Deck 11: Quadratic Equations and Functions

Question 1

Solve. Give exact solutions.
$$( x - 3 ) ^ { 2 } = 4$$

A) 7
B) $1 , - 5$
C) 5,1
D) $2 , - 2$

Answer 1

C

Question 2

Solve. Give exact solutions.
$$x ^ { 2 } + \frac { 5 } { 8 } x + \frac { 25 } { 256 } = \frac { 3 } { 128 }$$

A) $- \frac { 5 } { 16 } + \frac { \sqrt { 6 } } { 16 } , - \frac { 5 } { 16 } - \frac { \sqrt { 6 } } { 16 }$
B) $- \frac { 5 } { 8 } + \frac { \sqrt { 6 } } { 8 } , - \frac { 5 } { 8 } - \frac { \sqrt { 6 } } { 8 }$
C) $- \frac { 5 } { 8 } + \frac { \sqrt { 6 } } { 16 } , \frac { 5 } { 8 } + \frac { \sqrt { 6 } } { 16 }$
D) $- \frac { 5 } { 8 } + \frac { \sqrt { 6 } } { 16 } , - \frac { 5 } { 8 } - \frac { \sqrt { 6 } } { 16 }$

Answer 2

A

Question 3

Solve. Give exact solutions.
$$y ^ { 2 } = 6$$

A) 3
B) $\pm \sqrt { 6 }$
C) $\sqrt { 6 }$
D) 36

Answer 3

B

Question 4

Solve. Give exact solutions.
$- 7 \mathrm { k } ^ { 2 } - 11 = - 123$

A) $- 61.5$
B) $\pm 4$
C) 4
D) $\pm 8$

Question 5

Solve. Give exact solutions.
$$3 z ^ { 2 } + 12 = 0$$

A) $\pm 2 \mathrm { i }$
B) $2 \mathrm { i }$
C) 2
D) $\pm 2$

Question 6

Find the x-intercepts.
$$f ( x ) = x ^ { 2 } + 10 x$$

A) No x-intercept
B) $x$ -intercepts $( 0 , - 10 )$ and $( - 10,0 )$
C) x-intercepts $( 0,0 )$ and $( 10,0 )$
D) $x$ -intercepts $( 0,0 )$ and $( - 10,0 )$

Question 7

Solve. Give exact solutions.
$$x ^ { 2 } - 12 x + 36 = 9$$

A) 15
B) 9,3
C) $3 , - 9$
D) $3 , - 3$

Question 8

Solve. Give exact solutions.
$$( x + 4 ) ^ { 2 } - 2 = 0$$

A) $- 4 + \sqrt { 2 } , - 4 - \sqrt { 2 }$
B) $- 4 + i \sqrt { 2 } , - 4 - i \sqrt { 2 }$
C) $- 2 + \sqrt { 2 } , - 2 - \sqrt { 2 }$
D) $- 2,6$

Question 9

Solve. Give exact solutions.
$( p - 9 ) ^ { 2 } = 17$

A) $\sqrt { 17 } + 9$
B) $\sqrt { 17 } - 9 , - \sqrt { 17 } - 9$
C) $\sqrt { 17 } + 9 , - \sqrt { 17 } + 9$
D) $\sqrt { 17 } - \sqrt { - 9 }$

Question 10

Solve. Give exact solutions.
$$( x + 16 ) ^ { 2 } - 3 = 0$$

A) $- 4 \pm \sqrt { 3 }$
B) $16 \pm \sqrt { 3 }$
C) $- 13,19$
D) $- 16 \pm \sqrt { 3 }$

Question 11

Solve. Give exact solutions.
$$( x - 1 ) ^ { 2 } = - 16$$

A) $1 \pm 4 \mathrm { i }$
B) $1 \pm 4$
C) $4 \mathrm { i }$
D) $4 \mathrm { i } + 1$

Question 12

Solve. Give exact solutions.
$$x ^ { 2 } + 8 x + 16 = 17$$

A) $\sqrt { 17 } , \sqrt { 17 }$
B) 13
C) $- 4 + \sqrt { 17 } , - 4 - \sqrt { 17 }$
D) $4 + \sqrt { 17 } , 4 - \sqrt { 17 }$

Question 13

Solve. Give exact solutions.
$$( r + 4 ) ^ { 2 } = 17$$

A) $- 4 + \sqrt { 17 } , - 4 - \sqrt { 17 }$
B) $\sqrt { 17 } , \sqrt { 17 }$
C) 13
D) $4 + \sqrt { 17 } , 4 - \sqrt { 17 }$

Question 14

Solve. Give exact solutions.
$$64 x ^ { 2 } + 36 = 0$$

A) $\pm \frac { 3 } { 4 } \mathrm { i }$
B) $\frac { 3 } { 4 } \pm i$
C) $\pm \frac { 3 } { 4 } + i$
D) $\pm \frac { 3 } { 4 }$

Question 15

Solve. Give exact solutions.
$$4 x ^ { 2 } = 44$$

A) 12
B) 22
C) $\pm \sqrt { 11 }$
D) $\pm 11$

Question 16

Solve. Give exact solutions.
$$x ^ { 2 } = 100$$

A) 50
B) $\pm 11$
C) $\pm 10$
D) 10

Question 17

Find the x-intercepts.
$$f ( x ) = x ^ { 2 } - 5$$

A) $x$ -intercepts $( \sqrt { 5 } , 0 )$ and $( - \sqrt { 5 } , 0 )$
B) $x$ -intercepts $( 0,5 )$ and $( 0 , - 5 )$
C) $x$ -intercepts $( 0 , \sqrt { 5 } )$ and $( 0 , - \sqrt { 5 } )$
D) No x-intercepts

Question 18

Solve. Give exact solutions.
$$( x + 4 ) ^ { 2 } = 24$$

A) $- 4 + 2 \sqrt { 12 } , - 4 - 2 \sqrt { 12 }$
B) $- 4 + 2 \sqrt { 6 } , - 4 - 2 \sqrt { 6 }$
C) $2 \sqrt { 6 } - 4,2 \sqrt { 6 } + 4$
D) $2 \sqrt { 6 } , - 2 \sqrt { 6 }$

Question 19

Solve. Give exact solutions.
$$x ^ { 2 } + 8 x + 16 = 24$$

A) $2 \sqrt { 6 } - 4,2 \sqrt { 6 } + 4$
B) $2 \sqrt { 6 } , - 2 \sqrt { 6 }$
C) $- 4 + 2 \sqrt { 12 } , - 4 - 2 \sqrt { 12 }$
D) $- 4 + 2 \sqrt { 6 } , - 4 - 2 \sqrt { 6 }$

Question 20

Solve. Give exact solutions.
$$x ^ { 2 } + 3 = 172$$

A) $\pm 12$
B) 86
C) $\pm 13$
D) 13

Question 21

Solve by completing the square.
$$\mathrm { y } ^ { 2 } + 4 \mathrm { y } - 3 = 0$$

A) $- 1 \pm \sqrt { 7 }$
B) $- 2 \pm 2 \sqrt { 7 }$
C) $- 2 \pm \sqrt { 7 }$
D) $2 + \sqrt { 7 }$

Question 22

Solve the equation by completing the square.
$$x ^ { 2 } + x + 6 = 0$$

A) $- \frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 }$
B) $\frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 }$
C) $\frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 } \mathrm { i }$
D) $- \frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 } i$

Question 23

Solve the equation by completing the square.
$$z ^ { 2 } + 10 z + 12 = 0$$

A) $5 \pm 2 \sqrt { 3 }$
B) $5 + \sqrt { 13 }$
C) $- 5 \pm \sqrt { 13 }$
D) $- 10 + 2 \sqrt { 3 }$

Question 24

Solve by completing the square.
$$y ^ { 2 } = - 3 y + 9$$

A) $- 3 \pm 3 \sqrt { 5 }$
B) $\frac { - 3 - 3 \sqrt { 5 } } { 2 }$
C) $\frac { - 3 \pm 3 \sqrt { 5 } } { 2 }$
D) $\frac { 3 + 3 \sqrt { 5 } } { 2 }$

Question 25

Solve by completing the square.
$$x ^ { 2 } + 5 x - 5 = 0$$

A) $- 5 \pm 3 \sqrt { 5 }$
B) $\frac { - 5 - 3 \sqrt { 5 } } { 2 }$
C) $\frac { - 5 \pm 3 \sqrt { 5 } } { 2 }$
D) $\frac { 5 + 3 \sqrt { 5 } } { 2 }$

Question 26

Find the x-intercepts.
$$f ( x ) = 2 x ^ { 2 } - 10 x + 12$$

A) $x$ -intercepts $( - 3,0 )$ and $( - 2,0 )$
B) $x$ -intercepts $( 3,0 )$ and $( - 2,0 )$
C) $x$ -intercepts $( 3,0 )$ and $( 2,0 )$
D) $x$ -intercepts $( - 3,0 )$ and $( 2,0 )$

Question 27

Find the x-intercepts.
$$f ( x ) = 2 x ^ { 2 } - 13 x - 45$$

A) $x$ -intercepts $( 9,0 )$ and $\left( \frac { 5 } { 2 } , 0 \right)$
B) No x-intercepts
C) x-intercepts $( 9,0 )$ and $\left( - \frac { 5 } { 2 } , 0 \right)$
D) $x$ -intercepts $( - 5,0 )$ and $\left( \frac { 9 } { 2 } , 0 \right)$

Question 28

Solve by completing the square.
$$y ^ { 2 } + 3 y - 9 = 0$$

A) $\frac { - 3 - 3 \sqrt { 5 } } { 2 }$
B) $- 3 \pm 3 \sqrt { 5 }$
C) $\frac { - 3 \pm 3 \sqrt { 5 } } { 2 }$
D) $\frac { 3 + 3 \sqrt { 5 } } { 2 }$

Question 29

Solve the equation by completing the square.
$$a ^ { 2 } - 10 a + 9 = 0$$

A) $- 9 , - 1$
B) 8,1
C) $\sqrt { 9 } , - \sqrt { 9 }$
D) 9,1

Question 30

Solve the equation by completing the square.
$30 \mathrm {~d} ^ { 2 } + 61 \mathrm {~d} + 30 = 0$

A) $- \frac { 6 } { 5 } , - \frac { 6 } { 5 }$
B) $\frac { 5 } { 6 } , \frac { 6 } { 5 }$
C) $- \frac { 5 } { 6 } , - \frac { 6 } { 5 }$
D) $\frac { 6 } { 5 } , \frac { 5 } { 6 }$

Question 31

Solve the equation by completing the square.
$$5 x ^ { 2 } - 4 x - 9 = 0$$

A) $\frac { 5 } { 9 } , 1$
B) $\frac { 5 } { 9 } , - 1$
C) $\frac { 5 } { 9 } , 0$
D) $\frac { 9 } { 5 } , - 1$

Question 32

Find the x-intercepts.
$$25 x ^ { 2 } + 4 = 0$$

A) No x-intercepts
B) x-intercepts $\left( 0 , - i \sqrt { \frac { 2 } { 5 } } \right) , \left( 0 , i \sqrt { \frac { 2 } { 5 } } \right)$
C) $x$ -intercepts $\left( - \sqrt { \frac { 2 } { 5 } } , 0 \right) , \left( \sqrt { \frac { 2 } { 5 } } , 0 \right)$
D) $x$ -intercepts $\left( - i \sqrt { \frac { 2 } { 5 } } , 0 \right) , \left( i \sqrt { \frac { 2 } { 5 } } , 0 \right)$

Question 33

Solve the equation by completing the square.
$$9 m ^ { 2 } + 4 m = 0$$

A) 0
B) $\pm \frac { 4 } { 9 }$
C) $- \frac { 4 } { 9 } , 0$
D) $\frac { 4 } { 9 } , 0$

Question 34

Solve by completing the square.
$$z ^ { 2 } + 8 z - 5 = 0$$

A) $- 4 \pm 2 \sqrt { 21 }$
B) $- 1 \pm \sqrt { 21 }$
C) $4 + \sqrt { 21 }$
D) $- 4 \pm \sqrt { 21 }$

Question 35

Solve by completing the square.
$$\mathrm { q } ^ { 2 } + 8 \mathrm { q } - 3 = 0$$

A) $4 + \sqrt { 19 }$
B) $- 4 \pm \sqrt { 19 }$
C) $- 4 \pm 2 \sqrt { 19 }$
D) $- 1 \pm \sqrt { 19 }$

Question 36

Solve the equation by completing the square.
$$\mathrm { p } ^ { 2 } + 5 \mathrm { p } - 5 = 0$$

A) $- \frac { 5 } { 2 } \pm \frac { 3 \sqrt { 5 } } { 2 }$
B) $- \frac { 5 } { 2 } + \frac { 3 \sqrt { 5 } } { 2 }$
C) $- 5 \pm 3 \sqrt { 5 }$
D) $\frac { 5 } { 2 } \pm \frac { 3 \sqrt { 5 } } { 2 }$

Question 37

Find the x-intercepts.
$$f ( x ) = - x ^ { 2 } + 17 x - 72$$

A) $x$ -intercepts $( - 8,0 )$ and $( - 9,0 )$
B) $x$ -intercepts $( 8,0 )$ and $( 9,0 )$
C) No $x$ -intercepts
D) $x$ -intercepts $( 8,0 )$ and $( - 9,0 )$

Question 38

Solve the equation by completing the square.
$$x ^ { 2 } - 14 x + 74 = 0$$

A) $7 \pm 5 \mathrm { i }$
B) $- 7 \pm 5 \mathrm { i }$
C) $14 \pm 10 \mathrm { i }$
D) 12,2

Question 39

Solve by completing the square.
$$x ^ { 2 } = 7 - 8 x$$

A) $- 4 \pm \sqrt { 23 }$
B) $4 + \sqrt { 23 }$
C) $- 4 \pm 2 \sqrt { 23 }$
D) $- 1 \pm \sqrt { 23 }$

Question 40

Solve by completing the square.
$$x ^ { 2 } + 4 x = 7$$

A) $2 + \sqrt { 11 }$
B) $- 1 \pm \sqrt { 11 }$
C) $- 2 \pm \sqrt { 11 }$
D) $- 2 \pm 2 \sqrt { 11 }$

Question 41

Solve.
$5 m ^ { 2 } + 12 m + 5 = 0$

A) $\frac { - 6 \pm \sqrt { 11 } } { 5 }$
B) $\frac { - 12 \pm \sqrt { 11 } } { 5 }$
C) $\frac { - 6 \pm \sqrt { 11 } } { 10 }$
D) $\frac { - 6 \pm \sqrt { 61 } } { 5 }$

Question 42

Solve the problem. Give the answer to the nearest tenth.
A ball is thrown downward from a window in a tall building. Its position at time $t$ in seconds is $\mathrm { s } = 16 \mathrm { t } ^ { 2 } + 32 \mathrm { t }$ , where $s$ is in feet. How long (to the nearest tenth) will it take the ball to fall 280 feet?

A) $3.3 \mathrm { sec }$
B) $10.9 \mathrm { sec }$
C) $3.1 \mathrm { sec }$
D) $4.2 \mathrm { sec }$

Question 43

Solve.
$$4 x ^ { 2 } = 5 x - 6$$

A) $\frac { 5 } { 8 } \pm \frac { \sqrt { 71 } } { 8 } \mathrm { i }$
B) $\frac { 5 } { 8 } \pm \frac { \sqrt { 71 } } { 8 }$
C) $- \frac { 5 } { 8 } \pm \frac { \sqrt { 71 } } { 8 }$
D) $- \frac { 5 } { 8 } \pm \frac { \sqrt { 71 } } { 8 } i$

Question 44

Solve.
$$6 x ^ { 2 } = - 16 x - 1$$

A) $\frac { - 8 \pm \sqrt { 70 } } { 6 }$
B) $\frac { - 16 \pm \sqrt { 58 } } { 6 }$
C) $\frac { - 8 \pm \sqrt { 58 } } { 6 }$
D) $\frac { - 8 \pm \sqrt { 58 } } { 12 }$

Question 45

Solve.
$$x ^ { 2 } + x + 4 = 0$$

A) $\frac { 1 } { 2 } \pm \frac { \sqrt { 15 } } { 2 }$ i
B) $- \frac { 1 } { 2 } \pm \frac { \sqrt { 15 } } { 2 } i$
C) $- \frac { 1 } { 2 } \pm \frac { \sqrt { 15 } } { 2 }$
D) $\frac { 1 } { 2 } \pm \frac { \sqrt { 15 } } { 2 }$

Question 46

Solve.
$$9 x ^ { 2 } = - 20 x - 3$$

A) $\frac { - 10 \pm \sqrt { 73 } } { 18 }$
B) $\frac { - 10 \pm \sqrt { 127 } } { 9 }$
C) $\frac { - 20 \pm \sqrt { 73 } } { 9 }$
D) $\frac { - 10 \pm \sqrt { 73 } } { 9 }$

Question 47

Solve.
$$2 x ^ { 2 } + 6 x = - 1$$

A) $\frac { - 3 \pm \sqrt { 7 } } { 4 }$
B) $\frac { - 6 \pm \sqrt { 7 } } { 2 }$
C) $\frac { - 3 \pm \sqrt { 11 } } { 2 }$
D) $\frac { - 3 \pm \sqrt { 7 } } { 2 }$

Question 48

Solve.
$$\frac { 2 } { x } + \frac { 2 } { x + 3 } = 1$$

A) $2 , - 3$
B) 2
C) 3
D) $- 2,3$

Question 49

Solve.
$$7 x ^ { 2 } + 3 x + 2 = 0$$

A) $- \frac { 3 } { 14 } \pm \frac { \sqrt { 47 } } { 14 }$
B) $\frac { 3 } { 14 } \pm \frac { \sqrt { 47 } } { 14 } \mathrm { i }$
C) $- \frac { 3 } { 14 } \pm \frac { \sqrt { 47 } } { 14 } \mathrm { i }$
D) $\frac { 3 } { 14 } \pm \frac { \sqrt { 47 } } { 14 }$

Question 50

Find the x-intercepts.
$$f ( x ) = 3 x + x ( x - 5 )$$

A) $( 0,0 )$ and $( 2,0 )$
B) $( - 2,0 )$
C) $( 0,0 )$ and $( - 2,0 )$
D) $( 2,0 )$

Question 51

Solve.
$$3 = - \frac { 8 } { x } - \frac { 1 } { x ^ { 2 } }$$

A) $\frac { - 4 \pm \sqrt { 19 } } { 3 }$
B) $\frac { - 4 \pm \sqrt { 13 } } { 3 }$
C) $\frac { - 4 \pm \sqrt { 13 } } { 6 }$
D) $\frac { - 8 \pm \sqrt { 13 } } { 3 }$

Question 52

Solve.
$38 m ^ { 2 } + 48 m + 11 = 0$

A) $\frac { - 24 \pm \sqrt { 994 } } { 38 }$
B) $\frac { - 24 \pm \sqrt { 158 } } { 76 }$
C) $\frac { - 48 \pm \sqrt { 158 } } { 38 }$
D) $\frac { - 24 \pm \sqrt { 158 } } { 38 }$

Question 53

Solve the problem. Give the answer to the nearest tenth.
The position of an object moving in a straight line is given by $\mathrm { s } = \mathrm { t } ^ { 2 } - 8 \mathrm { t }$ , where $\mathrm { s }$ is in feet and $\mathrm { t }$ is the time in seconds the object has been in motion. How long (to the nearest tenth) will it take the object to move 16 feet?

A) $12.8 \mathrm { sec }$
B) $9.7 \mathrm { sec }$
C) $17.0 \mathrm { sec }$
D) $9.5 \mathrm { sec }$

Question 54

Solve the problem. Give the answer to the nearest tenth.
The position of an object moving in a straight line is given by $s = 2 t ^ { 2 } - 3 t$ , where s is in meters and $t$ is the time in seconds the object has been in motion. How long (to the nearest tenth) will it take the object to move 9 meters?

A) $3.0 \mathrm { sec }$
B) $13.5 \mathrm { sec }$
C) $10.0 \mathrm { sec }$
D) $2.8 \mathrm { sec }$

Question 55

Find the x-intercepts.
$$f ( x ) = 3 x ^ { 2 } - 5 x - 1$$

A) $\left( \frac { 5 + \sqrt { 37 } } { 6 } , 0 \right)$ and $\left( \frac { 5 - \sqrt { 37 } } { 6 } , 0 \right)$
B) $\left( \frac { - 5 + \sqrt { 37 } } { 6 } , 0 \right)$ and $\left( \frac { - 5 - \sqrt { 37 } } { 6 } , 0 \right)$
C) $\left( \frac { 5 + \sqrt { 13 } } { 6 } , 0 \right)$ and $\left( \frac { 5 - \sqrt { 13 } } { 6 } , 0 \right\}$
D) $\left\{ \frac { - 5 + \sqrt { 13 } } { 6 } , 0 \right)$ and $\left( \frac { - 5 - \sqrt { 13 } } { 6 } , 0 \right)$

Question 56

Solve.
$$4 x ^ { 2 } - 3 x = - 4$$

A) $- \frac { 3 } { 8 } \pm \frac { \sqrt { 55 } } { 8 } i$
B) $- \frac { 3 } { 8 } \pm \frac { \sqrt { 55 } } { 8 }$
C) $\frac { 3 } { 8 } \pm \frac { \sqrt { 55 } } { 8 }$
D) $\frac { 3 } { 8 } \pm \frac { \sqrt { 55 } } { 8 } \mathrm { i }$

Question 57

Solve.
$$5 r ^ { 2 } + 24 r = - 17$$

A) $\frac { - 12 \pm \sqrt { 59 } } { 10 }$
B) $\frac { - 12 \pm \sqrt { 229 } } { 5 }$
C) $\frac { - 24 \pm \sqrt { 59 } } { 5 }$
D) $\frac { - 12 \pm \sqrt { 59 } } { 5 }$

Question 58

Solve.
$$\frac { 1 } { x } + \frac { 3 } { x ^ { 2 } } = - 1$$

A) $\frac { 1 } { 2 } \pm \frac { \sqrt { 11 } } { 2 } \mathrm { i }$
B) $\frac { 1 } { 2 } \pm \frac { \sqrt { 11 } } { 2 }$
C) $- \frac { 1 } { 2 } \pm \frac { \sqrt { 11 } } { 2 }$
D) $- \frac { 1 } { 2 } \pm \frac { \sqrt { 11 } } { 2 } \mathrm { i }$

Question 59

Solve the problem. Give the answer to the nearest tenth.
The hang-time function $V ( T ) = 48 \mathrm {~T} ^ { 2 }$ , relates vertical leap to hang time. A player has a vertical leap of 30 in. What is his hang time?

A) $0.6 \mathrm { sec }$
B) $37.9 \mathrm { sec }$
C) $1.3 \mathrm { sec }$
D) $0.8 \mathrm { sec }$

Question 60

Solve.
$$3 n ^ { 2 } = - 8 n - 1$$

A) $\frac { - 4 \pm \sqrt { 13 } } { 3 }$
B) $\frac { - 4 \pm \sqrt { 13 } } { 6 }$
C) $\frac { - 4 \pm \sqrt { 19 } } { 3 }$
D) $\frac { - 8 \pm \sqrt { 13 } } { 3 }$

Question 61

Solve.
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)4 cm
C)12 cm
D)3 cm

Question 62

Find the x-intercepts.
$$f ( x ) = 64 x ^ { 2 } - 32 x + 4$$

A) No x-intercepts
B) $\left( - \frac { 1 } { 4 } , 0 \right)$
C) $\left( \frac { 1 } { 4 } , 0 \right)$ and $\left( - \frac { 1 } { 4 } , 0 \right)$
D) $\left( \frac { 1 } { 4 } , 0 \right)$

Question 63

Solve.
Bill can row 3 mph in still water. It takes him 3 hours 36 minutes to go 3 miles upstream and return. Find the speed of the current.

A)1.5 mph
B)2.5 mph
C)2 mph
D)3 mph

Question 64

Solve.
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)10 ft
B)6 ft
C)12 ft
D)8 ft

Question 65

Solve.
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 13 feet by 21 feet and the area of the rug is 153 square feet, how wide will the border be?

A)3 ft
B)2 ft
C)4.5 ft
D)4 ft

Question 66

Find the x-intercepts.
$$f ( x ) = 2 x ^ { 2 } - 3 x - 4$$

A) $\left( \frac { 3 + \sqrt { 41 } } { 4 } , 0 \right)$ and $\left( \frac { 3 - \sqrt { 41 } } { 4 } , 0 \right)$
B) No x-intercepts
C) $\left( \frac { 3 + \sqrt { 29 } } { 4 } , 0 \right)$ and $\left( \frac { 3 - \sqrt { 29 } } { 4 } , 0 \right)$
D) $( 0,0 )$ and $( 4,0 )$

Question 67

Solve.
A lot is in the shape of a right triangle. The shorter leg measures 180 m. The hypotenuse is 60 m longer than the length of the longer leg. How long is the longer leg?

A)300 m
B)240 m
C)360 m
D)180 m

Question 68

Solve. Round results to the nearest thousandth.
$$5 \mathrm { x } ^ { 2 } = 10 + 14 \mathrm { x }$$

A) $1.600,1.200$
B) $0.590 , - 3.390$
C) $- 1.200 , - 1.600$
D) $3.390 , - 0.590$

Question 69

Solve.
A square has an area of 49 square inches. If the same amount is added to the length and removed from the width, the resulting rectangle has an area of 45 square inches. Find the dimensions of the rectangle.

A)4 in. by 9 in.
B)3 in. by 4 in.
C)5 in. by 10 in.
D)5 in. by 9 in.

Question 70

Solve. Round results to the nearest thousandth.
$$2 y ^ { 2 } + 6 y = - 4$$

A) $- 1.000 , - 2.000$
B) $- 2.000 , - 4.000$
C) $2.000,1.000$
D) $0.562 , - 3.562$

Question 71

Solve. Round results to the nearest thousandth.
$$x ^ { 2 } - 10 x - 36 = 0$$

A) $23.276 , - 13.276$
B) $12.810 , - 2.810$
C) $13.276 , - 23.276$
D) $2.810 , - 12.810$

Question 72

Solve.
Sue rowed her boat across Lake Bend and back in 3 hours. If her rate returning was 2 mph less than the rate going, and if the distance each way was 7 miles, find her rate going.

A)1.5 mph
B)3.7 mph
C)5.5 mph
D)5.9 mph

Question 73

Solve.
A picture 13 inches by 23 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 border is 252 square inches?

A)4 in
B)3 in
C)5 in
D)5.5 in

Question 74

Solve. Round results to the nearest thousandth.
$$3 x ^ { 2 } - 6 x = 2$$

A) $0.291 , - 2.291$
B) $2.291 , - 0.291$
C) $4.582 , - 0.582$
D) $1.577,0.423$

Question 75

Solve.
A rectangular garden has dimensions of 23 feet by 20 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 294 square feet?

A)5.5 ft
B)4 ft
C)5 ft
D)3 ft

Question 76

Solve.
Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 15 mi, the distance between the cars was 5 mi more than the distance traveled by the car heading east. How far had
The eastbound car traveled?

A)15 mi
B)30 mi
C)20 mi
D)25 mi

Question 77

Solve. Round results to the nearest thousandth.
$$x ^ { 2 } - 8 x = 6$$

A) $12.690,12.690$
В) $7.162,0.838$
C) $8.690 , - 0.690$
D) $0.690 , - 8.690$

Question 78

Solve. Round results to the nearest thousandth.
$9 x ^ { 2 } - 2 x - 8 = 0$

A) $1.060 , - 0.838$
B) $0.537 , - 0.759$
C) $0.838 , - 1.060$
D) $0.759 , - 0.537$

Question 79

Solve.
A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time for the trip was 5 hours. If his rate when he was riding a bicycle was 10 miles per hour faster than his rate walking, what was each rate?

A)Bike: 11.5 mph
B)Bike: 12 mph
C)Bike: 14.5 mph
D)Bike: 13 mph Hike: 1.5 mph Hike: 2 mph Hike: 4.5 mph Hike: 3 mph

Question 80

Solve.
A jet plane traveling at a constant speed goes 1200 miles with the wind, then turns around and travels for 1000 miles against the wind. If the speed of the wind is 50 mph and the total flight took 4 hours, find the speed of the
Plane in still air.

A)435 mph
B)525 mph
C)550 mph
D)605 mph