 + 5i} D) {-6 ± 5i}

208)

209) x2 + x + 1 = 0

A) -1 ± 32

B) 1 ± i 32

C) -1 ± i 32

D) 1 ± 32

209)

210) 5x2 - 2x - 4 = 0

A) -1 - 215

, -1 + 215

B) -4, 225

C) 1 - 215

, 1 + 215

D) 5 - 2125

, 5 + 2125

210)

211) 16x2 - 3x + 1 = 0

A) 3 - i 5532

, -3 + i 5532

B) -3 ± i 5532

C) 3 ± i 5532

D) 3 ± 5532

211)

Solve the equation using the quadratic formula.

212) x2 + 7x - 60 = 0

A) {-5, 12} B) {12, 5} C) {-12, 5} D) {-12, 1}

212)

213) x2 + 7x + 3 = 0

A) 7 - 372

, 7 + 372

B) -7 - 372

, -7 + 372

C) -7 - 3714

, -7 + 3714

D) -7 - 612

, -7 + 612

213)

214) 7x2 + 12x + 3 = 0

A) -6 - 1514

, -6 + 1514

B) -12 - 157

, -12 + 157

C) -6 - 157

, -6 + 157

D) -6 - 577

, -6 + 577

214)

46

215) 5x2 + x - 1 = 0

A) 1 - 2110

, 1 + 2110

B) -1 - 212

, -1 + 212

C) ∅ D) -1 - 2110

, -1 + 2110

215)

216) 3x2 = -9x - 3

A) -3 - 52

, -3 + 52

B) -9 - 52

, -9 + 52

C) -3 - 132

, -3 + 132

D) -3 - 56

, -3 + 56

216)

217) x2 - 10x + 34 = 0

A) {2, 8} B) {5 - 9i, 5 + 9i} C) {5 + 3i} D) {5 - 3i, 5 + 3i}

217)

218) 9x2 + 7x + 2 = 0

A) -7 ± i 2318

B) 7 ± 2318

C) 7 ± i 2318

D) -7 ± 2318

218)

219) 8x2 + 1 = 3x

A) -3 ± 2316

B) 3 ± 2316

C) 3 ± i 2316

D) -3 ± i 2316

219)

Compute the discriminant. Then determine the number and type of solutions for the given equation.

220) x2 + 6x + 5 = 0

A) -56; two complex imaginary solutions

B) 16; two unequal real solutions

C) 0; one real solution

220)

221) x2 - 12x + 36 = 0

A) -144; two complex imaginary solutions

B) 0; one real solution

C) 144; two unequal real solutions

221)

222) 8x2 = 6x - 4

A) 0; one real solution

B) 164; two unequal real solutions

C) -92; two complex imaginary solutions

222)

47

Solve the equation by the method of your choice.

223) (4x + 6)2 = 25

A) - 14, 0 B) 19

4C) - 11

4, - 1

4D) 1

4, 11

4

223)

224) 4x2 - 19x - 5 = 0

A) - 14, 4 B) - 1

4, 119

C) {-4, 5} D) - 14, 5

224)

225) 3x2 + 8x = - 1

A) -6 - 426

, -6 + 426

B) -4 - 136

, -4 + 136

C) -12 - 306

, -12 + 306

D) -4 - 133

, -4 + 133

225)

226) 3x2 = -12x - 7

A) -6 - 573

, -6 + 573

B) -6 - 156

, -6 + 156

C) -6 - 153

, -6 + 153

D) -12 - 153

, -12 + 153

226)

227) 6x2 + 10x + 1 = 0

A) -10 - 196

, -10 + 196

B) -5 - 196

, -5 + 196

C) -5 - 1912

, -5 + 1912

D) -5 - 316

, -5 + 316

227)

228) 3x2 = 45

A) {- 15 , 15} B) {-15, 15} C) {16} D) {22.5}

228)

229) 5x2 - 10 = 0

A) { 2} B) {- 10 , 10} C) { - 2 , 2} D) - 105 , 10

5

229)

230) x2 + 18x + 62 = 0

A) {9 + 19} B) {9 - 62, 9 + 62}

C) {-9 - 19, -9 + 19} D) {-18 + 62}

230)

231) 4x2 - 56x + 260 = 0

A) {7 - 16i, 7 + 16i} B) {3, 11} C) {7 + 4i} D) {7 - 4i, 7 + 4i}

231)

48

232) (3x + 5)2 = 7

A) 7 ± 53

B) -5 ± 73

C) 5 ± 73

D) - 4, 23

232)

233) (x + 2)(x - 1) = 2

A) 1 ± i 172

B) -1 ± i 172

C) -1 ± 172

D) 1 ± 172

233)

234) x218 + x + 35

9 = 0

A) {-9 ± 11} B) {-18 + 70} C) {9 ± 70} D) {9 + 11}

234)

235) 1x + 3

+ 1x = 1

10

A) 23 ± 4092

B) -17 ± 4092

C) -23 ± 4092

D) 17 ± 4092

235)

236) 2xx - 9

- xx - 8

= 5x2 - 17x + 72

A) 7 ± 292

B) -7 ± 292

C) 7 ± 692

D) -7 ± 692

236)

237) 7x2 - 5x - 2 = 0

A) - 5 ± 6114

B) 5 ± 6114

C) 5 ± 8114

D) 5 ± i 5114

237)

Find the x-intercept(s) of the graph of the equation. Graph the equation.

238) y = x2 + 5x + 4

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

238)

49

A) x-intercepts: -1 and -4

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

B) x-intercepts: -1 and -4

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C) x-intercepts: 1 and 4

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

D) x-intercepts: 1 and 4

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

239) y = x2 + 2x + 1

x-10 -5 5 10

y40

20

-20

-40

x-10 -5 5 10

y40

20

-20

-40

239)

50

A) x-intercept: 2

x-10 -5 5 10

y40

20

-20

-40

x-10 -5 5 10

y40

20

-20

-40

B) x-intercept: none

x-10 -5 5 10

y40

20

-20

-40

x-10 -5 5 10

y40

20

-20

-40

C) x-intercept: 1

x-10 -5 5 10

y40

20

-20

-40

x-10 -5 5 10

y40

20

-20

-40

D) x-intercept: -1

x-10 -5 5 10

y40

20

-20

-40

x-10 -5 5 10

y40

20

-20

-40

240) y = x2 + 4x - 7

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

240)

51

A) x-intercepts: -4 and 3

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

B) x-intercepts: none

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C) x-intercept: 4

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D) x-intercepts: -2 ± 11

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

241) y = x2 - 5x + 1

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

241)

52

A) x-intercepts: none

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B) x-intercepts: -5 ± 212

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C) x-intercepts: -1 and 5

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

D) x-intercepts: 5 ± 212

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

242) y = -x2 - 2x + 3

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

242)

53

A) x-intercepts: -1 and 3

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

B) x-intercepts: -3 and 1

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C) x-intercepts: -3 and 1

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

D) x-intercepts: -1 and 3

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

243) y = -3x2 - 12x - 13

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

243)

54

A) x-intercepts: none

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

B) x-intercepts: none

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C) x-intercepts: none

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D) x-intercepts: none

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10


244) y = x2 + 4x and y = 24

A) 2 7 ± 2 B) -2 ± 2 7 C) ± 2 7 D) -2 ± 2 14

244)

245) y = 8x2 - 23x - 3 and y = 0

A) -8, 3 B) - 18, 3 C) 1

23, - 1

8D) - 1

8, 8

245)

246) y1 = (x + 8), y2 = (x - 9), and y1y2 = 5

A) 1 ± 3092

B) -1 ± i 3092

C) -1 ± 3092

D) 1 ± i 3092

246)

247) y1 = 1

x + 3, y2 =

1x, and y1 + y2 =

115

A) -33 ± 3 1012

B) -27 ± 3 1012

C) 33 ± 3 1012

D) 27 ± 3 1012

247)

55

248) y1 = 7 - 7x, y2 = (4x + 9)(x - 1), and y1 - y2 = 0

A) -1, 4 B) 1, - 94

C) 1 D) -4, 1

248)

Solve the problem.

249) The formula N = 3x2 + 4x + 2 represents the number of households N, in thousands, in a certaincity that have a computer x years after 1990. According to the formula, in what year were there 134thousand households with computers in this city?

A) 1994 B) 1997 C) 1995 D) 1996

249)

250) The formula P = 0.64x2 - 0.045x + 1 models the approximate population P, in thousands, for aspecies of fish in a local pond, x years after 1997. During what year will the population reach64,550 fish?

A) 2006 B) 2008 C) 2007 D) 2009

250)

251) The revenue for a small company is given by the quadratic function r(t) = 10t2 + 18t + 700 where tis the number of years since 1998 and r(t) is in thousands of dollars. If this trend continues, find theyear after 1998 in which the companyʹs revenue will be $932 thousand. Round to the nearest wholeyear.

A) 2004 B) 2003 C) 2002 D) 2006

251)

252) A square sheet of paper measures 43 centimeters on each side. What is the length of the diagonalof this paper?

A) 43 2 cm B) 43 cm C) 86 cm D) 3698 cm

252)

253) A ladder that is 17 feet long is 8 feet from the base of a wall. How far up the wall does the ladderreach?

A) 15 ft B) 3 ft C) 353 ft D) 225 ft

253)

254) A 12-foot pole is supported by two wires that extend from the top of the pole to points that areeach 15 feet from the base of the pole. Find the total length of the two wires.

A) 54 ft B) 6 41 ft C) 738 ft D) 3 41 ft

254)

255) The length of a rectangular storage room is 3 feet longer than its width. If the area of the room is180 square feet, find its dimensions.

A) 13 feet by 16 feet B) 12 feet by 15 feet

C) 11 feet by 14 feet D) 11 feet by 16 feet

255)

256) A machine produces open boxes using square sheets of plastic. The machine cuts equal-sizedsquares measuring 4 inches on a side from each corner of the sheet, and then shapes the plasticinto an open box by turning up the sides. If each box must have a volume of 1600 cubic inches, findthe length of one side of the open box.

A) 24 in. B) 19 in. C) 28 in. D) 20 in.

256)

56

257) Suppose that an open box is to be made from a square sheet of cardboard by cutting out 4-inchsquares from each corner as shown and then folding along the dotted lines. If the box is to have avolume of 100 cubic inches, find the original dimensions of the sheet of cardboard.

A) 5 in. by 5 in. B) 13 in. by 13 in.

C) 10 in. by 10 in. D) 5 in. by 2 5 in.

257)

258) A rain gutter is made from sheets of aluminum that are 27 inches wide. The edges are turned up toform right angles. Determine the depth of the gutter that will allow a cross-sectional area of 58square inches. There are two solutions to this problem. Round to the nearest tenth of an inch.

A) 2.4 in. and 24.6 in. B) 1.9 in. and 19.7 in.

C) 2.7 in. and 10.8 in. D) 3.2 in. and 13.0 in.

258)

Solve the polynomial equation by factoring and then using the zero product principle.

259) 5x4 - 45x2 = 0

A) {-3 5, 0, 3 5} B) {-3, 0, 3} C) {-3, 3} D) {0}

259)

260) 5x4 = 135x

A) {0} B) {0, 5, 3} C) {-3, 0, 3} D) {0, 3}

260)

261) 3x3 + 2x2 = 12x + 8

A) {-2, 2} B) -2, - 23, 2 C) - 2

3, 0 D) - 2

3, 2

261)

262) 3x - 2 = 27x3 - 18x2

A) - 13, 13, 32

B) - 19, 19, 23

C) - 13, 13, 23

D) 0, 23

262)

263) x3 + 6x2 + 8x = 0

A) {0, 2, 4} B) {0, -2, -4} C) {-2, -4} D) {2, 4}

263)

264) x3 + 3x2 - x - 3 = 0

A) {1, -3, 3} B) {9} C) {-1, 1, -3} D) {-3, 3}

264)

57

265) 6x3 + 54x2 + 120x = 0

A) {0, 5, 4} B) {-5, -4} C) {- 15, -4} D) {0, -5, -4}

265)

Solve the radical equation, and check all proposed solutions.

266) x + 3 = 9

A) {144} B) {84} C) {81} D) {78}

266)

267) 3x - 2 = 2

A) {2} B) 23

C) {4} D) ∅

267)

268) 3x + 40 = x

A) {-5, 8} B) {8} C) {- 20} D) ∅

268)

269) 28x - 28 = x + 6

A) {-8} B) {-7} C) {8} D) {9}

269)

270) x - 3x - 2 = 4

A) {-1} B) {9} C) {2, 9} D) {1, 2}

270)

271) 2x + 8 = x + 4

A) -4, 43

B) {8} C) {2, 8} D) {-4}

271)

272) 2x + 3 - x + 1 = 1

A) {-3, -1} B) ∅ C) {-1, 3} D) {3}

272)

273) 2x + 5 - x - 2 = 3

A) {3, 8} B) {2, 38} C) {-2} D) {2}

273)

274) x + 6 + 2 - x = 4

A) {2, -2} B) {0} C) { 31, -2} D) {-2}

274)

275) 2 x + 3 = 4x - 5

A) ∅ B) 112

C) 11 - 698

, 11 + 698

D) 11 + 698

275)

58

276) 1 + 14 x = 1 + x

A) {0, 256} B) {0, 144} C) {0, 196} D) 0, 413

276)

Find the x-intercepts of the graph of the equation.

277) y = 2x + 3 - x + 1 - 1

A) -3, -1 B) 3, -1

C) 3 D) No x-intercepts

277)

278) y = 2x + 5 - x - 2 - 3

A) 2, 38 B) 3, 8 C) -2 D) 2

278)

279) y = 3x - 2 + 11 + x + 1

A) 5 B) - 52

C) 0 D) No x-intercepts

279)

280) y = x + 6 + 2 - x - 4

A) 31, -2 B) -2 C) 2, -2 D) 0

280)


281) y = x - 3x - 2 and y = 4

A) -1 B) 9 C) 1, 2 D) 2, 9

281)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the problem.

282) Solve the formula r = 3Vπh for V. 282)

283) Solve the formula r = 2Aθ for θ. 283)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

284) For a culture of 40,000 bacteria of a certain strain, the number of bacteria N that will survive xhours is modeled by the formula N = 4000 100 - x. After how many hours will 20,000 bacteriasurvive?

A) 25 hours B) 80 hours C) 95 hours D) 75 hours

284)

59

285) A formula for the length of a diagonal from the upper corner of a box to the opposite lower corner

is d = L2 + W2 + H2, where L, W, and H are the length, width, and height, respectively. Find thelength of the diagonal of the box if the length is 22 inches, width is 15 inches, and height is 7inches. Leave your answer in simplified radical form.

A) 2 379 inches B) 758 inches C) 2 22 inches D) 2 11 inches

285)

286) A balloon is secured to rope that is staked to the ground. A breeze blows the balloon so that therope is taut while the balloon is directly above a flag pole that is 20 feet from where the rope isstaked down. Find the altitude of the balloon if the rope is 100 feet long.

A) 20 26 ft B) 8 15 ft C) 40 6 ft D) 4 5 ft

286)

287) A formula used to determine the velocity v in feet per second of an object (neglecting airresistance) after it has fallen a certain height is v = 2gh, where g is the acceleration due to gravityand h is the height the object has fallen. If the acceleration g due to gravity on Earth isapproximately 32 feet per second per second, find the velocity of a bowling ball after it has fallen70 feet. (Round to the nearest tenth.)

A) 66.9 ft per sec B) 4480 ft per sec C) 47.3 ft per sec D) 11.8 ft per sec

287)

288) For a cone, the formula r = 3Vπh describes the relationship between the radius r of the base, the

volume V, and the height h. Find the volume if the radius is 8 inches and the cone is 5 inches high.(Use 3.14 as an approximation for π, and round to the nearest tenth.)

A) 67.0 cubic in. B) 41.9 cubic in. C) 3014.4 cubic in. D) 334.9 cubic in.

288)

289) The formula v = 2.5r can be used to estimate the maximum safe velocity v, in miles per hour, atwhich a car can travel along a curved road with a radius of curvature r, in feet. To the nearestwhole number, find the radius of curvature if the maximum safe velocity is 25 miles per hour.

A) 250 ft B) 100 ft C) 1563 ft D) 625 ft

289)

60

290) The function f(x) = 6.75 x + 12 models the amount, f(x), in billions of dollars of new student loansx years after 1993. According to the model, in what year is the amount loaned expected to reach$39 billion?

A) 2013 B) 2012 C) 2014 D) 2009

290)

291) When an object is dropped to the ground from a height of h meters, the time it takes for the object

to reach the ground is given by the equation t = h4.9

, where t is measured in seconds. Solve the

equation for h. Use the result to determine the height from which an object was dropped if it hitsthe ground after falling for 6 seconds.

A) h = 24.01t; 144.1 meters B) h = 4.9t2; 176.4 meters

C) h = 4.9t; 29.4 meters D) h = 24.01t2; 864.4 meters

291)

292) The maximum number of volts, E, that can be placed across a resistor is given by the formulaE = PR, where P is the number of watts of power that the resistor can absorb and R is theresistance of the resistor in ohms. Solve this equation for R. Use the result to determine the

resistance of a resistor if P is 18 watts and E is 10 volts.

A) R = E2P; 800 ohms B) R = E2P

; 800 ohms

C) R = E2

P2; 6400 ohms D) R = E2P2; 6400 ohms

292)

293) The number of centimeters, d, that a spring is compressed from its natural, uncompressed position

is given by the formula d = 2Wk

, where W is the number of joules of work done to move the

spring and k is the spring constant. Solve this equation for W. Use the result to determine thework needed to move a spring 5 centimeters if it has a spring constant of 0.2.

A) W = d2k2

; 2.5 joules B) W = d2k24

; 0.3 joules

C) W = 2d2k; 10 joules D) W = 2d2

k; 250 joules

293)

Solve and check the equation.

294) x3/2 = 343

A) {7} B) {49} C) {2401 7} D)37

294)

295) 2x5/2 - 6 = 0

A) ∅ B) 65

C)53 D)

59

295)

61

296) (x + 4)3/2 = 8

A) {8} B) {0} C)32 - 4 D) {-2}

296)

297) (3x + 1)1/2 = 3

A) 3 B) 83

C) 3 D) - 13

297)

298) (2x + 3)1/3 = 2

A) 12

B) 2 C) 4 D) 52

298)

299) (2x - 2)1/3 + 2 = 6

A) - 32

B) 112

C) - 292

D) ∅

299)

300) (x2 + 16x + 64)3/4 - 3 = 24

A) {27} B) {-17, 1} C) {-17, 0, 1} D) {1}

300)


301) y = (x + 9)3/2 and y = 343

A) {-2} B) {58} C)37 - 9 D) {40}

301)

Solve the equation by making an appropriate substitution.

302) x4 - 40x2 + 144 = 0

A) {4, 36} B) {2, 6} C) {-2, 2, -6, 6} D) {-2i, 2i, -6i, 6i}

302)

303) x4 - 12x2 + 27 = 0

A) {3, 3} B) {-3, 3, -i 3, i 3}

C) {9, 3} D) {-3, 3, - 3, 3}

303)

304) x4 - 31x2 - 180 = 0

A) {-6, 6, -i 5, i 5} B) {-36, 5}

C) {6, i 5} D) {- 5, 5, -6i, 6i}

304)

305) x - 32 x - 2048 = 0

A) {3072} B) {4096} C) {8192} D) {2048}

305)

306) x - 13 x + 30 = 0

A) {9, 100} B) {- 3, 3, - 10, 10}

C) {3, 10} D) {-3, 3, -10, 10}

306)

62

307) 2x - 14 x - 60 = 0

A) 9, 100 B) {10} C) 3, 10 D) {100}

307)

308) x-2 - x-1 - 20 = 0

A) {5, -4} B) - 15, 14

C) 15, - 1

4D) {-5, 4}

308)

309) x-2 - 3x-1 + 2 = 0

A) - 12, -1 B) 1

2, 1 C) {-1, -2} D) {1, 2}

309)

310) 6x-2 - 7x-1 + 1 = 0

A) {-1, -6} B) {1, 6} C) 16, 1 D) - 1

6, -1

310)

311) x-2 - 10x-1 + 23 = 0

A) 5 ± 2 223

B) -5 ± 223

C) 5 ± 227

D) 5 ± 223

311)

312) x - 32x1/2 - 2048 = 0

A) {4096} B) {8192} C) {3072} D) {2048}

312)

313) x2/3 - 4x1/3 + 3 = 0

A) {-3, -1} B) {-27, -1} C) {1, 3} D) {1, 27}

313)

314) x2/5 - x1/5 - 20 = 0

A) {-5, 4} B) {-3125, 1024} C) {5, -4} D) {3125, -1024}

314)

315) 2x1/2 - 9x1/4 - 18 = 0

A) {-6, -3} B) 6, - 32

C) {1296} D) 1296, 8116

315)

316) x1/2 - 14x1/4 + 45 = 0

A) {5, 9} B) {25, 81} C) {-5, -9} D) {625, 6561}

316)

317) (x + 1)2 + 8(x + 1) + 12 = 0

A) {1, 5} B) {-5, -1} C) {3, 7} D) {-7, -3}

317)

318) (-7x - 5)2 + 3(-7x - 5) - 28 = 0

A) {-7, 4} B) 27, - 1 2

7C) - 2

7, 1 2

7D) 1 5

7, 17

318)

63

319) (2x - 7)2 - 10(2x - 7) + 24 = 0

A) 132, 112

B) 12, - 3

2C) - 13

2, - 11

2D) - 1

7, 32

319)

320) (x2 - 3x)2 - 14(x2 - 3x) + 40 = 0

A) {10, 4} B) {- 2, - 1, 10, 4, 5, 4}

C) {5, 4} D) {- 2, - 1, 5, 4}

320)

321) y - 10y

2 - 6 y - 10

y - 27 = 0

A) {- 5, - 1, 2, 10} B) {-3, 9} C) no solution D) {- 5, 2}

321)

Match the graph with its function using the x-intercepts.

322)

x-8 -4 4 8

y16

12

8

4

-4

-8

-12

-16

x-8 -4 4 8

y16

12

8

4

-4

-8

-12

-16

A) y = x4 + 5x2 - 4 B) y = x4 + 5x2 + 4 C) y = x4 - 5x2 - 4 D) y = x4 - 5x2 + 4

322)

323)

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

A) y = x4 - 2x2 + 1 B) y = x4 - 2x2 - 1 C) y = x4 + 2x2 + 1 D) y = x4 + 2x2 - 1

323)

64

324)

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y654321

-1-2-3-4-5-6

A) y = x1/3 + 8x1/6 + 9 B) y = x1/3 + 8x1/6 - 9

C) y = x1/3 - 8x1/6 + 9 D) y = x1/3 - 8x1/6 - 9

324)

325)

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

A) y = x1/2 + 2x1/4 - 1 B) y = x1/2 + 2x1/4 + 1

C) y = x1/2 - 3x1/4 - 4 D) y = x1/2 + 3x1/4 - 4

325)

65

326)

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

A) y = x-2 - x-1 - 2 B) y = x-2 + x-1 - 2

C) y = x-2 - x-1 + 2 D) y = x-2 + x-1 + 2

326)

327)

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

x-5 -4 -3 -2 -1 1 2 3 4 5

y5

4

3

2

1

-1

-2

-3

-4

-5

A) y = x-2 + 2x-1 + 3 B) y = x-2 + 2x-1 - 3

C) y = x-2 - 2x-1 - 3 D) y = x-2 - 2x-1 + 3

327)

66

328)

x-10 -8 -6 -4 -2 2 4 6 8

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8

y10

8

6

4

2

-2

-4

-6

-8

-10

A) y = 6x-2 - 5x-1 + 1 B) y = 6x-2 + 5x-1 - 1

C) y = 6x-2 - 5x-1 - 1 D) y = 6x-2+ 5x-1 + 1

328)

329)

x-10 -5 5

y10

5

-5

-10

x-10 -5 5

y10

5

-5

-10

A) y = (x + 3)2 - 8(x + 3) + 16 B) y = (x + 3)2 - 2(x + 3) + 1

C) y = (x + 3)2 + 2(x + 3) + 1 D) y = (x + 3)2 + 8(x + 3) + 16

329)

67

330)

x-10 -5 5

y10

5

-5

-10

x-10 -5 5

y10

5

-5

-10

A) y = 2(x - 1)2 + 3(x - 1) - 5 B) y = 2(x - 1)2 - 3(x - 1) - 5

C) y = 2(x + 1)2 - 3(x + 1) - 5 D) y = 2(x + 1)2 + 3(x + 1) - 5

330)

331)

x-10 -8 -6 -4 -2 2 4 6 8 10

y

120

80

40

-40

-80

-120

x-10 -8 -6 -4 -2 2 4 6 8 10

y

120

80

40

-40

-80

-120

A) y = x4 - 29x2 + 100 B) y = x4 + 29x2 - 10

C) y = x4 - 29x2 + 10 D) y = x4 + 29x2 + 100

331)


332) y = (x2 - 4x)2 - 17(x2 - 4x) and y = -60

A) 5, 12 B) - 1, - 2, 5, 12, 5, 6

C) 5, 6 D) - 1, - 2, 5, 6

332)

333) y = x - 12x

2 - 3 x - 12

x and y = 4

A) -1, 4 B) - 4, 3 C) - 4, - 2, 3, 6 D) No solution

333)

68

334) y = x2/3 - 5x1/3 and y = -4

A) -4, -1 B) 1, 4 C) 1, 64 D) -64, -1

334)

335) y1 = 5(4x - 1)-1, y2 = 2(4x - 1)-2, and y1 exceeds y2 by 2

A) - 34, 38

B) -2, - 12

C) - 14, - 1

8D) - 1

4, 0

335)

336) y1 = x

x - 4 + 18, y2 = 9

xx - 4

, and y1 = y2

A) 6, 245

B) 3, 6 C) 92, 14435

D) - 92, - 144

35

336)

Solve the absolute value equation or indicate that the equation has no solution.

337) x = 5

A) {25} B) {-5} C) {-5, 5} D) {5}

337)

338) x + 7 = 8

A) {15, 1} B) {-1} C) {-15, 1} D) ∅

338)

339) x + 3 = 4

A) {1} B) {-1, 7} C) {-7, 1} D) ∅

339)

340) 8x + 6 = 2

A) 12, 1 B) - 1

2, - 1 C) - 2

3, - 4

3D) ∅

340)

341) 3 x - 3 = 18

A) {3} B) {9, -3} C) {3, -9} D) ∅

341)

342) 6x + 9 + 6 = 11

A) - 73, - 2

3B) 2

3, 73

C) {- 149, - 4

9} D) ∅

342)

343) 4x - 6 - 7 = -12

A) 114, - 1

4B) 1

4, - 11

4C) 1

4D) ∅

343)

344) 3x + 6 = x + 3

A) - 32, - 9

4B) 3

2, 94

C) - 32, 94

D) ∅

344)

69

345) 12x + 2 = 3

4x - 2

A) {10, 10} B) {16, 12} C) {16, 0} D) ∅

345)

346) 11x + 333

= 11

A) {-6, 6} B) {6, 0} C) {-6, 0} D) ∅

346)

347) 2(x + 1) + 4 = 8

A) {-7, 1} B) {-5, 0} C) {-7, 0} D) {-5, 3}

347)

348) x2 + 1x = 0

A) {1, 0, -1} B) {1, 0} C) {0, -1} D) ∅

348)

349) x2 - 4x - 4 = 8

A) {-2, 2} B) {2, 6} C) {-2, 2, -6} D) {-2, 2, 6}

349)

350) 2x2 - x - 1 = 3

A) - 1 - 334

, - 1 + 334

B) 1 - 334

, 1 + 334

C) 1 - 334

, - 1 + 334

D) ∅

350)

351) x2 - 4x + 4 = 2

A) {2 - 2} B) {2 + 2} C) {2 - 2, 2 + 2} D) ∅

351)


352) y = x - 5 and y = 8

A) -13, 3 B) 13 C) -3, 13 D) No solutions

352)

353) y = 8x + 2 and y = 4

A) 14, - 3

4B) - 1

4, 34

C) 1, - 3 D) No solutions

353)

70

Express the interval in set-builder notation and graph the interval on a number line.

354) (-1, 3]

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) {x -1 < x < 3}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) {x x ≤ 3}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) {x -1 ≤ x ≤ 3}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) {x -1 < x ≤ 3}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

354)

355) [-9, 6)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) {x -9 ≤ x ≤ 6}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) {x -9 < x ≤ 6}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) {x -9 ≤ x < 6}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) {x x < 6}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

355)

356) -∞, 53

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) x x ≤ 53

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) x x > 53

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) x x < 53

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) {x 3 ≤ x ≤ 5}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

356)

71

357) [-6, 9]

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) {x -6 ≤ x ≤ 9}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) {x -6 < x ≤ 9}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) {x -6 ≤ x < 9}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) {x -6 < x < 9}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

357)

358) (7, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) {x x ≥ 7}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) {x x ≥ 7}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) {x x > 7}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) {x x > 7}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

358)

359) [-9, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) {x x ≥ -9}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) {x x ≥ -9}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) {x x > -9}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) {x x > -9}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

359)

360) (-∞, 3.5]

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) {x x < 3.5}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) {x x > 3.5}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) {x x ≤ 3.5}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) {x x ≥ 3.5}

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

360)

72

Use graphs to find the set.

361) (-5, 0) ∩ [-2, 3]

A) (-5, -2] B) (0, 3] C) (-5, 3] D) [-2, 0)

361)

362) (-6, 0) ∪ [-3, 10]

A) [-3, 0) B) (0, 10] C) (-6, -3] D) (-6, 10]

362)

363) (-∞, 9) ∩ [-3, 18)

A) (9, 18) B) [-3, 9) C) (-∞, 18) D) (-∞, -3]

363)

364) (-∞, 6) ∪ [-7, 13)

A) (-∞, 13) B) (6, 13) C) [-7, 6) D) (-∞, -7]

364)

365) (1, ∞) ∩ [17, ∞)

A) (1, ∞) B) (-∞, ∞) C) (1, 17] D) [17, ∞)

365)

366) (3, ∞) ∪ [17, ∞)

A) [17, ∞) B) (3, ∞) C) (3, 17] D) (-∞, ∞)

366)

Solve the linear inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on anumber line.

367) 4x + 3 < 39

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) [9, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) (-∞, 9]

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) (-∞, 9)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) (9, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

367)

368) -4x ≥ 36

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) [-9, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) [9, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) (-∞, 9]

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) (-∞, -9]

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

368)

73

369) 6x + 3 > 5x + 7

A) (-∞, 4]

-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

B) (10, ∞)

3 4 5 6 7 8 9 10 11 12 13 14 15 16 173 4 5 6 7 8 9 10 11 12 13 14 15 16 17

C) [4, ∞)

-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

D) (4, ∞)

-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

369)

370) 6x - 2 ≥ 5x - 3

A) (-5, ∞)

-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

B) (-∞, -1]

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

C) (-∞, -1)

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

D) [-1, ∞)

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

370)

74

371) 12x + 21 > 3(3x + 8)

A) (1, ∞)

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

B) (15, ∞)

8 9 10 11 12 13 14 15 16 17 18 19 20 21 228 9 10 11 12 13 14 15 16 17 18 19 20 21 22

C) [1, ∞)

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

D) (-∞, 1)

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

371)

372) -4(5x - 3) < -24x + 28

A) (-∞, 4]

-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

B) (-∞, -10]

-17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3-17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3

C) (4, ∞)

-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

D) (-∞, 4)

-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

372)

75

373) -24x + 30 ≤ -6(3x - 11)

A) [-6, ∞)

-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1

B) (-∞, -6)

-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1

C) (-∞, -6]

-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1

D) (-6, ∞)

-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1

373)

374) 20x + 28 ≤ 4(4x + 5)

A) (-∞, -2)

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

B) (-∞, -2]

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

C) [-2, ∞)

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

D) [-∞, 12)

5 6 7 8 9 10 11 12 13 14 15 16 17 18 195 6 7 8 9 10 11 12 13 14 15 16 17 18 19

374)

76

375) x7 - 1

2 ≤ x

2 + 1

-40 -32 -24 -16 -8 0 8 16 24 32 40-40 -32 -24 -16 -8 0 8 16 24 32 40

A) -∞, - 215

-40 -32 -24 -16 -8 0 8 16 24 32 40-40 -32 -24 -16 -8 0 8 16 24 32 40

B) - 215, ∞

-40 -32 -24 -16 -8 0 8 16 24 32 40-40 -32 -24 -16 -8 0 8 16 24 32 40

C) - 215, ∞

-40 -32 -24 -16 -8 0 8 16 24 32 40-40 -32 -24 -16 -8 0 8 16 24 32 40

D) -∞, - 215

-40 -32 -24 -16 -8 0 8 16 24 32 40-40 -32 -24 -16 -8 0 8 16 24 32 40

375)

376) x - 115

≥ x - 518

+ 190

-20 -16 -12 -8 -4 0 4 8 12 16 20 24 28-20 -16 -12 -8 -4 0 4 8 12 16 20 24 28

A) (-18, ∞)

-20 -16 -12 -8 -4 0 4 8 12 16 20 24 28-20 -16 -12 -8 -4 0 4 8 12 16 20 24 28

B) [-18, ∞)

-20 -16 -12 -8 -4 0 4 8 12 16 20 24 28-20 -16 -12 -8 -4 0 4 8 12 16 20 24 28

C) (-∞, -18]

-20 -16 -12 -8 -4 0 4 8 12 16 20 24 28-20 -16 -12 -8 -4 0 4 8 12 16 20 24 28

D) (-∞, -18)

-20 -16 -12 -8 -4 0 4 8 12 16 20 24 28-20 -16 -12 -8 -4 0 4 8 12 16 20 24 28

376)

Use interval notation to represent all values of x satisfying the given conditions.

377) y1 = 5x + 6, y2 = 4x + 7, and y1 > y2.

A) (13, ∞) B) (-∞, 1] C) (1, ∞) D) [1, ∞)

377)

378) y1 = 6x - 6, y2 = 5x - 4, and y1 ≤ y2.

A) (-∞, 2) B) [2, ∞) C) [-10, ∞) D) (-∞, 2]

378)

379) y1 = x3, y2 = 2 +

x9, and y1 ≥ y2.

A) (-∞, 9] B) [9, ∞) C) (9, ∞) D) [-9, ∞)

379)

380) y = 8 - 2(3 - x) and y is at most 0.

A) (-∞, -1) B) (-∞, 0] C) (-∞, -1] D) [-1, ∞)

380)

381) y = x - 49 - x - 1

12 - 1

36 and y is at least 0.

A) (-∞, 14) B) [14, ∞) C) (-∞, 14] D) (14, ∞)

381)

77

Solve the problem.

382) When making a long distance call from a certain pay phone, the first three minutes of a call cost$3.00. After that, each additional minute or portion of a minute of that call costs $0.50. Use aninequality to find the number of minutes one can call long distance for $10.50.

A) 21 minutes or fewer B) 18 minutes or fewer

C) 15 minutes or fewer D) 4 minutes or fewer

382)

383) It takes 27 minutes to set up a candy making machine. Once the machine is set up, it produces 12candies per minute. Use an inequality to find the number of candies that can be produced in 3hours if the machine has not yet been set up.

A) 4536 candies or fewer B) 1836 candies or fewer

C) 36 candies or fewer D) 972 candies or fewer

383)

384) A certain store has a fax machine available for use by its customers. The store charges $2.05 to sendthe first page and $0.45 for each subsequent page. Use an inequality to find the number of pagesthat can be faxed for $7.00.

A) 16 pages or fewer B) 12 pages or fewer

C) 3 pages or fewer D) 52 pages or fewer

384)

385) Claire has received scores of 85, 88, 87, and 75 on her algebra tests. What score must she receive onthe fifth test to have an overall test score average of at least 83?

A) 78 or greater B) 81 or greater C) 79 or greater D) 80 or greater

385)

386) Using data from 1996-1998, the annual number of cars sold at a certain dealership can be modeledby the formula

y = 2x + 2,where y is the number of cars, in thousands, sold x years after 1996. According to this formula, inwhich years will the number of cars sold exceed 18 thousand?

A) Years after 2006 B) Years after 2004 C) Years after 2008 D) Years after 2002

386)

387) ABC phone company charges $25 per month plus 6¢ per minute of phone calls. XYZ phonecompany charges $13 per month plus 8¢ per minute of phone calls. How many minutes of phonecalls in a month make XYZ phone company the better deal?

A) More than 600 minutes B) Less than 600 minutes

C) More than 60 minutes D) Less than 60 minutes

387)

388) Greg is opening a car wash. He estimates his cost equation as C = 6000 + 0.06x and his revenueequation as R = 1.7x, where x is the number of cars washed in a six-month period. Find thenumber of cars that must be washed in a six-month period for Greg to make a profit.

A) At least 2659 cars B) At least 36,586 cars

C) At least 3659 cars D) At least 366 cars

388)

78

389) A standard train ticket in a certain city costs $1.50 per ride. People who use the train also have theoption of purchasing a frequent-rider pass for $17.25 each month. With the pass, a ticket costs only $0.75 per ride. How many train rides in a month make the frequent-rider pass a better deal thanstandard train tickets?

A) 22 or more rides B) 23 or more rides

C) 25 or more rides D) 24 or more rides

389)

390) Every Sunday, Jarod buys a loaf of fresh bread for his family from the corner bakery for $3.00. Thelocal department store has a sale on breadmakers for $59. If the bread-making supplies cost $0.67per week, for how many weeks would Jarod have to bake a loaf of bread at home before thebreadmaker starts saving him money?

A) At least 25 weeks B) At least 27 weeks

C) At least 28 weeks D) At least 26 weeks

390)

Solve the linear inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on anumber line.

391) 5(4x + 5) - 4x < 4(6 + 4x) - 6

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) ∅

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) (-∞, 5)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) (5, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) (-∞, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

391)

392) 6(x + 2) ≥ 5(x - 1) + x

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) (-∞, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) ∅

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) [5, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) (-∞, 5]

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

392)

79

393) -5x ≤ -5(x - 3)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) (-∞, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) (-∞, -3]

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) [-3, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) ∅

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

393)

Solve the compound inequality. Other than ∅, use interval notation to express the solution set and graph the solution seton a number line.

394) 15 < 5x ≤ 30

-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12

A) (-∞, 3] ∪ (6, ∞)

-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12

B) (-∞, 3) ∪ [6, ∞)

-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12

C) [3, 6)

-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12

D) (3, 6]

-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12

394)

395) -4 < x - 3 ≤ 6

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) [-1, 9)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) (-1, 9]

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) (-7, 3]

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) [-7, 3)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

395)

80

396) 7 ≤ 4x - 5 ≤ 19

A) [3, 6]

-2 -1 0 1 2 3 4 5 6 7 8 9 10 11-2 -1 0 1 2 3 4 5 6 7 8 9 10 11

B) (-6, -3)

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

C) [-6, -3]

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

D) (3, 6)

-2 -1 0 1 2 3 4 5 6 7 8 9 10 11-2 -1 0 1 2 3 4 5 6 7 8 9 10 11

396)

397) -35 ≤ -5x - 5 < -15

A) (-6, -2]

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3

B) [-6, -2)

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3

C) (2, 6]

-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

D) [2, 6)

-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

397)

81

398) -17 ≤ -3x + 4 ≤ -8

A) [-7, -4]

-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1

B) (4, 7)

-1 0 1 2 3 4 5 6 7 8 9 10 11 12-1 0 1 2 3 4 5 6 7 8 9 10 11 12

C) [4, 7]

-1 0 1 2 3 4 5 6 7 8 9 10 11 12-1 0 1 2 3 4 5 6 7 8 9 10 11 12

D) (-7, -4)

-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1

398)

399) -4 ≤ -4x - 12 < 4

-10 -5 0 5 10-10 -5 0 5 10

A) (-4, -2]

-10 -5 0 5 10-10 -5 0 5 10

B) (-∞, -4) or [-2, ∞)

-10 -5 0 5 10-10 -5 0 5 10

C) (-∞, -4]

-10 -5 0 5 10-10 -5 0 5 10

D) [-4, -2)

-10 -5 0 5 10-10 -5 0 5 10

399)

400) 6 ≤ 75x - 1 < 13

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 101112131415-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 101112131415

A) (5, 10]

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 101112131415-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 101112131415

B) (5, 6]

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 101112131415-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 101112131415

C) [5, 10)

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 101112131415-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 101112131415

D) [5, 6)

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 101112131415-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 101112131415

400)

82

Solve the problem.

401) The formula for converting Fahrenheit temperature, F, to Celsius temperature, C, is

C = 59(F - 32).

If Celsius temperature ranges from 80° to 125°, inclusive, what is the range for the Fahrenheittemperature?

A) (176°F, 257°F) B) (-9°F, -4°F) C) [176°F, 257°F] D) [-9°F, -4°F]

401)

402) The formula for converting Celsius temperature, C, to Fahrenheit temperature, F, is

F = 95C + 32.

If Fahrenheit temperature ranges from -4° to 131°, inclusive, what is the range for the Celsiustemperature?

A) (25°C, 268°C) B) [-20°C, 55°C]

C) (-20°C, 55°C) D) [25°C, 268°C]

402)

403) On the first four exams, your grades are 76, 83, 68, and 77. You are hoping to earn a C in thecourse. This will occur if the average of your five exam grades is greater than or equal to 70 andless than 80. What range of grades on the fifth exam will result in earning a C?

A) [36, 86) B) [46, 96) C) (46, 96] D) (36, 86]

403)

404) On the first four exams, your grades are 76, 78, 73, and 77. There is still a final exam, and it countsas two grades. You are hoping to earn a C in the course. This will occur if the average of your sixexam grades is greater than or equal to 70 and less than 80. What range of grades on the final examwill result in earning a C?

A) [46, 96] B) [46, 96) C) [58, 88] D) [58, 88)

404)

405) Parts for an automobile repair cost $448. The mechanic charges $28 per hour. If you receive anestimate for at least $532 and at most $616 for fixing the car, what is the time interval, in hours, thatthe mechanic will be working on the job?

A) [3, 6] B) [1, 6] C) [1, 3] D) [19, 22]

405)

406) The formula C = 1.5x + 18 represents the estimated future cost of yearly attendance at StateUniversity, where C is the cost in thousands of dollars x years after 2002. Use a compoundinequality to determine when the attendance costs will range from 25.5 to 31.5 thousand dollars.

A) From 2008 to 2012 B) From 2006 to 2010

C) From 2008 to 2010 D) From 2007 to 2011

406)

83

Solve the absolute value inequality. Other than ∅, use interval notation to express the solution set and graph thesolution set on a number line.

407) x < 9

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) (-∞, -9) ∪ (9, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) (-9, 9)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) [-9, 9]

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) (-∞, -9] ∪ [9, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

407)

408) x > 5

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) (-∞, -5) ∪ (5, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) [-5, 5]

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) (-∞, -5] ∪ [5, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) (-5, 5)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

408)

409) |x - 9| < 0

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

A) (-∞, 9)

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

B) (-9, ∞)

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

C) (-9, 9)

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

D) ∅

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

409)

84

410) |x + 6| > 0

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

A) (-6, 6)

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

B) (-6, ∞)

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

C) (-∞, -6) ∪ (-6, ∞)

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

D) ∅

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

410)

411) |x - 5| ≤ 0

-10 -8 -6 -4 -2 0 2 4 6 8 10-10 -8 -6 -4 -2 0 2 4 6 8 10

A) (-∞, 5)

-10 -8 -6 -4 -2 0 2 4 6 8 10-10 -8 -6 -4 -2 0 2 4 6 8 10

B) {5}

-10 -8 -6 -4 -2 0 2 4 6 8 10-10 -8 -6 -4 -2 0 2 4 6 8 10

C) {-5}

-10 -8 -6 -4 -2 0 2 4 6 8 10-10 -8 -6 -4 -2 0 2 4 6 8 10

D) ∅

-10 -8 -6 -4 -2 0 2 4 6 8 10-10 -8 -6 -4 -2 0 2 4 6 8 10

411)

85

412) |x + 6| ≥ 0

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

A) (-∞, ∞)

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

B) (-6, ∞)

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

C) (-6, 6)

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

D) {-6}

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

412)

413) |x + 8| < 2

-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

A) ∅

-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

B) (-∞, -10) ∪ (-6, ∞)

-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

C) (-10, -6)

-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

D) [-10, -6]

-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

413)

86

414) |x - 3| + 8 ≤ 14

A) (-∞, -3] ∪ [9, ∞)

-8 -6 -4 -2 0 2 4 6 8 10 12 14-8 -6 -4 -2 0 2 4 6 8 10 12 14

B) [-3, 14]

-8 -6 -4 -2 0 2 4 6 8 10 12 14-8 -6 -4 -2 0 2 4 6 8 10 12 14

C) [-3, 9]

-8 -6 -4 -2 0 2 4 6 8 10 12 14-8 -6 -4 -2 0 2 4 6 8 10 12 14

D) (-3, 9)

-8 -6 -4 -2 0 2 4 6 8 10 12 14-8 -6 -4 -2 0 2 4 6 8 10 12 14

414)

415) 2(x + 1) + 6 ≤ 8

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) (-8, 0)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) (-6, 2)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) [-8, 0]

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) [-6, 2]

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

415)

416) 2y + 63

< 2

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) (-6, 6)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) (-∞, -6) ∪ (0, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) (-∞, -6) ∪ (6, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) (-6, 0)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

416)

87

417) 3 + 1 - x2 ≥ 5

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) [-2, 6]

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

B) (-∞, -6] ∪ [2, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) [-6, 2]

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) (-∞, -2] ∪ [6, ∞)

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

417)

418) |7x - 8| - 6 < -13

0 1 2 3 4 5 6 7 8 90 1 2 3 4 5 6 7 8 9

A) -∞, 17

0 1 2 3 4 5 6 7 8 90 1 2 3 4 5 6 7 8 9

B) -∞, 157

0 1 2 3 4 5 6 7 8 90 1 2 3 4 5 6 7 8 9

C) 17, 157

0 1 2 3 4 5 6 7 8 90 1 2 3 4 5 6 7 8 9

D) ∅

0 1 2 3 4 5 6 7 8 90 1 2 3 4 5 6 7 8 9

418)

88

419) |2x - 3| - 8 > -12

0 2 4 6 8 10 12 140 2 4 6 8 10 12 14

A) - 12, ∞

0 2 4 6 8 10 12 140 2 4 6 8 10 12 14

B) (-∞, ∞)

0 2 4 6 8 10 12 140 2 4 6 8 10 12 14

C) - 12, 72

0 2 4 6 8 10 12 140 2 4 6 8 10 12 14

D) ∅

0 2 4 6 8 10 12 140 2 4 6 8 10 12 14

419)

Solve the problem.

420) A spinner has ten regions numbered 1 through 10. If the spinner is spun 100 times, we wouldexpect about 10 of the outcomes to be Region 1. It can be determined that the spinner is

unbalanced if x, the number of outcomes that result in Region 1, satisfies x - 103

≥ 1.645. Describe

the number of outcomes that determine an unbalanced spinner that is spun 100 times.

A) Fewer than 9 or more than 17 outcomes B) Between 9 and 17 outcomes

C) Fewer than 6 or more than 14 outcomes D) Between 6 and 14 outcomes

420)

421) When a number is subtracted from -7, the absolute value of the difference is more than 3. Useinterval notation to express the set of all numbers that satisfy this condition.

A) (-∞, -4) ∪ (10, ∞) B) (-10, -4)

C) (-∞, -10] ∪ [-4, ∞) D) (-∞, -10) ∪ (-4, ∞)

421)

422) A landscaping company sells 40-pound bags of top soil. The actual weight x of a bag, however,may differ from the advertised weight by as much as 0.75 pound. Write an inequality involvingabsolute value that expresses the relationship between the actual weight x of a bag and 40 pounds.Solve the inequality, and express the answer in interval form.

A) |40 - x|≤ 0.75; [39.25, 40.75] B) |x + 0.75| ≤ 40; [39.25, ∞)

C) |x|- 40 ≤ 0.75 ; (-∞, 40.75] D) |40 + x| ≤ 0.75; [39.25, 40.75]

422)

89

Answer KeyTestname: UNTITLED1

1) A2) D3) C4) B5) B6) B7) D8) D9) C10) C11) A12) B13) B14) D15) A16) C17) A18) A19) B20) B21) D22) C23) D24) B25) B26) A27) D28) B29) B30) C31) A32) D33) C34) D35) B36) A37) D38) C39) C40) A41) C42) C43) D44) A45) B46) D47) B48) C49) D50) A

90


51) A52) B53) A54) B55) A56) B57) C58) D59) D60) B61) A62) A63) D64) C65) D66) D67) A68) C69) B70) B71) B72) D73) B74) A75) C76) A77) D78) B79) D80) C81) A82) A83) A84) A85) B86) C87) B88) A89) C90) A91) C92) B93) B94) C95) C96) B97) B98) A99) A

100) B91


101) B102) B103) D104) D105) D106) A107) B108) A109) A110) B111) A112) D113) B114) D115) C116) C117) C118) B119) C120) C121) A122) C123) D124) B125) B126) D127) A128) D129) A130) C131) C132) B133) A134) D135) C136) D137) A138) D139) D140) B141) B142) C143) A144) C145) A146) A147) A148) A149) D150) A

92


151) A152) B153) C154) D155) D156) A157) B158) C159) A160) C161) A162) D163) D164) A165) D166) C167) C168) A169) A170) A171) B172) A173) A174) C175) C176) B177) A178) A179) A180) C181) B182) D183) B184) A185) C186) A187) D188) A189) A190) A191) C192) D193) C194) D195) D196) B197) A198) D199) D200) D

93


201) C202) C203) D204) B205) A206) A207) D208) D209) C210) C211) C212) C213) B214) C215) D216) A217) D218) A219) C220) B221) B222) C223) C224) D225) D226) C227) B228) A229) C230) C231) D232) B233) C234) A235) D236) C237) B238) A239) D240) D241) D242) C243) C244) B245) B246) A247) D248) D249) D250) C

94


251) C252) A253) A254) B255) B256) D257) B258) C259) B260) D261) B262) C263) B264) C265) D266) D267) A268) B269) C270) B271) B272) C273) B274) D275) D276) B277) B278) A279) D280) B281) B

282) V = πr2h3

283) θ = 2Ar2

284) D285) B286) C287) A288) D289) A290) D291) B292) B293) A294) B295) D296) B297) B

95


298) D299) C300) B301) D302) C303) D304) A305) B306) A307) D308) C309) B310) B311) D312) A313) D314) D315) C316) D317) D318) B319) A320) D321) A322) D323) A324) B325) D326) A327) B328) C329) C330) D331) A332) D333) C334) C335) A336) C337) C338) C339) C340) B341) B342) A343) D344) A345) C346) C347) A

96


348) C349) D350) B351) C352) C353) A354) D355) C356) C357) A358) C359) B360) C361) D362) D363) B364) A365) D366) B367) C368) D369) D370) D371) A372) D373) A374) B375) C376) B377) C378) D379) B380) C381) B382) B383) B384) B385) D386) B387) B388) C389) D390) D391) A392) A393) A394) D395) B396) A397) C

97


398) C399) A400) C401) C402) B403) B404) D405) A406) D407) B408) A409) D410) C411) B412) A413) C414) C415) C416) D417) D418) D419) B420) C421) D422) A

98

exam · 2017-04-13 · exam name_____ multiple choice. choose the one alternative that best...

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