Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

A)  $\frac { - 12 \pm \sqrt { 59 } } { 10 }$ 
B)  $\frac { - 12 \pm \sqrt { 229 } } { 5 }$ 
C)  $\frac { - 24 \pm \sqrt { 59 } } { 5 }$ 
D)  $\frac { - 12 \pm \sqrt { 59 } } { 5 }$ 
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 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

A)  $\frac { - 4 \pm \sqrt { 13 } } { 3 }$ 
B)  $\frac { - 4 \pm \sqrt { 13 } } { 6 }$ 
C)  $\frac { - 4 \pm \sqrt { 19 } } { 3 }$ 
D)  $\frac { - 8 \pm \sqrt { 13 } } { 3 }$ 
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 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

A)  $\frac { - 3 - 3 \sqrt { 5 } } { 2 }$ 
B)  $- 3 \pm 3 \sqrt { 5 }$ 
C)  $\frac { - 3 \pm 3 \sqrt { 5 } } { 2 }$ 
D)  $\frac { 3 + 3 \sqrt { 5 } } { 2 }$ 
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 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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 $( - 10,0 )$ 
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 11

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?

Accepted Answer

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

Question 12

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

Accepted Answer

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)  $\frac { 3 } { 14 } \pm \frac { \sqrt { 47 } } { 14 }$ 
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 13

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

Accepted Answer

A)  $- 4 + \sqrt { 2 } , - 4 - \sqrt { 2 }$ 
B)  $- 4 + i \sqrt { 2 } , - 4 - i \sqrt { 2 }$ 
C)  $- 2 + \sqrt { 2 } , - 2 - \sqrt { 2 }$ 
D)  $- 2,6$ 
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 14

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?

Accepted Answer

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 
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 15

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

Accepted Answer

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 
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 16

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

Accepted Answer

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)  $2 \sqrt { 6 } , - 2 \sqrt { 6 }$ 
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 17

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?

Accepted Answer

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

Question 18

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

Accepted Answer

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)  $- \frac { 1 } { 2 } \pm \frac { \sqrt { 11 } } { 2 } \mathrm { i }$ 
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 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

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)  $- \frac { 5 } { 8 } + \frac { \sqrt { 6 } } { 16 } , - \frac { 5 } { 8 } - \frac { \sqrt { 6 } } { 16 }$ 
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)  $- \frac { 5 } { 8 } + \frac { \sqrt { 6 } } { 16 } , - \frac { 5 } { 8 } - \frac { \sqrt { 6 } } { 16 }$

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

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

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

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

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

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

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

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

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

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

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?

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

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

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?

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

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

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

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

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

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Exponential Functions and Logarithmic Functions

Finding Measures of Central Tendency for Prices and Heights

Filters

Exam 11: Quadratic Equations and Functions

Solve. - 2x+2x+3=1\frac { 2 } { x } + \frac { 2 } { x + 3 } = 1x2​+x+32​=1

Solve. - 5r2+24r=−175 r ^ { 2 } + 24 r = - 175r2+24r=−17

Solve by completing the square. - q2+8q−3=0\mathrm { q } ^ { 2 } + 8 \mathrm { q } - 3 = 0q2+8q−3=0

Solve. - 3n2=−8n−13 n ^ { 2 } = - 8 n - 13n2=−8n−1

Solve the equation by completing the square. - 9m2+4m=09 m ^ { 2 } + 4 m = 09m2+4m=0

Solve the equation by completing the square. - 5x2−4x−9=05 x ^ { 2 } - 4 x - 9 = 05x2−4x−9=0

Solve. Round results to the nearest thousandth. - 9x2−2x−8=09 x ^ { 2 } - 2 x - 8 = 09x2−2x−8=0

Solve by completing the square. - y2+3y−9=0y ^ { 2 } + 3 y - 9 = 0y2+3y−9=0

Solve. Give exact solutions. - x2−12x+36=9x ^ { 2 } - 12 x + 36 = 9x2−12x+36=9

Find the x-intercepts. - f(x)=x2+10xf ( x ) = x ^ { 2 } + 10 xf(x)=x2+10x