Question 1

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 676 }$ ____ $j$

Accepted Answer

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

Question 2

Solve the equation using the quadratic formula. Check your solution. $11 x ^ { 2 } + 114 x - 77 = 0$

Accepted Answer

A)  $x _ { 1 } = 11 , x _ { 2 } = - \frac { 1 } { 2 }$ 
B)  $x _ { 1 } = - \frac { 7 } { 11 } , x _ { 2 } = 11$ 
C)  $x _ { 1 } = 11 , x _ { 2 } = \frac { 11 } { 7 }$ 
D)  $x _ { 1 } = \frac { 7 } { 11 } , x _ { 2 } = - 11$ 
E)  $x _ { 1 } = - \frac { 11 } { 3 } , x _ { 2 } = 11$ 
A)  $x _ { 1 } = 11 , x _ { 2 } = - \frac { 1 } { 2 }$ 
B)  $x _ { 1 } = - \frac { 7 } { 11 } , x _ { 2 } = 11$ 
C)  $x _ { 1 } = 11 , x _ { 2 } = \frac { 11 } { 7 }$ 
D)  $x _ { 1 } = \frac { 7 } { 11 } , x _ { 2 } = - 11$ 
E)  $x _ { 1 } = - \frac { 11 } { 3 } , x _ { 2 } = 11$

Question 3

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 5 }$

Accepted Answer

A)  $- 2.24 j$ 
B)  $2.24$ 
C)  $2.24 j$ 
D)  $- 5$ 
E)  $5 j$ 
A)  $- 2.24 j$ 
B)  $2.24$ 
C)  $2.24 j$ 
D)  $- 5$ 
E)  $5 j$

Question 4

Solve the equation. $x ^ { 2 } - 13 x = - 40$

Accepted Answer

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

Question 5

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 32 }$ ____ j

Accepted Answer

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

Question 6

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

Accepted Answer

A)  -0.382, -2.62 
B)  1.242, -2.62 
C)  -2.618, -2.62 
D)  -0.382, -3.75 
E)  1.242, -3.75 
A)  -0.382, -2.62 
B)  1.242, -2.62 
C)  -2.618, -2.62 
D)  -0.382, -3.75 
E)  1.242, -3.75

Question 7

Solve the equation. $c ^ { 2 } - 4 c = 12$

Accepted Answer

A)  $C = 2$ 
B)  $c = - 2$ , $C = 6$ 
C)  $C = 2$ , $c = - 6$ 
D)  $c = - 2$ , $c = - 6$ 
E)  $C = 2$ , $C = 6$ 
A)  $C = 2$ 
B)  $c = - 2$ , $C = 6$ 
C)  $C = 2$ , $c = - 6$ 
D)  $c = - 2$ , $c = - 6$ 
E)  $C = 2$ , $C = 6$

Question 8

A rectangular field is fenced in by using a river as one side. If $1,400$ m of fencing are used for the $240,000$ -m2 field, find its dimensions.

Accepted Answer

A)  $300 \mathrm {~m} \times 800 \mathrm {~m} , 400 \mathrm {~m} \times 600 \mathrm {~m}$ 
B)  $450 \mathrm {~m} \times 900 \mathrm {~m} , 400 \mathrm {~m} \times 650 \mathrm {~m}$ 
C)  $300 \mathrm {~m} \times 800 \mathrm {~m} , 450 \mathrm {~m} \times 600 \mathrm {~m}$ 
D)  $300 \mathrm {~m} \times 1,000 \mathrm {~m} , 400 \mathrm {~m} \times 600 \mathrm {~m}$ 
E)  $200 \mathrm {~m} \times 700 \mathrm {~m} , 500 \mathrm {~m} \times 700 \mathrm {~m}$ 
A)  $300 \mathrm {~m} \times 800 \mathrm {~m} , 400 \mathrm {~m} \times 600 \mathrm {~m}$ 
B)  $450 \mathrm {~m} \times 900 \mathrm {~m} , 400 \mathrm {~m} \times 650 \mathrm {~m}$ 
C)  $300 \mathrm {~m} \times 800 \mathrm {~m} , 450 \mathrm {~m} \times 600 \mathrm {~m}$ 
D)  $300 \mathrm {~m} \times 1,000 \mathrm {~m} , 400 \mathrm {~m} \times 600 \mathrm {~m}$ 
E)  $200 \mathrm {~m} \times 700 \mathrm {~m} , 500 \mathrm {~m} \times 700 \mathrm {~m}$

Question 9

Draw the graph of the equation and label the vertex. $y = x ^ { 2 } - 3$

Accepted Answer

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

Question 10

The area of a rectangular lot $120 \mathrm {~m}$ by $90 \mathrm {~m}$ is to be increased by $7,200 \mathrm {~m} ^ { 2 }$ . (See the figure below.) The length and the width will be increased by the same amount. What are the dimensions of the larger lot?

Accepted Answer

A)  $150 \mathrm {~m} \times 180 \mathrm {~m}$ 
B)  $170 \mathrm {~m} \times 200 \mathrm {~m}$ 
C)  $110 \mathrm {~m} \times 200 \mathrm {~m}$ 
D)  $120 \mathrm {~m} \times 150 \mathrm {~m}$ 
E)  $90 \mathrm {~m} \times 120 \mathrm {~m}$ 
A)  $150 \mathrm {~m} \times 180 \mathrm {~m}$ 
B)  $170 \mathrm {~m} \times 200 \mathrm {~m}$ 
C)  $110 \mathrm {~m} \times 200 \mathrm {~m}$ 
D)  $120 \mathrm {~m} \times 150 \mathrm {~m}$ 
E)  $90 \mathrm {~m} \times 120 \mathrm {~m}$

Question 11

Draw the graph of the equation and label the vertex. $y = 2 ( x + 3 ) ^ { 2 } - 3$

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Determine the nature of the roots of the quadratic equation without solving it. $7 x + 2 = 2 x ^ { 2 }$ __________ root(s)

Accepted Answer

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

Question 14

Simplify. $j ^ { 70 }$

Accepted Answer

The answer of Simplify. $j ^ { 70 }$...

Question 15

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 6 }$

Accepted Answer

A)  $- 2.45 j$ 
B)  $6 j$ 
C)  $2.45$ 
D)  $2.45 j$ 
E)  $- 2.45$ 
A)  $- 2.45 j$ 
B)  $6 j$ 
C)  $2.45$ 
D)  $2.45 j$ 
E)  $- 2.45$

Question 16

A rectangle is 7 ft longer than it is wide. The area of the rectangle is 98 ft 2. Use a quadratic equation to find the dimensions of the rectangle.   length = __________ ft
width = __________ ft

Accepted Answer

Question 17

A variable voltage in an electrical circuit is given by $V = t ^ { 2 } - 9 t + 22$ , where t is in seconds. Find the values of t when the voltage V equals $4 \mathrm {~V}$ .

Accepted Answer

A)  $t _ { 1 } = 2 , t _ { 2 } = 6 ,$ 
B)  $t _ { 1 } = 3 , \quad t _ { 2 } = 6 ,$ 
C)  $t _ { 1 } = 9 , t _ { 2 } = 16$ 
D)  $t _ { 1 } = 4 , t _ { 2 } = 8$ 
E)  $t _ { 1 } = 5 , t _ { 2 } = 9$ 
A)  $t _ { 1 } = 2 , t _ { 2 } = 6 ,$ 
B)  $t _ { 1 } = 3 , \quad t _ { 2 } = 6 ,$ 
C)  $t _ { 1 } = 9 , t _ { 2 } = 16$ 
D)  $t _ { 1 } = 4 , t _ { 2 } = 8$ 
E)  $t _ { 1 } = 5 , t _ { 2 } = 9$

Question 18

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 34 }$

Accepted Answer

A)  $34$ 
B)  $34$ j 
C)  $5.83$ 
D)  $5.83 j$ 
E)  - $5.83$ j 
A)  $34$ 
B)  $34$ j 
C)  $5.83$ 
D)  $5.83 j$ 
E)  - $5.83$ j

Question 19

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $2 x ^ { 2 } = 4 x - 6$

Accepted Answer

A)  $x = 4.5 , x = 3.5$ 
B)  $x = 1 + 4 j , \quad x = 1 - 4 j$ 
C)  $x = 2 + 4 j , \quad x = 2 - 4 j$ 
D)  $x = 2 + 4 j , \quad x = 1 - 4 j$ 
E)  $x = 2 + 1.66 j , \quad x = 2 - 1.66 j$ 
A)  $x = 4.5 , x = 3.5$ 
B)  $x = 1 + 4 j , \quad x = 1 - 4 j$ 
C)  $x = 2 + 4 j , \quad x = 2 - 4 j$ 
D)  $x = 2 + 4 j , \quad x = 1 - 4 j$ 
E)  $x = 2 + 1.66 j , \quad x = 2 - 1.66 j$

Question 20

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $13.1 x ^ { 2 } - 39 x = 22.1$

Accepted Answer

A)  3.46, -1.49 
B)  4.46, -1.49 
C)  3.46 
D)  3.46, -0.487 
E)  4.46, -0.487 
A)  3.46, -1.49 
B)  4.46, -1.49 
C)  3.46 
D)  3.46, -0.487 
E)  4.46, -0.487

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 676 }$ ____ $j$

Solve the equation using the quadratic formula. Check your solution. $11 x ^ { 2 } + 114 x - 77 = 0$

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 5 }$

Solve the equation. $x ^ { 2 } - 13 x = - 40$

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 32 }$ ____ j

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

Solve the equation. $c ^ { 2 } - 4 c = 12$

A rectangular field is fenced in by using a river as one side. If $1,400$ m of fencing are used for the $240,000$ -m² field, find its dimensions.

Draw the graph of the equation and label the vertex. $y = x ^ { 2 } - 3$

Draw the graph of the equation and label the vertex. $y = 2 ( x + 3 ) ^ { 2 } - 3$

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

Determine the nature of the roots of the quadratic equation without solving it. $7 x + 2 = 2 x ^ { 2 }$ __________ root(s)

Simplify. $j ^ { 70 }$

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 6 }$

A rectangle is 7 ft longer than it is wide. The area of the rectangle is 98 ft ². Use a quadratic equation to find the dimensions of the rectangle. length = ft width = ft

A variable voltage in an electrical circuit is given by $V = t ^ { 2 } - 9 t + 22$ , where t is in seconds. Find the values of t when the voltage V equals $4 \mathrm {~V}$ .

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 34 }$

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $2 x ^ { 2 } = 4 x - 6$

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $13.1 x ^ { 2 } - 39 x = 22.1$

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

Express the number in terms of j (if necessary, round the result to three significant digits). −676\sqrt { - 676 }−676​ ____ jjj

Solve the equation using the quadratic formula. Check your solution. 11x2+114x−77=011 x ^ { 2 } + 114 x - 77 = 011x2+114x−77=0

Express the number in terms of j (if necessary, round the result to three significant digits). −5\sqrt { - 5 }−5​

Solve the equation. x2−13x=−40x ^ { 2 } - 13 x = - 40x2−13x=−40

Express the number in terms of j (if necessary, round the result to three significant digits). −32\sqrt { - 32 }−32​ ____ j

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). 2z2+6z+2=02 z ^ { 2 } + 6 z + 2 = 02z2+6z+2=0

Solve the equation. c2−4c=12c ^ { 2 } - 4 c = 12c2−4c=12

A rectangular field is fenced in by using a river as one side. If 1,4001,4001,400 m of fencing are used for the 240,000240,000240,000 -m2 field, find its dimensions.

Draw the graph of the equation and label the vertex. y=x2−3y = x ^ { 2 } - 3y=x2−3

The area of a rectangular lot 120 m120 \mathrm {~m}120 m by 90 m90 \mathrm {~m}90 m is to be increased by 7,200 m27,200 \mathrm {~m} ^ { 2 }7,200 m2 . (See the figure below.) The length and the width will be increased by the same amount. What are the dimensions of the larger lot?

Draw the graph of the equation and label the vertex. y=2(x+3)2−3y = 2 ( x + 3 ) ^ { 2 } - 3y=2(x+3)2−3

Draw the graph of the equation and label the vertex. y=−x2−2xy = - x ^ { 2 } - 2 xy=−x2−2x

Determine the nature of the roots of the quadratic equation without solving it. 7x+2=2x27 x + 2 = 2 x ^ { 2 }7x+2=2x2 __________ root(s)

Simplify. j70j ^ { 70 }j70

Express the number in terms of j (if necessary, round the result to three significant digits). −6\sqrt { - 6 }−6​

A rectangle is 7 ft longer than it is wide. The area of the rectangle is 98 ft 2. Use a quadratic equation to find the dimensions of the rectangle. length = __________ ft width = __________ ft

A variable voltage in an electrical circuit is given by V=t2−9t+22V = t ^ { 2 } - 9 t + 22V=t2−9t+22 , where t is in seconds. Find the values of t when the voltage V equals 4 V4 \mathrm {~V}4 V .

Express the number in terms of j (if necessary, round the result to three significant digits). −34\sqrt { - 34 }−34​

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). 2x2=4x−62 x ^ { 2 } = 4 x - 62x2=4x−6

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). 13.1x2−39x=22.113.1 x ^ { 2 } - 39 x = 22.113.1x2−39x=22.1

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

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 676 }$ ____ $j$

Solve the equation using the quadratic formula. Check your solution. $11 x ^ { 2 } + 114 x - 77 = 0$

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 5 }$

Solve the equation. $x ^ { 2 } - 13 x = - 40$

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 32 }$ ____ j

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

Solve the equation. $c ^ { 2 } - 4 c = 12$

A rectangular field is fenced in by using a river as one side. If $1,400$ m of fencing are used for the $240,000$ -m² field, find its dimensions.

Draw the graph of the equation and label the vertex. $y = x ^ { 2 } - 3$

Draw the graph of the equation and label the vertex. $y = 2 ( x + 3 ) ^ { 2 } - 3$

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

Determine the nature of the roots of the quadratic equation without solving it. $7 x + 2 = 2 x ^ { 2 }$ __________ root(s)

Simplify. $j ^ { 70 }$

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 6 }$

A rectangle is 7 ft longer than it is wide. The area of the rectangle is 98 ft ². Use a quadratic equation to find the dimensions of the rectangle. length = ft width = ft

A variable voltage in an electrical circuit is given by $V = t ^ { 2 } - 9 t + 22$ , where t is in seconds. Find the values of t when the voltage V equals $4 \mathrm {~V}$ .

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 34 }$

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $2 x ^ { 2 } = 4 x - 6$

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $13.1 x ^ { 2 } - 39 x = 22.1$