Question 1

Determine the nature of the roots of the quadratic equation without solving it. $4 x ^ { 2 } - 7 x + 3 = 0$

Accepted Answer

A)  two irrational roots 
B)  one rational root 
C)  two rational roots 
D)  two imaginary roots 
A)  two irrational roots 
B)  one rational root 
C)  two rational roots 
D)  two imaginary roots

Question 2

Solve the equation. $25 x ^ { 2 } = 81$

Accepted Answer

A)  $x = - \frac { 9 } { 10 } , \quad x = \frac { 9 } { 10 }$ 
B)  $x = - \frac { 9 } { 5 } , x = \frac { 9 } { 5 }$ 
C)  $x = - \frac { 9 } { 5 } , x = \frac { 5 } { 9 }$ 
D)  $x = - \frac { 5 } { 9 } , x = \frac { 9 } { 5 }$ 
E)  $x = - \frac { 5 } { 9 } , x = \frac { 5 } { 9 }$ 
A)  $x = - \frac { 9 } { 10 } , \quad x = \frac { 9 } { 10 }$ 
B)  $x = - \frac { 9 } { 5 } , x = \frac { 9 } { 5 }$ 
C)  $x = - \frac { 9 } { 5 } , x = \frac { 5 } { 9 }$ 
D)  $x = - \frac { 5 } { 9 } , x = \frac { 9 } { 5 }$ 
E)  $x = - \frac { 5 } { 9 } , x = \frac { 5 } { 9 }$

Question 3

Simplify. $j ^ { 46 }$

Accepted Answer

A)  $- j ^ { 3 }$ 
B)  $- j$ 
C)  $1$ 
D)  $- 1$ 
E)  $j$ 
A)  $- j ^ { 3 }$ 
B)  $- j$ 
C)  $1$ 
D)  $- 1$ 
E)  $j$

Question 4

Determine the nature of the roots of the quadratic equation without solving it. $8 x - 1 = 5 x ^ { 2 }$

Accepted Answer

A)  two imaginary roots 
B)  one rational root 
C)  two irrational roots 
D)  two rational roots 
A)  two imaginary roots 
B)  one rational root 
C)  two irrational roots 
D)  two rational roots

Question 5

Determine the nature of the roots of the quadratic equation without solving it. $x ^ { 2 } + 5 = x$

Accepted Answer

A)  two imaginary roots 
B)  two rational roots 
C)  one rational root 
D)  two irrational roots 
A)  two imaginary roots 
B)  two rational roots 
C)  one rational root 
D)  two irrational roots

Question 6

Solve the equation. $10 n ^ { 2 } - 35 n = 0$

Accepted Answer

A)  $n = 0 , \quad n = - \frac { 2 } { 7 }$ 
B)  $n = 0 , \quad n = \frac { 2 } { 7 }$ 
C)  $n = 0 , \quad n = - \frac { 7 } { 2 }$ 
D)  $n = 0$ 
E)  $n = 0 , \quad n = \frac { 7 } { 2 }$ 
A)  $n = 0 , \quad n = - \frac { 2 } { 7 }$ 
B)  $n = 0 , \quad n = \frac { 2 } { 7 }$ 
C)  $n = 0 , \quad n = - \frac { 7 } { 2 }$ 
D)  $n = 0$ 
E)  $n = 0 , \quad n = \frac { 7 } { 2 }$

Question 7

Simplify. $j ^ { 6 }$

Accepted Answer

The answer of Simplify. $j ^ { 6 }$...

Question 8

Solve the equation. $c ^ { 2 } + 56 = 15 c$

Accepted Answer

A)  $c = - 7$ , $c = - 8$ 
B)  $c = 7$ , $C = 8$ 
C)  $c = 7$ , $c = - 8$ 
D)  $c = 7$ 
E)  $c = - 7$ , $C = 8$ 
A)  $c = - 7$ , $c = - 8$ 
B)  $c = 7$ , $C = 8$ 
C)  $c = 7$ , $c = - 8$ 
D)  $c = 7$ 
E)  $c = - 7$ , $C = 8$

Question 9

A variable electric current is given by $t = t ^ { 2 } - 7 t + 14$ , where t is in seconds. At what time is the current i is equal to 4 A.

Accepted Answer

A)  At times 2 and 5 seconds the current i is equal to 4 A. 
B)  At times 3 and 4 seconds the current i is equal to 4 A. 
C)  At times 4 and 5 seconds the current i is equal to 4 A. 
D)  At times 2 and 2.5 seconds the current i is equal to 4 A. 
E)  At time 2 seconds the current i is equal to 4 A. 
A)  At times 2 and 5 seconds the current i is equal to 4 A. 
B)  At times 3 and 4 seconds the current i is equal to 4 A. 
C)  At times 4 and 5 seconds the current i is equal to 4 A. 
D)  At times 2 and 2.5 seconds the current i is equal to 4 A. 
E)  At time 2 seconds the current i is equal to 4 A.

Question 10

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

Accepted Answer

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

Question 11

Determine the nature of the roots of the quadratic equation without solving it. $x ^ { 2 } + 5 = x$ __________ root(s)

Accepted Answer

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

Question 12

Determine the nature of the roots of the quadratic equation without solving it. $4 x ^ { 2 } - 8 = x$ __________ root(s)

Accepted Answer

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

Question 13

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $3 x ^ { 2 } = 6 x - 9$ x = _____ $\pm$ _____j

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

A border of uniform width is printed on a page measuring 18 in. by 11 in. (See the figure below.) The area of the border is 28 in.2. Find the width of the border.

Accepted Answer

A)  1 in. 
B)  $\frac { 1 } { 3 }$ in. 
C)  $\frac { 1 } { 2 }$ in. 
D)  $\frac { 1 } { 4 }$ in. 
E)  $1 \frac { 1 } { 2 }$ in. 
A)  1 in. 
B)  $\frac { 1 } { 3 }$ in. 
C)  $\frac { 1 } { 2 }$ in. 
D)  $\frac { 1 } { 4 }$ in. 
E)  $1 \frac { 1 } { 2 }$ in.

Question 16

Find the value of a, b, and c in the equation. $- 6 y ^ { 2 } + 8 y + 7 = 0$

Accepted Answer

A)  a = -6, b = -8, c = 7 
B)  a = 7, b = -6, c = 8 
C)  a = -6, b = 8, c = 7 
D)  a = 8, b = 7, c = - 6 
E)  a = 6, b = -8, c = 7 
A)  a = -6, b = -8, c = 7 
B)  a = 7, b = -6, c = 8 
C)  a = -6, b = 8, c = 7 
D)  a = 8, b = 7, c = - 6 
E)  a = 6, b = -8, c = 7

Question 17

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

Accepted Answer

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

Determine the nature of the roots of the quadratic equation without solving it. $4 x ^ { 2 } - 7 x + 3 = 0$

Solve the equation. $25 x ^ { 2 } = 81$

Simplify. $j ^ { 46 }$

Determine the nature of the roots of the quadratic equation without solving it. $8 x - 1 = 5 x ^ { 2 }$

Determine the nature of the roots of the quadratic equation without solving it. $x ^ { 2 } + 5 = x$

Solve the equation. $10 n ^ { 2 } - 35 n = 0$

Simplify. $j ^ { 6 }$

Solve the equation. $c ^ { 2 } + 56 = 15 c$

A variable electric current is given by $t = t ^ { 2 } - 7 t + 14$ , where t is in seconds. At what time is the current i is equal to 4 A.

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

Determine the nature of the roots of the quadratic equation without solving it. $x ^ { 2 } + 5 = x$ __________ root(s)

Determine the nature of the roots of the quadratic equation without solving it. $4 x ^ { 2 } - 8 = x$ __________ root(s)

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $3 x ^ { 2 } = 6 x - 9$ x = _ $\pm$ _j

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

A border of uniform width is printed on a page measuring 18 in. by 11 in. (See the figure below.) The area of the border is 28 in.². Find the width of the border.

Find the value of a, b, and c in the equation. $- 6 y ^ { 2 } + 8 y + 7 = 0$

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

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

Determine the nature of the roots of the quadratic equation without solving it. 4x2−7x+3=04 x ^ { 2 } - 7 x + 3 = 04x2−7x+3=0

Solve the equation. 25x2=8125 x ^ { 2 } = 8125x2=81

Simplify. j46j ^ { 46 }j46

Determine the nature of the roots of the quadratic equation without solving it. 8x−1=5x28 x - 1 = 5 x ^ { 2 }8x−1=5x2

Determine the nature of the roots of the quadratic equation without solving it. x2+5=xx ^ { 2 } + 5 = xx2+5=x

Solve the equation. 10n2−35n=010 n ^ { 2 } - 35 n = 010n2−35n=0

Simplify. j6j ^ { 6 }j6

Solve the equation. c2+56=15cc ^ { 2 } + 56 = 15 cc2+56=15c

A variable electric current is given by t=t2−7t+14t = t ^ { 2 } - 7 t + 14t=t2−7t+14 , where t is in seconds. At what time is the current i is equal to 4 A.

Solve the equation. x2−x=12x ^ { 2 } - x = 12x2−x=12

Determine the nature of the roots of the quadratic equation without solving it. x2+5=xx ^ { 2 } + 5 = xx2+5=x __________ root(s)

Determine the nature of the roots of the quadratic equation without solving it. 4x2−8=x4 x ^ { 2 } - 8 = x4x2−8=x __________ root(s)

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). 3x2=6x−93 x ^ { 2 } = 6 x - 93x2=6x−9 x = _____ ±\pm± _____j

Draw the graph of the equation and label the vertex. y=x2−2x+1y = x ^ { 2 } - 2 x + 1y=x2−2x+1

A border of uniform width is printed on a page measuring 18 in. by 11 in. (See the figure below.) The area of the border is 28 in.2. Find the width of the border.

Find the value of a, b, and c in the equation. −6y2+8y+7=0- 6 y ^ { 2 } + 8 y + 7 = 0−6y2+8y+7=0

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

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

Determine the nature of the roots of the quadratic equation without solving it. $4 x ^ { 2 } - 7 x + 3 = 0$

Solve the equation. $25 x ^ { 2 } = 81$

Simplify. $j ^ { 46 }$

Determine the nature of the roots of the quadratic equation without solving it. $8 x - 1 = 5 x ^ { 2 }$

Determine the nature of the roots of the quadratic equation without solving it. $x ^ { 2 } + 5 = x$

Solve the equation. $10 n ^ { 2 } - 35 n = 0$

Simplify. $j ^ { 6 }$

Solve the equation. $c ^ { 2 } + 56 = 15 c$

A variable electric current is given by $t = t ^ { 2 } - 7 t + 14$ , where t is in seconds. At what time is the current i is equal to 4 A.

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

Determine the nature of the roots of the quadratic equation without solving it. $x ^ { 2 } + 5 = x$ __________ root(s)

Determine the nature of the roots of the quadratic equation without solving it. $4 x ^ { 2 } - 8 = x$ __________ root(s)

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $3 x ^ { 2 } = 6 x - 9$ x = _ $\pm$ _j

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

A border of uniform width is printed on a page measuring 18 in. by 11 in. (See the figure below.) The area of the border is 28 in.². Find the width of the border.

Find the value of a, b, and c in the equation. $- 6 y ^ { 2 } + 8 y + 7 = 0$

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