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Question : Solve. 1) z^4 - 8z^2 + 12 = 0 : 2157367

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

Solve.

1) z^{4} - 8z^{2} + 12 = 0

A) ±√(6), ±√(2)

B) √(6), √(2)

C) √(-6), √(-2)

D) √(-6), √(2)

2) (2m - 3)^{2} - 10(2m - 3) + 24 = 0

A) - (1/2), - (3/2)

B) (7/2), (9/2)

C) - (7/2), - (9/2)

D) (1/3), (3/2)

3) (2p + 6)^{2} = 2(2p + 6) + 35

A) - (1/2), (11/2)

B) (1/2), - (11/2)

C) - (13/2), - (1/2)

D) - (13/6), (1/2)

4) √(x) = 20 - x

A) ±√(20)

B) ±9

C) 16

D) -25, -16

5) m^{2/5} + 2m^{1/5} - 8 = 0

A) 32

B) -32, 1024

C) 1024, 1,048,576

D) 32, -1024

6) 12 = (m^{2} + 5m)^{2} + (m^{2} + 5m)

A) 4, -1, (-5 - √(37) /2) , (-5 + √(37) /2)

B) -2, -1, (-5 - √(37) i/2) , (-5 + √(37) i/2)

C) -4, -1

D) -4, -1, (-5 - √(37)/2) , (-5 + √(37)/2)

7) x - 5√(x) - 24 = 0

A) -64, 64, -3i, 3i

B) -64, -9, 9, 64

C) 64

D) -8i, 8i

8) x^{2/5} - 7x^{1/5} + 10 = 0

A) ±1, 3125

B) 32, 3125

C) ±32, ±3125

D) -32, 625

Solve the problem.

9) A stuntman jumps from a rooftop 360 ft off the ground. How long will it take him, falling freely, to reach the ground? (Use the formula s = 16t^{2})

A) About 22.5 sec

B) About 4.7 sec

C) About 75.9 sec

D) About 11.3 sec

10) Your company uses the quadratic model y = -11x^{2} + 350x to represent how many units (y) of a new product will be sold (x) weeks after its release. How many units can you expect to sell in week 9?

A) 3249 units

B) 4041 units

C) 3051 units

D) 2259 units

11) A grasshopper is perched on a reed 5 inches above the ground. It hops off the reed and lands on the ground about 7.9 inches away. During its hop, its height is given by the equation h = -0.3x^{2} + 1.75x + 5, where x is the distance in inches from the base of the reed, and h is in inches. How far was the grasshopper from the base of the reed when it was 3.75 inches above the ground? Round to the nearest tenth.

A) 0.8 in.

B) 7.9 in.

C) 6.5 in.

D) 0.6 in.

12) The length of a rectangle is three inches more than the width. The area of the rectangle is 418 inches. Find the width of the rectangle.

A) 10 in.

B) 11 in.

C) 22 in.

D) 19 in.

13) A rectangular garden has dimensions of 16 feet by 13 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 492 square feet?

A) 8.5 ft

B) 6 ft

C) 7 ft

D) 8 ft

14) The area of a square is 81 square centimeters. If the same amount is added to one dimension and removed from the other, the resulting rectangle has an area 9 square centimeters less than the area of the square. How much is added and subtracted?

A) 9 cm

B) 3 cm

C) 12 cm

D) 4 cm

15) A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 ft. Find the length of the ladder if the length is 2 ft more than its distance from the wall.

A) 8 ft

B) 12 ft

C) 6 ft

D) 10 ft

16) A lot is in the shape of a right triangle. The shorter leg measures 150 m. The hypotenuse is 50 m longer than the length of the longer leg. How long is the longer leg?

A) 150 m

B) 200 m

C) 250 m

D) 300 m

17) A picture 10 inches by 14 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the border be if the area of the mounted picture is 252 square inches?

A) 4 in.

B) 2 in.

C) 4.5 in.

D) 3 in.

18) A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 23 feet by 25 feet and the area of the rug is 288 square feet, how wide will the border be?

A) 4.5 ft

B) 6 ft

C) 3.5 ft

D) 5.5 ft

State whether the function is linear or quadratic.

19) f(x) = 4x - 9

A) Linear

B) Quadratic

20) f(x) = 4x + (1.9)^{2}

A) Linear

B) Quadratic

21) f(x) = 48x + 6x^{2}

A) Linear

B) Quadratic

22) f(x) = 4x

A) Linear

B) Quadratic

23) f(x) = 7 + 8x^{2}

A) Linear

B) Quadratic

24) f(x) = 4

A) Linear

B) Quadratic

25) f(x) = 0.6x^{2} - 10x + 9

A) Linear

B) Quadratic

26) f(x) = 9x^{2} - 18x

A) Linear

B) Quadratic

27) f(x) = -4x - 5

A) Linear

B) Quadratic

28) f(x) = - 7x^{2}

A) Linear

B) Quadratic