Question 1

Solve the equation. $9 x = x ^ { 2 }$

Accepted Answer

A)  $x = 9 , \quad x = 9$ 
B)  $x = 0 , \quad x = - 9$ 
C)  $x = 9$ 
D)  $x = 0 , \quad x = 9$ 
E)  $x = 0$ 
A)  $x = 9 , \quad x = 9$ 
B)  $x = 0 , \quad x = - 9$ 
C)  $x = 9$ 
D)  $x = 0 , \quad x = 9$ 
E)  $x = 0$

Question 2

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $- 4 z ^ { 2 } + z + 6 = 0$

Accepted Answer

The answer of Solve the equation using the quadratic formula...

Question 3

Solve the equation using the quadratic formula. $3 x ^ { 2 } + x - 5 = 0$ Round your answer to three significant digits.

Accepted Answer

A)  x1 = 0.11, x2 = - 0.15 
B)  x1 = 1.14, x2 = - 1.47 
C)  x1 = 1.03, x2 = - 1.58 
D)  x1 = 1.15, x2 = - 1.46 
E)  x1 = 1.25, x2 = - 1.36 
A)  x1 = 0.11, x2 = - 0.15 
B)  x1 = 1.14, x2 = - 1.47 
C)  x1 = 1.03, x2 = - 1.58 
D)  x1 = 1.15, x2 = - 1.46 
E)  x1 = 1.25, x2 = - 1.36

Question 4

Solve the equation. $x ^ { 2 } - 4 x + 3 = 0$

Accepted Answer

A)  $x = + 1$ , $x = - 3$ 
B)  $x = 1$ , $x = 3$ 
C)  $x = - 3$ , $x = - 3$ 
D)  $x = - 1$ , $x = + 3$ 
E)  $x = - 1$ , $x = - 3$ 
A)  $x = + 1$ , $x = - 3$ 
B)  $x = 1$ , $x = 3$ 
C)  $x = - 3$ , $x = - 3$ 
D)  $x = - 1$ , $x = + 3$ 
E)  $x = - 1$ , $x = - 3$

Question 5

Draw the graph of the equation and label the vertex. $y = - \frac { 1 } { 5 } x ^ { 2 }$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

Solve the equation. $4 x ^ { 2 } = 25$

Accepted Answer

A)  $x = - \frac { 5 } { 2 } , x = \frac { 2 } { 5 }$ 
B)  $x = - \frac { 2 } { 5 } , x = \frac { 5 } { 2 }$ 
C)  $x = - \frac { 5 } { 2 } , x = \frac { 5 } { 2 }$ 
D)  $x = - \frac { 5 } { 2 }$ 
E)  $x = - \frac { 2 } { 5 } , x = \frac { 2 } { 5 }$ 
A)  $x = - \frac { 5 } { 2 } , x = \frac { 2 } { 5 }$ 
B)  $x = - \frac { 2 } { 5 } , x = \frac { 5 } { 2 }$ 
C)  $x = - \frac { 5 } { 2 } , x = \frac { 5 } { 2 }$ 
D)  $x = - \frac { 5 } { 2 }$ 
E)  $x = - \frac { 2 } { 5 } , x = \frac { 2 } { 5 }$

Question 7

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 3 }$ ___ $j$

Accepted Answer

The answer of Express the number in terms of j...

Question 8

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $2 x ^ { 2 } + 2 = x$ x = ____ $\pm$ ____j

Accepted Answer

The answer of Solve the quadratic equation using the quadratic...

Question 9

Solve the equation. $x ^ { 2 } + x - 56 = 0$

Accepted Answer

The answer of Solve the equation. \(x ^ { 2...

Question 10

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $$- 3 z ^ { 2 } - 8 = - 7 z ^ { 2 }$$

Accepted Answer

A)  1.41, 1.41 
B)  1.41, -2.41 
C)  2.41, -2.41 
D)  2.41, -1.41 
E)  1.41, -1.41 
A)  1.41, 1.41 
B)  1.41, -2.41 
C)  2.41, -2.41 
D)  2.41, -1.41 
E)  1.41, -1.41

Question 11

A square, $1$ . on a side, is cut out of each corner of a square sheet of aluminum. (See the figure below.) The sides are folded up to form a rectangular container with no top. The volume of the resulting container is $$225 \mathrm { in } ^ { 3 }$$ . What was the size of the original sheet of aluminum?

Accepted Answer

A)  $18 \mathrm { in } \times 18 \mathrm { in }$ 
B)  $17 \text { in } \times 17 \text { in }$ 
C)  $10 \text { in } \times 10 \text { in }$ 
D)  $19 \text { in } \times 19 \text { in }$ 
E)  $16 \text { in } \times 16 \text { in }$ 
A)  $18 \mathrm { in } \times 18 \mathrm { in }$ 
B)  $17 \text { in } \times 17 \text { in }$ 
C)  $10 \text { in } \times 10 \text { in }$ 
D)  $19 \text { in } \times 19 \text { in }$ 
E)  $16 \text { in } \times 16 \text { in }$

Question 12

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $4 x ^ { 2 } + x + 9 = 0$

Accepted Answer

A)  $x = 1.62 , \quad x = 1.62$ 
B)  $x = - 0.063 + 1.50 j , \quad x = - 0.063 - 1.50 j$ 
C)  $x = - 0.125 + 1.50 j , \quad x = - 0.125 - 1.50 j$ 
D)  $x = - 0.063 + 1.49 j , \quad x = - 0.063 - 1.49 j$ 
E)  $x = - 0.125 + 1.49 j , \quad x = - 0.125 - 1.49 j$ 
A)  $x = 1.62 , \quad x = 1.62$ 
B)  $x = - 0.063 + 1.50 j , \quad x = - 0.063 - 1.50 j$ 
C)  $x = - 0.125 + 1.50 j , \quad x = - 0.125 - 1.50 j$ 
D)  $x = - 0.063 + 1.49 j , \quad x = - 0.063 - 1.49 j$ 
E)  $x = - 0.125 + 1.49 j , \quad x = - 0.125 - 1.49 j$

Question 13

A hole in the side of a large metal tank needs to be repaired. A piece of rectangular sheet metal of area $143 \mathrm { ft } ^ { 2 }$ will patch the hole. If the length of the sheet metal must be $2$ ft longer than its width what will the dimensions of the sheet metal be?

Accepted Answer

A)  The width is 44 ft,
The length is 3.25 ft. 
B)  The width is 11 ft,
The length is 13 ft. 
C)  The width is 13 ft,
The length is 11 ft. 
D)  The width is 11 ft,
The length is 11 ft. 
E)  The width is 13 ft,
The length is 13 ft. 
A)  The width is 44 ft,
The length is 3.25 ft. 
B)  The width is 11 ft,
The length is 13 ft. 
C)  The width is 13 ft,
The length is 11 ft. 
D)  The width is 11 ft,
The length is 11 ft. 
E)  The width is 13 ft,
The length is 13 ft.

Question 14

Solve the equation. $2 x ^ { 2 } = 15 x - 7$

Accepted Answer

The answer of Solve the equation. \(2 x ^ {...

Question 15

Solve the equation. $x ^ { 2 } = 64$

Accepted Answer

A)  $x = - 8 , \quad x = - 8$ 
B)  $x = - 64 , \quad x = 8$ 
C)  $x = - 8 , \quad x = 8$ 
D)  $x = - 64 , \quad x = - 8$ 
E)  $x = - 64 , \quad x = 64$ 
A)  $x = - 8 , \quad x = - 8$ 
B)  $x = - 64 , \quad x = 8$ 
C)  $x = - 8 , \quad x = 8$ 
D)  $x = - 64 , \quad x = - 8$ 
E)  $x = - 64 , \quad x = 64$

Question 16

Solve the equation using the quadratic formula. $2 x ^ { 2 } + 5 x - 9 = 0$ Round your answer to three significant digits.

Accepted Answer

The answer of Solve the equation using the quadratic formula....

Question 17

Find the value of a, b, and c in the equation. $7 x ^ { 2 } + 3 x + 5 = 0$

Accepted Answer

A)  a = 5, b = 7, c = 3 
B)  a = 3, b = 5, c = 7 
C)  a = 7, b = -3, c = 5 
D)  a = 7, b = -3, c = -5 
E)  a = 7, b = 3, c = 5 
A)  a = 5, b = 7, c = 3 
B)  a = 3, b = 5, c = 7 
C)  a = 7, b = -3, c = 5 
D)  a = 7, b = -3, c = -5 
E)  a = 7, b = 3, c = 5

Question 18

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $3 x ^ { 2 } = 11 x - 5$

Accepted Answer

A)  4.14, -0.468 
B)  4.14, 0.532 
C)  3.14 
D)  3.14, -0.468 
E)  3.14, 0.532 
A)  4.14, -0.468 
B)  4.14, 0.532 
C)  3.14 
D)  3.14, -0.468 
E)  3.14, 0.532

Question 19

The perimeter of a rectangle is $50$ cm, and its area is $126 \mathrm {~cm} ^ { 2 }$ . Find its dimensions.

Accepted Answer

A)  $7 \mathrm {~cm} \times 18 \mathrm {~cm}$ 
B)  $8 \mathrm {~cm} \times 20 \mathrm {~cm}$ 
C)  $8 \mathrm {~cm} \times 19 \mathrm {~cm}$ 
D)  $6 \mathrm {~cm} \times 19 \mathrm {~cm}$ 
E)  $9 \mathrm {~cm} \times 20 \mathrm {~cm}$ 
A)  $7 \mathrm {~cm} \times 18 \mathrm {~cm}$ 
B)  $8 \mathrm {~cm} \times 20 \mathrm {~cm}$ 
C)  $8 \mathrm {~cm} \times 19 \mathrm {~cm}$ 
D)  $6 \mathrm {~cm} \times 19 \mathrm {~cm}$ 
E)  $9 \mathrm {~cm} \times 20 \mathrm {~cm}$

Question 20

Determine the nature of the roots of the quadratic equation without solving it. $6 x ^ { 2 } - 9 x + 3 = 0$ __________ root(s)

Accepted Answer

The answer of Determine the nature of the roots of...

Solve the equation. $9 x = x ^ { 2 }$

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $- 4 z ^ { 2 } + z + 6 = 0$

Solve the equation using the quadratic formula. $3 x ^ { 2 } + x - 5 = 0$ Round your answer to three significant digits.

Solve the equation. $x ^ { 2 } - 4 x + 3 = 0$

Draw the graph of the equation and label the vertex. $y = - \frac { 1 } { 5 } x ^ { 2 }$

Solve the equation. $4 x ^ { 2 } = 25$

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 3 }$ ___ $j$

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $2 x ^ { 2 } + 2 = x$ x = $\pm$ j

Solve the equation. $x ^ { 2 } + x - 56 = 0$

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $- 3 z ^ { 2 } - 8 = - 7 z ^ { 2 }$

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $4 x ^ { 2 } + x + 9 = 0$

A hole in the side of a large metal tank needs to be repaired. A piece of rectangular sheet metal of area $143 \mathrm { ft } ^ { 2 }$ will patch the hole. If the length of the sheet metal must be $2$ ft longer than its width what will the dimensions of the sheet metal be?

Solve the equation. $2 x ^ { 2 } = 15 x - 7$

Solve the equation. $x ^ { 2 } = 64$

Solve the equation using the quadratic formula. $2 x ^ { 2 } + 5 x - 9 = 0$ Round your answer to three significant digits.

Find the value of a, b, and c in the equation. $7 x ^ { 2 } + 3 x + 5 = 0$

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $3 x ^ { 2 } = 11 x - 5$

The perimeter of a rectangle is $50$ cm, and its area is $126 \mathrm {~cm} ^ { 2 }$ . Find its dimensions.

Determine the nature of the roots of the quadratic equation without solving it. $6 x ^ { 2 } - 9 x + 3 = 0$ __________ root(s)

Basic Concepts

Signed Numbers and Powers of 10

The Metric System

Measurement

Polynomials: an Introduction to Algebra

Equations and Formulas

Ratio and Proportion

Graphing Linear Equations

Systems of Linear Equations

Factoring Algebraic Expressions

Geometry

Right Triangle Trigonometry

Trigonometry With Any Angle

Basic Statistics

Binary and Hexadecimal Numbers

Filters

Exam 11: Quadratic Equations

Solve the equation. 9x=x29 x = x ^ { 2 }9x=x2

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). −4z2+z+6=0- 4 z ^ { 2 } + z + 6 = 0−4z2+z+6=0

Solve the equation using the quadratic formula. 3x2+x−5=03 x ^ { 2 } + x - 5 = 03x2+x−5=0 Round your answer to three significant digits.

Solve the equation. x2−4x+3=0x ^ { 2 } - 4 x + 3 = 0x2−4x+3=0

Draw the graph of the equation and label the vertex. y=−15x2y = - \frac { 1 } { 5 } x ^ { 2 }y=−51​x2

Solve the equation. 4x2=254 x ^ { 2 } = 254x2=25

Express the number in terms of j (if necessary, round the result to three significant digits). −3\sqrt { - 3 }−3​ ___ jjj

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). 2x2+2=x2 x ^ { 2 } + 2 = x2x2+2=x x = ____ ±\pm± ____j

Solve the equation. x2+x−56=0x ^ { 2 } + x - 56 = 0x2+x−56=0

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). −3z2−8=−7z2- 3 z ^ { 2 } - 8 = - 7 z ^ { 2 }−3z2−8=−7z2

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). 4x2+x+9=04 x ^ { 2 } + x + 9 = 04x2+x+9=0

A hole in the side of a large metal tank needs to be repaired. A piece of rectangular sheet metal of area 143ft2143 \mathrm { ft } ^ { 2 }143ft2 will patch the hole. If the length of the sheet metal must be 222 ft longer than its width what will the dimensions of the sheet metal be?

Solve the equation. 2x2=15x−72 x ^ { 2 } = 15 x - 72x2=15x−7

Solve the equation. x2=64x ^ { 2 } = 64x2=64

Solve the equation using the quadratic formula. 2x2+5x−9=02 x ^ { 2 } + 5 x - 9 = 02x2+5x−9=0 Round your answer to three significant digits.

Find the value of a, b, and c in the equation. 7x2+3x+5=07 x ^ { 2 } + 3 x + 5 = 07x2+3x+5=0

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). 3x2=11x−53 x ^ { 2 } = 11 x - 53x2=11x−5

The perimeter of a rectangle is 505050 cm, and its area is 126 cm2126 \mathrm {~cm} ^ { 2 }126 cm2 . Find its dimensions.

Determine the nature of the roots of the quadratic equation without solving it. 6x2−9x+3=06 x ^ { 2 } - 9 x + 3 = 06x2−9x+3=0 __________ root(s)

Basic Concepts

Signed Numbers and Powers of 10

The Metric System

Measurement

Polynomials: an Introduction to Algebra

Equations and Formulas

Ratio and Proportion

Graphing Linear Equations

Systems of Linear Equations

Factoring Algebraic Expressions

Geometry

Right Triangle Trigonometry

Trigonometry With Any Angle

Basic Statistics

Binary and Hexadecimal Numbers

Filters

Solve the equation. $9 x = x ^ { 2 }$

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $- 4 z ^ { 2 } + z + 6 = 0$

Solve the equation using the quadratic formula. $3 x ^ { 2 } + x - 5 = 0$ Round your answer to three significant digits.

Solve the equation. $x ^ { 2 } - 4 x + 3 = 0$

Draw the graph of the equation and label the vertex. $y = - \frac { 1 } { 5 } x ^ { 2 }$

Solve the equation. $4 x ^ { 2 } = 25$

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 3 }$ ___ $j$

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $2 x ^ { 2 } + 2 = x$ x = $\pm$ j

Solve the equation. $x ^ { 2 } + x - 56 = 0$

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $- 3 z ^ { 2 } - 8 = - 7 z ^ { 2 }$

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $4 x ^ { 2 } + x + 9 = 0$

A hole in the side of a large metal tank needs to be repaired. A piece of rectangular sheet metal of area $143 \mathrm { ft } ^ { 2 }$ will patch the hole. If the length of the sheet metal must be $2$ ft longer than its width what will the dimensions of the sheet metal be?

Solve the equation. $2 x ^ { 2 } = 15 x - 7$

Solve the equation. $x ^ { 2 } = 64$

Solve the equation using the quadratic formula. $2 x ^ { 2 } + 5 x - 9 = 0$ Round your answer to three significant digits.

Find the value of a, b, and c in the equation. $7 x ^ { 2 } + 3 x + 5 = 0$

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $3 x ^ { 2 } = 11 x - 5$

The perimeter of a rectangle is $50$ cm, and its area is $126 \mathrm {~cm} ^ { 2 }$ . Find its dimensions.

Determine the nature of the roots of the quadratic equation without solving it. $6 x ^ { 2 } - 9 x + 3 = 0$ __________ root(s)