Deck 8: Squares and Square Roots

Question 1

Use the variable expressions and the Pythagorean theorem and solve for x. Sides are listed smallest to largest. Round your answer to 1 decimal place. $$\{ x , x , 19 \}$$

A) $x \approx 14.4$
B) $x \approx 11.4$
C) $x \approx 14.9$
D) $x \approx 13.4$
E) $x \approx 10.9$

Answer 1

$x \approx 13.4$

Question 2

The sides of the following equilateral triangle are length 6. Find the height x of the triangle. Round your answer to 2 decimal places.

A) 6.71
B) 5.66
C) 8.49
D) 5.20
E) 5.74

Answer 2

5.20

Question 3

Simplify the expression. $- \sqrt { 100 }$

A) -100
B) 100
C) -9
D) 10
E) -10

Answer 3

-10

Question 4

Simplify: $\sqrt { 64 }$

A) $64$
B) $8$
C) $8 \sqrt { 4 }$
D) $4 \sqrt { 8 }$
E) $4$

Question 5

A safe ladder position for reaching 8 feet up a wall is 2 feet from the base of the ladder to the wall. How long a ladder is needed? Round your answer to the nearest tenth.

A) 10.2 ft
B) 8.2 ft
C) 5.2 ft
D) 5.7 ft
E) 7.2 ft

Question 6

A square has side length 5. Find the length of a diagonal. Round your answer to two decimal places.

A) 3.16
B) 25.00
C) 7.07
D) 10.00
E) 8.66

Question 7

A safe ladder position for reaching 26 feet up a wall is 6.5 feet from the base of the ladder to the wall. How long a ladder is needed? Round your answer to the nearest tenth.

A) $x \approx$ 24.8 ft
B) $x \approx$ 29.8 ft
C) $x \approx$ 26.8 ft
D) $x \approx$ 6.5 ft
E) $x \approx$ 25.8 ft

Question 8

Use the variable expressions and the Pythagorean theorem and solve for x. Sides are listed smallest to largest. Round your answer to 1 decimal place. $$\{ x , 7 x , 55 \}$$

A) $x \approx 7.8$
B) $x \approx 5.8$
C) $x \approx 4.8$
D) $x \approx 5.3$
E) $x \approx 68$

Question 9

Is this set of numbers a Pythagorean triple? The numbers might not be listed in a, b, c order. $$( 5 , \sqrt { 6 } , 4 )$$

A) yes
B) no

Question 10

An airplane flies east for 1 hour from Missoula, Montana, at 220 miles per hour. A 30-mile per hour wind from the north blows the plane off course. How far will the airplane travel?

A) 222 miles
B) 223 miles
C) 218 miles
D) 232 miles
E) 220 miles

Question 11

Does this set satisfy the Pythagorean theorem? The numbers might not be listed in a, b, c order. $$( - 20 , - 21 , - 29 )$$

A) no
B) yes

Question 12

What is the radicand in the expression? $\sqrt { 9 x ^ { 10 } }$

A) $9 x ^ { 10 }$
B) $x ^ { 10 }$
C) 9
D) $3 x ^ { 5 }$
E) $x ^ { 5 }$

Question 13

Find the safe ladder position for a ladder with length of 16 feet. Use a safe-ladder ratio, height to base, of 4 to 1. Give your answers first in feet rounded to the nearest hundredth, and then in feet and inches rounded to the nearest inch.

A) Base $\approx$ 4.88 ft $\approx$ 4 ft 11 inches
Height $\approx$ 15.52 ft $\approx$ 15 ft 6 inches
B) Base $\approx$ 3.88 ft $\approx$ 3 ft 11 inches
Height $\approx$ 14.52 ft $\approx$ 14 ft 6 inches
C) Base $\approx$ 3.88 ft $\approx$ 3 ft 11 inches
Height $\approx$ 15.52 ft $\approx$ 15 ft 6 inches
D) Base $\approx$ 3.88 ft $\approx$ 3 ft 12 inches
Height $\approx$ 15.52 ft $\approx$ 15 ft 6 inches
E) Base $\approx$ 3.88 ft $\approx$ 3 ft 11 inches
Height $\approx$ 15.52 ft $\approx$ 15 ft 7 inches

Question 14

Could this set of three numbers represent the sides of a right triangle? $$( 5,15,23 )$$

A) yes
B) no

Question 15

Could this set of three numbers represent the sides of a right triangle? $$( 7,24,25 )$$

A) yes
B) no

Question 16

Use the variable expressions and the Pythagorean theorem and solve for x. Sides are listed smallest to largest. Round your answer to 1 decimal place. $$\{ x , 2 x , 11 \}$$

A) $x \approx 5.9$
B) $x \approx 69$
C) $x \approx 3.4$
D) $x \approx 2.4$
E) $x \approx 4.9$

Question 17

A rectangular prefabricated house is 28 feet by 56 feet with no overhang on the roof. The peak of the roof is above the center of each end of the house. The roof has two rectangular sections that rise 4 feet for a run of 14 feet, a slope of 4 to 14. How many square feet of roofing material are needed?

A) 1568 square feet
B) 1165 square feet
C) 6272 square feet
D) 1631 square feet
E) 3136 square feet

Question 18

An airplane flies for 3 hours on a heading due north from San Francisco. The airplane is flying at 250 miles per hour while a 33-mile per hour wind is blowing from the west. What is the total distance flown?

A) 757.8 miles
B) 756.5 miles
C) 752 miles
D) 766.5 miles
E) 758.6 miles

Question 19

A rectangle has length 7 and width 4. Find the length of a diagonal. Round your answer to two decimal places.

A) 8.06
B) 3.32
C) 4.69
D) 5.29
E) 7.28

Question 20

Find the square root of 78. Round to the nearest thousandth.

A) 8.832
B) 6084.000
C) 39.000
D) 0.013
E) 4.357

Question 21

For the pair of points, find the distance between the points. (-4, -2) and (4, -4)

A) $4 \sqrt { 17 }$
B) 8
C) 10
D) $2 \sqrt { 5 }$
E) $2 \sqrt { 17 }$

Question 22

Find the slope of the line segments connecting the two points.
( $-$ 4, $-$ 2) and (4, $-$ 4)

A) 4
B) $-$ 4
C) $- \frac { 1 } { 4 }$
D) $\frac { 1 } { 4 }$
E) $\frac { 1 } { 2 }$

Question 23

Simplify the expression without a calculator. Assume variables are positive. $$- \sqrt { \frac { 75 x ^ { 4 } y } { 3 x ^ { 2 } y } }$$

A) $- 5 x$
B) $25 y$
C) $75 x ^ { 2 }$
D) 6
E) $\frac { 75 } { 3 } x$

Question 24

Evaluate the expression without a calculator. Hint: Change decimals to fractions. $$\left( \frac { 1 } { 7 } \right) ^ { 0 }$$

A) 70
B) 0
C) 7
D) $\frac { 1 } { 7 }$
E) 1

Question 25

Simplify: $\sqrt { 700 }$

A) $10 \sqrt { 7 }$
B) $7 \sqrt { 50 }$
C) $70$
D) $7 \sqrt { 10 }$
E) $10 \sqrt { 70 }$

Question 26

Simplify. Assume that the variables are positive. $$\sqrt { y ^ { 17 } }$$

A) $y ^ { 9 } \sqrt { y ^ { 8 } }$
B) $y ^ { 8 } \sqrt { y }$
C) $y ^ { 8 }$
D) $17 y ^ { 8 } \sqrt { y }$
E) $y ^ { 7 } \sqrt { y }$

Question 27

Find the equation of the line passing through the points. (2, 5) and (10, 9)

A) $y = - \frac { 1 } { 2 } x + 4$
B) $y = - 2 x + 4$
C) $y = \frac { 1 } { 2 } x + 4$
D) $y = 2 x + 4$
E) $y = - 2 x + 2$

Question 28

For what x is the function defined? $$y = \sqrt { - 9 x }$$

A) $0 \leq x$
B) $x \geq 3$
C) $x \neq 9$
D) $0 \geq x$
E) The function is undefined for any x.

Question 29

Simplify. Assume that the variables are positive. $\sqrt { x ^ { 8 } }$

A) $4 \sqrt { x ^ { 4 } }$
B) $x ^ { 4 }$
C) $x ^ { 6 }$
D) $4 x$
E) $4 \sqrt { x }$

Question 30

Find the slope of the line segment connecting the two points. (2, 6) and (4, 10)

A) $\frac { 1 } { 2 }$
B) 2
C) -2
D) $- \frac { 1 } { 2 }$
E) 4

Question 31

The vertices of a triangle are given. Use the distance formula to find what kind of triangle each is. A sketch of the graph might be helpful. Note: An isosceles triangle has two equal sides. An equilateral triangle has three equal sides. A right triangle satisfies the Pythagorean Theorem.
(4, 8), (1, 6), (5, 0)

A) isosceles equilateral
B) isosceles right
C) right, not isosceles
D) equilateral
E) isosceles

Question 32

For the pair of points, find the distance between the two points. Simplify the expression. (2, 5) and (10, 9)

A) $5 \sqrt { 4 }$
B) 4
C) $2 \sqrt { 40 }$
D) $4 \sqrt { 5 }$
E) $8 \sqrt { 10 }$

Question 33

Find the equation of the line passing through the points. (2, 6) and (4, 10)

A) $y = \frac { 1 } { 2 } x + 2$
B) $y = 2 x + 2$
C) $y = - 2 x + 2$
D) $y = - \frac { 1 } { 2 } x + 2$
E) $y = - 2 x - 2$

Question 34

The vertices of a triangle are given. Use the distance formula to find what kind of triangle each is. A sketch of the graph might be helpful. Note: An isosceles triangle has two equal sides. An equilateral triangle has three equal sides. A right triangle satisfies the Pythagorean Theorem.
(6, 7), (4, 4), (6, 1)

A) equilateral isosceles right
B) isosceles
C) right, not isosceles
D) equilateral
E) equilateral right

Question 35

Find the slope of the line segment connecting the two points. (2, 5) and (10, 9)

A) $- \frac { 1 } { 2 }$
B) $- 2$
C) $\frac { 1 } { 2 }$
D) 2
E) 4

Question 36

Evaluate the expression without a calculator. Hint: Change decimals to fractions. $$9 ^ { 0.5 }$$

A) 9
B) 4
C) 0
D) 3
E) 10

Question 37

For the pair of points, find the distance between the two points. Simplify the expression. (2, 6) and (4, 10)

A) $5 \sqrt { 2 }$
B) 6
C) $\sqrt { 6 }$
D) $2 \sqrt { 2 }$
E) $2 \sqrt { 5 }$

Question 38

Evaluate the function for $$f ( 5 )$$ $$f ( x ) = \sqrt { 9 - x }$$

A) 3
B) 1
C) 2
D) $\sqrt { 5 }$
E) no real number

Question 39

Simplify the expression without a calculator. $\sqrt { 27 } \sqrt { 75 }$

A) 44
B) 2,025
C) 45
D) 0
E) -45

Question 40

Evaluate the expression without a calculator. Hint: Change decimals to fractions. $$( 0.1 ) ^ { - 1 }$$

A) 10
B) 9
C) 8
D) 13
E) 6

Question 41

Solve and check: $$\sqrt { 11 n - 6 } = 11$$

A) $\frac { 289 } { 11 }$
B) $\frac { \sqrt { 11 } + 6 } { 11 }$
C) $\frac { 127 } { 11 }$
D) $\frac { 289 } { 121 }$
E) No solution

Question 42

Name a, b, and c. $$6 t ^ { 2 } - 54 t = 0$$

A) $a = 6 , b = - 54 , c = 0$
B) $a = 6 , b = 0 , c = - 54$
C) $a = 0 , b = - 54 , c = 6$
D) $a = 0 , b = 6 , c = - 54$
E) $a = - 54 , b = 6 , c = 0$

Question 43

Name a, b, and c. $$y = 7 x ^ { 2 } + 4 x - 1$$

A) $a = 7 , b = - 1 , c = 4$
B) $a = 4 , b = 7 , c = - 1$
C) $a = 7 , b = 4 , c = - 1$
D) $a = 1 , b = 4 , c = - 7$
E) $a = 4 , b = - 1 , c = 7$

Question 44

Find the x- and y-intercepts: $$f ( x ) = 4 x ^ { 2 } - 6 x + 9$$

A) $\left( \frac { - 4 + \sqrt { 13 } } { 7 } , 0 \right) , \left( \frac { - 4 - \sqrt { 13 } } { 7 } , 0 \right) ; ( 0,9 )$
B) No x-intercepts; (0, 9)
C) $\left( \frac { 4 + \sqrt { 13 } } { 7 } , 0 \right) , \left( \frac { 4 - \sqrt { 13 } } { 7 } , 0 \right) ; ( 0 , - 9 )$
D) $\left( \frac { 4 + \sqrt { 13 } } { 14 } , 0 \right) , \left( \frac { 4 - \sqrt { 13 } } { 14 } , 0 \right) ; ( 0,9 )$
E) $( 4 + \sqrt { 13 } , 0 ) , ( 4 - \sqrt { 13 } , 0 ) ; ( 0,9 )$

Question 45

Find the x- and y-intercepts: $$y = 7 x ^ { 2 } + 5 x - 2$$

A) (1,0), $\left( \frac { 2 } { 7 } , 0 \right)$ ; (0,-2)
B) $\left( 1 , \frac { 2 } { 7 } \right)$ ; (0,-2)
C) (-1, 0), $\left( \frac { 2 } { 7 } , 0 \right)$ ; (0,2)
D) (-1,0), $\left( \frac { 2 } { 7 } , 0 \right)$ ; (0,-2)
E) (0,-1), $\left( 0 , \frac { 2 } { 7 } \right)$ ; (0,-2)

Question 46

Solve this electric formula for the indicated variable. $$E = \sqrt { W R } \text { for } W$$

A) $W = \frac { R } { E ^ { 2 } }$
B) $W = E ^ { 2 } R$
C) $W = \frac { E } { R }$
D) $W = \sqrt { \frac { E ^ { 2 } } { R } }$
E) $W = \frac { E ^ { 2 } } { R }$

Question 47

How high do we need to be on Earth to see 7 miles? On Earth, the distance to the horizon is given by $d \approx \sqrt { \frac { 3 h } { 2 } }$ , where d is in miles to the horizon and h is in feet above sea level.

A) $32 \frac { 2 } { 3 }$ feet
B) $31 \frac { 2 } { 3 }$ feet
C) $34 \frac { 1 } { 4 }$ feet
D) $2 \frac { 2 } { 3 }$ feet
E) $10 \frac { 2 } { 3 }$ feet

Question 48

Find the x- and y-intercepts: $$y = 6 x ^ { 2 } + 7 x - 10$$

A) (2,0), $\left( \frac { 5 } { 6 } , 0 \right)$ ; (0,-10)
B) $\left( 2 , \frac { 5 } { 6 } \right)$ ; (0,-10)
C) (0,-2), $\left( \frac { 5 } { 6 } , 0 \right)$ ; (0, 10)
D) (-2,0), $\left( \frac { 5 } { 6 } , 0 \right)$ ; (0, -10)
E) (0,-2), $\left( 0 , \frac { 5 } { 6 } \right)$ ; (0, -10)

Question 49

Name a, b, and c. $$x ^ { 2 } = 5 - x$$

A) $a = 1 , b = - 5 , c = 1$
B) $a = - 5 , b = 1 , c = 1$
C) $a = 1 , b = 1 , c = - 5$
D) $a = - 1 , b = 1 , c = - 5$
E) $a = - 1 , b = - 5 , c = 1$

Question 50

Find the x- and y-intercepts: $$f ( x ) = 36 x ^ { 2 } - 48 x + 5$$

A) $\left( \frac { - 4 + \sqrt { 11 } } { 6 } , 0 \right) , \left( \frac { - 4 - \sqrt { 11 } } { 6 } , 0 \right) ; ( 0,5 )$
B) $\left( \frac { 4 + \sqrt { 11 } } { 6 } , 0 \right) , \left( \frac { 4 - \sqrt { 11 } } { 6 } , 0 \right) ; ( 0,5 )$
C) $\left( \frac { 4 + \sqrt { 11 } } { 6 } , 0 \right) , \left( \frac { 4 - \sqrt { 11 } } { 6 } , 0 \right) ; ( 0 , - 5 )$
D) $\left( \frac { 4 + \sqrt { 11 } } { 12 } , 0 \right) , \left( \frac { 4 - \sqrt { 11 } } { 12 } , 0 \right) ; ( 0,5 )$
E) No intercepts; (0, 5)

Question 51

Solve the formula for the indicated variable. Orbital velocity: $$V = \sqrt { \frac { G M } { R } } \text { for } M$$

A) $M = V ^ { 2 } R G$
B) $M = G ^ { 2 } R V$
C) $M = \sqrt { \frac { R V } { G } }$
D) $M = \frac { R V ^ { 2 } } { G }$
E) $M = \left( \frac { R V } { G } \right) ^ { 2 }$

Question 52

For what inputs is the expression defined? $$\sqrt { x - 8 }$$

A) $x \geq 7$
B) $x \geq 8$
C) $x \leq 8$
D) $x \geq 1$
E) $x > 7$

Question 53

Name a, b, and c. $$r ^ { 2 } + 12 r + 36 = 0$$

A) $a = 1 , b = 36 , c = 12$
B) $a = 12 , b = 1 , c = 36$
C) $a = 12 , b = 36 , c = 1$
D) $a = 1 , b = 12 , c = 36$
E) $a = 36 , b = 12 , c = 1$

Question 54

The time required for a dropped object to hit the ground is given by $t = \sqrt { \frac { 2 h } { g } }$ , where h is the vertical distance traveled and g is the acceleration due to gravity (32.2 feet per second squared). How long will it take an object to fall from the top of the Torre Commercial America, in Monterrey, Mexico at 427 feet tall? Round the answer to the nearest tenth.

A) t = 26.5 sec.
B) t = 5.1 sec.
C) t = 10.9 sec.
D) t = 5.7 sec.
E) t = 6.4 sec.

Question 55

Name a, b, and c. $$y = 4 x ^ { 2 } - 81$$

A) $a = 4 , b = - 81 , c = 0$
B) $a = 0 , b = 4 , c = - 81$
C) $a = 0 , b = - 81 , c = 4$
D) $a = - 81 , b = 0 , c = 4$
E) $a = 4 , b = 0 , c = - 81$

Question 56

Use the graph to solve the following equation. $$\sqrt { x + 2 } = 1$$

A) $x =$ 0
B) $x =$ -1
C) $x =$ 1
D) $x =$ -2
E) $x =$ -3

Question 57

Find the x- and y-intercepts: $$y = x ^ { 2 } + 18 x + 81$$

A) (9,0), (0, 0); (0,81)
B) (-9,0); (0,-81)
C) (-9, 0); (0, 81)
D) (-9,0), (9,0); (0,81)
E) (9,0); (0,81)

Question 58

Solve and check: $$0 = 7 - \sqrt { - 6 + 7 v }$$

A) $\frac { \sqrt { 7 } + 6 } { 7 }$
B) $\frac { 55 } { 7 }$
C) $\frac { 169 } { 49 }$
D) $\frac { 169 } { 7 }$
E) No solution

Question 59

The time required for a dropped object to hit the ground is given by $t \equiv \sqrt { \frac { 2 h } { g } }$ , where h is the vertical distance traveled and g is the acceleration due to gravity, assumed to be 32.2 feet per second squared. How tall a building is required for an object to take 9 seconds to fall to the ground?

A) h = 2,409.1 feet
B) h = 1,142.8 feet
C) h = 1,304.1 feet
D) h = 2,035.1 feet
E) h = 3,865.4 feet

Question 60

Assume a clear day and flat terrain in the nearby region. How far could you see, in miles, from the top of this building whose height is given? Transamerica Pyramid, San Francisco, h = 853 feet
On Earth, the distance to the horizon is given by $d \approx \sqrt { \frac { 3 h } { 2 } }$ , where d is in miles to the horizon and h is in feet above sea level. Please round your answer to the nearest tenth.

A) 44.1 miles
B) 37.8 miles
C) 35.8 miles
D) 39.4 miles
E) 47.4 miles

Question 61

Write a two-variable quadratic equation with a = 16, b = 0, and c = -36.

A) $y = 16 x ^ { 2 } + 36$
B) $y = 16 x ^ { 2 } - 36$
C) $y = 16 x ^ { 2 } - 36 x$
D) $y = 36 x ^ { 2 } - 16$
E) $y = 36 x ^ { 2 } - 16 x$

Question 62

Write a two-variable quadratic equation with a = 36, b = -12, and c = 1.

A) $y = 36 x ^ { 2 } - 12 x + 1$
B) $y = 12 x ^ { 2 } - 36 x$
C) $y = - 36 x ^ { 2 } + x$
D) $y = x ^ { 2 } - 12 x + 36$
E) $y = 12 x ^ { 2 } - x + 36$

Question 63

Solve by taking square roots: $$v ^ { 2 } - 18 = 0$$

A) $- 3 \sqrt { 2 } , 4 \sqrt { 2 }$
B) $- 3 \sqrt { 2 } , 3 \sqrt { 2 }$ .
C) $- 4 \sqrt { 2 } , 4 \sqrt { 2 }$ .
D) $- 3 \sqrt { 2 } , 3 \sqrt { 2 }$
E) $3 \sqrt { 2 } , 3 \sqrt { 2 }$

Question 64

Solve by taking square roots: $$9 v ^ { 2 } - 4 = 0$$

A) $\frac { 2 } { 3 }$
B) $\frac { 4 } { 9 }$
C) $- \frac { 4 } { 9 } , \frac { 4 } { 9 }$
D) $- \frac { 3 } { 2 } , \frac { 3 } { 2 }$
E) $- \frac { 2 } { 3 } , \frac { 2 } { 3 }$

Question 65

Solve for x: $$( x - 4 ) ( 8 x - 12 ) = 0$$

A) $\frac { 3 } { 2 }$ , 4
B) 1, 4
C) $\frac { 3 } { 2 }$ , 5
D) 0, 5
E) $\frac { 2 } { 3 }$ , 4

Question 66

Solve by factoring: $$x ^ { 2 } + 5 x = - 4$$

A) -4, -1
B) -4, 3
C) -7, -1
D) -4, -3
E) 0, -1

Question 67

Solve by taking square roots: $$121 p ^ { 2 } = 36$$

A) $\frac { 6 } { 11 }$
B) $\frac { 36 } { 121 }$
C) $- \frac { 6 } { 11 } , \frac { 6 } { 11 }$
D) $- \frac { 11 } { 6 } , \frac { 11 } { 6 }$
E) $- \frac { 36 } { 121 } , \frac { 36 } { 121 }$

Question 68

For what values of x is the equation true? $$( x + 5 ) ( x - 8 ) = 0$$

A) $x = 7 \text { or } x = - 8$
B) $x = 6 \text { or } x = - 4$
C) $x = 3 \text { or } x = 6$
D) $x = - 5 \text { or } x = 8$
E) $x = - 7 \text { or } x = - 4$

Question 69

Solve for x: $$x ( x - 2 ) = 0$$

A) 0, 1
B) 1, 2
C) 0, 2
D) 0, 3
E) 1, 1

Question 70

Name a, b, and c. $$x = 6 - 3 x ^ { 2 }$$

A) $a = 3 , b = - 6 , c = 1$
B) $a = 3 , b = 1 , c = - 6$
C) $a = 6 , b = 3 , c = 0$
D) $a = 1 , b = 3 , c = - 6$
E) $a = 6 , b = 0 , c = 3$

Question 71

Name a, b, and c. Area of a circle: $$A = \pi r ^ { 2 }$$

A) $a = 0 , b = 0 , c = \pi$
B) $a = - \pi , b = 0 , c = 0$
C) $a = 0 , b = 0 , c = - \pi$
D) $a = 0 , b = \pi , c = \pi$
E) $a = \pi , b = 0 , c = 0$

Question 72

Solve by taking square roots: $p ^ { 2 } - 4 = 0$

A) -2, 1
B) -1, 2
C) -1, 1
D) -2, 3
E) -2, 2

Question 73

Solve by factoring: $x ^ { 2 } - 9 = 0$

A) -3, 4
B) -2, -3
C) 2, -7
D) -3, 3
E) 4, -3

Question 74

Solve by taking square roots: $v ^ { 2 } = 1$

A) -1, 0
B) 0, 1
C) -1, 1
D) -1, 2
E) 0, 0

Question 75

Solve by factoring: $$9 y ^ { 2 } + 7 y = 0$$

A) $\frac { 7 } { 9 }$ , 0
B) 1, 0
C) $- \frac { 7 } { 9 }$ , 0
D) 0, 1
E) $- \frac { 9 } { 7 }$ , 0

Question 76

Write a two-variable quadratic equation with a = 4, b = 8, and c = 0.

A) $y = 4 x ^ { 2 } + 8$
B) $y = 8 x ^ { 2 } + 4 x$
C) $y = 4 x ^ { 2 } + 8 x$
D) $y = - 8 x ^ { 2 } + 4$
E) $y = 4 x ^ { 2 } - 8$

Question 77

For what values of x is the equation true? $$( 2 x + 1 ) ( 5 x - 9 ) = 0$$

A) $x = - \frac { 1 } { 3 } \text { or } x = \frac { 11 } { 6 }$
B) $x = - \frac { 1 } { 5 } \text { or } x = - \frac { 6 } { 11 }$
C) $x = \frac { 1 } { 3 } \text { or } x = - \frac { 5 } { 9 }$
D) $x = - \frac { 1 } { 2 } \text { or } x = \frac { 6 } { 11 }$
E) $x = - \frac { 1 } { 2 } \text { or } x = \frac { 9 } { 5 }$

Question 78

Name a, b, and c. Angle swept in time t for circular motion: $$A = 0.5 \alpha t ^ { 2 } + w t$$

A) $a = w , b = 0 , c = 0.5 \alpha$
B) $a = 0 , b = w , c = 0.5 \alpha$
C) $a = 0.5 \alpha , b = 0 , c = w$
D) $a = 0.5 \alpha , b = w , c = 0$
E) $a = w , b = 0.5 \alpha , c = 0$

Question 79

Assume that the formula $h = h _ { 0 } - \frac { 1 } { 2 } g t ^ { 2 }$ holds true. Let g = 32.2 feet per second squared. Suppose a drop of water starts at the top of the falls and descends 130 feet. How long will it take the drop to reach halfway? How long will it take the drop to reach the bottom? Please round answers to the nearest tenth.

A) 2.4 sec; 3.2 sec
B) 2.2 sec; 3.0 sec
C) 2.0 sec; 3.0 sec
D) 2.2 sec; 2.8 sec
E) 2.0 sec; 2.8 sec

Question 80

Solve by factoring: $$x ^ { 2 } - 15 x + 50 = 0$$

A) 5, 10
B) 5, 12
C) 3, 10
D) 5, 8
E) 6, 10