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Question : Solve the quadratic equation by completing the square. 1) x^2 - 8x + 7 = 0 : 2158625

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

Solve the quadratic equation by completing the square.

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

A) {6, 1}

B) {-7, -1}

C) {√(7), √(-7)}

D) {7, 1}

2) x^{2} + 18x + 70 = 0

A) {-18 + √(70)}

B) {9 ± √(70)}

C) {-9 ± √(11)}

D) {9 + √(11)}

3) x^{2} + 5x - 5 = 0

A) {(5 ± 3√(5)/2)}

B) {-5 ± 3√(5)}

C) {(-5 ± 3√(5)/2)}

D) {(-5 + 3√(5)/2)}

4) x^{2} - 8x = 15

A) {-4 ± √(31)}

B) {8 ± √(79 )}

C) {4 ± √(15)}

D) {4 ± √(31)}

5) 36x^{2} + 72x + 11 = 0

A) {(1/6), (11/6)}

B) {- (1/6), - (11/6)}

C) {- (11/18), (11/18)}

D) {- (1/36), - (11/36)}

6) x^{2} - (5/2)x + (25/16) = 0

A) {(5/4), (5/4)}

B) {- (5/4), - (5/4)}

C) {(5/4), - (5/4)}

D) {- (5/4), (5/4)}

7) 5x^{2} - 2x - 1 = 0

A) {(5 ± √(6)/25)}

B) {(-1 ± √(6)/5)}

C) {(1 ± √(6)/5)}

D) {-1, (7/5)}

8) x^{2} - 6x + 25 = 0

A) {-1, 7}

B) {3 + 4i}

C) {3 ± 16i}

D) {3 ± 4i}

9) x^{2} + x + 9 = 0

A) {(-1 ± √(35)/2)}

B) {(1 ± i√(35)/2)}

C) {(-1 ± i√(35)/2)}

D) {(1 ± √(35)/2)}

10) 8x^{2} - 3x + 1 = 0

A) {(-3 ± √(23)/16)}

B) {(3 ± √(23)/16)}

C) {- (3/16) ± i(√(23)/16)}

D) {(3/16) ± i(√(23)/16)}

Solve.

11) Seven times the square of the difference between a number and 5 is -252. Find the number(s).

A) 5 + 6i√(7) and 5 - 6i√(7)

B) -5 + 6i and -5 - 6i

C) 5i + 6 and 5i - 6

D) 5 + 6i and 5 - 6i

12) If a $3000 investment compounded to $3967.50 after 2 years, determine the annual interest rate of the investment. Use the compound interest formula A = P(1 + r)^{t}.

A) 15%

B) 1.5%

C) 150%

D) 1500%

13) Imelda inherited $20,000 and invested it in a mutual fund for two years. At the end of the two years, her investment had grown to $22,898. Determine the annual compound interest rate that would yield this amount of money. Use the compound interest formula A = P(1 + r)^{t}.

A) 70%

B) 7%

C) 0.7%

D) 0.07%

14) The annual strawberry yield (in bushels per acre) for a farm in Springfield is given by the equation y = 5x^{2} + 25, where x = 0 represents 2010. Assume this trend continues and predict the year in which the Springfield farm's strawberry yield will be 345 bushels per acre.

A) 2018

B) 2020

C) 2017

D) 2019

15) The formula F = 0.03x^{2} + 24 models the percentage of female tenured faculty, F, at State University x years after 2010. According to the formula, in what year will the percentage of female tenured faculty reach 39.87?

A) 2034

B) 2032

C) 2033

D) 2035

16) A supporting wire is to be attached to the top of a 39-foot antenna. If the wire must be anchored 39 feet from the base of the antenna, what length of wire is required?

A) 39√(2) ft

B) 3042 ft

C) 39 ft

D) 78 ft

17) A ladder that is 26 feet long is 10 feet from the base of a wall. How far up the wall does the ladder reach?

A) 576 ft

B) 24 ft

C) 2√(194) ft

D) 4 ft

18) A 16-foot pole is supported by two wires that extend from the top of the pole to points that are each 12 feet from the base of the pole. Find the total length of the two wires.

A) 40 ft

B) 800 ft

C) 56 ft

D) 20 ft

19) A rectangular park is 16 km long and 16 km wide. How long is a pedestrian route that runs diagonally across the park?

A) 32√(2) km

B) 1024 km

C) 16√(2) km

D) 64 km

20) The function s(t) = 16t^{2} models the distance, s(t), in feet, that an object falls in t seconds. Find the number of seconds a sky diver is in free fall after jumping from a plane if she falls 1504 feet before opening a parachute. Express your answer in simplified radical form.

A) 16√(94) sec

B) √(94) sec

C) 94 sec

D) 376 sec

21) The distance, s(t), in feet traveled by a freely falling object is given by the function s(t) = 16t^{2}, where t is time in seconds. Use this formula to find the time it would take for an object to fall to the ground from a cliff that is 144 feet high.

A) 2 sec

B) 4 sec

C) 9 sec

D) 3 sec

22) A square flower bed is to be enlarged by adding 3 meters on each side. If the larger square has an area of 169 square meters, what is the length of a side of the original square?

A) 19 m

B) 7 m

C) 10 m

D) 16 m