# The Man

1-75

Practice Test

MIXED REVIEW

1. Find the allowable values for each expression. Write

your response in interval notation.

10

Ϫ5

a.

b.

3x ϩ 4

1x Ϫ 8

2. Perform the operations indicated.

a. 1Ϫ18 ϩ 1Ϫ50

b. 11 Ϫ 2i2 2

3i

c.

d. 12 ϩ i132 12 Ϫ i132

1ϩi

3. Solve each equation or inequality.

a. Ϫ2x3 ϩ 4x2 ϭ 50x Ϫ 100

b. Ϫ3x4 Ϫ 375x ϭ 0 c. Ϫ2Ϳ3x ϩ 1Ϳ ϭ Ϫ12

4

x

d. Ϫ3 ` Ϫ 5 ` Յ Ϫ12 e. v3 ϭ 81

3

1

f. Ϫ21x ϩ 12 4 ϭ Ϫ6

Solve for the variable indicated.

2

1

4. V ϭ r2h ϩ r3; for h 5. 3x ϩ 4y ϭ Ϫ12; for y

3

3

Solve as indicated, using the method of your choice.

6. a. Ϫ20 Յ 4x ϩ 8 6 56

b. Ϫ2x ϩ 7 Յ 12 and 3 Ϫ 4x 7 Ϫ5

7. a. 5x Ϫ 12x Ϫ 32 ϩ 3x ϭ Ϫ415 ϩ x2 ϩ 3

n

5

4

b. Ϫ 2 ϭ 2 Ϫ Ϫ n

5

3

15

8. 5x1x Ϫ 102 1x ϩ 12 ϭ 0

9. x2 Ϫ 18x ϩ 77 ϭ 0

17. a. 12v Ϫ 3 ϩ 3 ϭ v

3

3

b. 2 x2 Ϫ 9 ϩ 1 x Ϫ 11 ϭ 0

c. 1x ϩ 7 Ϫ 12x ϭ 1

75

18. The local Lion’s Club rents out two banquet halls for

large meetings and other events. The records show

that when they charge $250 per day for use of the

halls, there are an average of 156 bookings per year.

For every increase of $20 per day, there will be three

less bookings. (a) What price per day will bring in

$61,950 for the year? (b) How many bookings will

there be at the price from part (a)?

19. The Jefferson College basketball team has two

guards who are 6¿3– tall and two forwards who are

6¿7– tall. How tall must their center be to ensure the

“starting ﬁve” will have an average height of at least 6¿6–?

20. The volume of an inﬂatable hot-air balloon can be

approximated using the formulas for a hemisphere

and a cone: V ϭ 2r3 ϩ 1r2h. Assume the conical

3

3

portion has height h ϭ 24 ft. During inﬂation, what

is the radius of the balloon at the moment the

volume of air is numerically equal to 126 times

this radius?

10. 3x2 Ϫ 10 ϭ 5 Ϫ x ϩ x2

11. 4x2 Ϫ 5 ϭ 19

12. 31x ϩ 52 2 Ϫ 3 ϭ 30

13. 25x2 ϩ 16 ϭ 40x

14. 3x2 Ϫ 7x ϩ 3 ϭ 0

15. 2x4 Ϫ 50 ϭ 0

x

1

2

2

1

b.

Ϫ

ϭ0

Ϫ 2

ϭϪ

x

5x ϩ 12

nϪ1

2

n Ϫ1

2x

36

x

c.

Ϫ 2

ϭ

xϩ3

xϪ3

x Ϫ9

16. a.

PRACTICE TEST

1. Solve each equation.

2

a. Ϫ x Ϫ 5 ϭ 7 Ϫ 1x ϩ 32

3

b. Ϫ5.7 ϩ 3.1x ϭ 14.5 Ϫ 41x ϩ 1.52

c. P ϭ C ϩ kC; for C

d. 2Ϳ2x ϩ 5Ϳ Ϫ 17 ϭ Ϫ11

2. How much water that is 102°F must be mixed with

25 gal of water at 91°F, so that the resulting

temperature of the water will be 97°F?

Precalculus—

76

1-76

CHAPTER 1 Equations and Inequalities

3. Solve each equation or inequality.

2

a. Ϫ x ϩ 7 6 19

5

b. Ϫ1 6 3 Ϫ x Յ 8

1

2

c. x ϩ 3 6 9 or

xϪ1Ն3

2

3

1

5

7

d. Ϳx Ϫ 3Ϳ ϩ ϭ

2

4

4

2

e. Ϫ Ϳx ϩ 1Ϳ Ϫ 5 6 Ϫ7

3

revenue of $405? (b) How many tins will be sold at

the price from part (a)?

16. Due to the seasonal nature of the business, the

revenue of Wet Willey’s Water World can be

modeled by the equation r ϭ Ϫ3t2 ϩ 42t Ϫ 135,

where t is the time in months 1t ϭ 1 corresponds to

January) and r is the dollar revenue in thousands.

(a) What month does Wet Willey’s open? (b) What

month does Wet Willey’s close? (c) Does Wet

Willey’s bring in more revenue in July or August?

How much more?

4. To make the bowling team, Jacques needs a threegame average of 160. If he bowled 141 and 162 for the ﬁrst two games, what score S must be obtained in the

third game so that his average is at least 160?

7. 1x Ϫ 12 ϩ 3 ϭ 0

5. z2 Ϫ 7z Ϫ 30 ϭ 0

6. x2 ϩ 25 ϭ 0

2

4

a. x ϩ y

2

8. x ϩ 16 ϭ 17x

2

9. 3x Ϫ 20x ϭ Ϫ12

10. 4x3 ϩ 8x2 Ϫ 9x Ϫ 18 ϭ 0

2

2x

x ϩ 16

2

ϩ

ϭ 2

xϪ3

xϩ2

x ϪxϪ6

4

5x

ϩ2ϭ 2

12.

xϪ3

x Ϫ9

13. 1x ϩ 1 ϭ 12x Ϫ 7

11.

14. 1x ϩ 32

17.

19. Given x ϭ

Solve each equation.

Ϫ2

3

Ϫ8 ϩ 1Ϫ20

6

1

ϭ

4

15. The Spanish Club at Rock Hill Community College

has decided to sell tins of gourmet popcorn as a fundraiser. The suggested selling price is $3.00 per tin, but Maria, who also belongs to the Math Club,

decides to take a survey to see if they can increase

“the fruits of their...

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