Question 1

Solve the radical equation. Don t forget, you must check potential solutions. $7 \sqrt { x } = x + 12$ Enter your answer as two numbers, separated by a comma.

Accepted Answer

The answer of Solve the radical equation. Don t forget,...

Question 2

Find two consecutive whole numbers such that the sum of their squares is 41.

Accepted Answer

A)  7 and 2 
B)  6 and 3 
C)  2 and 7 
D)  4 and 5 
E)  0 and 9 
A)  7 and 2 
B)  6 and 3 
C)  2 and 7 
D)  4 and 5 
E)  0 and 9

Question 3

Find each of the products and match each expression with the corresponding answer.
-$60 - 32 i$

Accepted Answer

A)  $( 8 + 2 i ) ^ { 2 }$ 
B)  $( 8 - 2 i ) ^ { 2 }$ 
A)  $( 8 + 2 i ) ^ { 2 }$ 
B)  $( 8 - 2 i ) ^ { 2 }$

Question 4

Use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. $x ^ { 2 } - 8 x + 17 = 0$

Accepted Answer

two nonrea

Question 5

The method of completing the square will solve any linear equation.

Accepted Answer

A) True 
 B)False

Question 6

Solve the inequality. $\frac { x - 1 } { x - 5 } \leq 5$

Accepted Answer

A)  $( - \infty , - 6 ) \cup ( - 5 , \infty )$ 
B)  $( - \infty , 5 ) \cup ( 6 , \infty )$ 
C)  $( 5,6 )$ 
A)  $( - \infty , - 6 ) \cup ( - 5 , \infty )$ 
B)  $( - \infty , 5 ) \cup ( 6 , \infty )$ 
C)  $( 5,6 )$

Question 7

Solve the quadratic equation by factoring and applying the property ab = 0 if and only if a = 0 or b = 0. x 2 + 3 kx $-$ 28 k 2 = 0 Enter your answer as two numbers, separated by a comma.

Accepted Answer

The answer of Solve the quadratic equation by factoring and...

Question 8

Solve the quadratic equation using the method that seems most appropriate to you. $\frac { 49 } { x + 12 } - \frac { 19 } { x } = - 6$

Accepted Answer

A)  { 38, 4 } 
B)  { 19, 2 } 
C)  { $-$ 38, $-$ 4 } 
D)  { 38, $-$ 4 } 
E)  { $-$ 19, 2 } 
A)  { 38, 4 } 
B)  { 19, 2 } 
C)  { $-$ 38, $-$ 4 } 
D)  { 38, $-$ 4 } 
E)  { $-$ 19, 2 }

Question 9

The quadratic formula is $\frac { - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$ , where $a \neq 0$ .

Accepted Answer

A) True 
 B)False

Question 10

Write $\sqrt { - 108 }$ in terms of i and simplify.

Accepted Answer

The answer of Write $\sqrt { - 108 }$ in...

Question 11

Solve the quadratic equation using the method that seems most appropriate to you. $16 x ^ { 4 } + 55 x ^ { 2 } - 125 = 0$ Please separate your answers with commas.

Accepted Answer

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

Question 12

For this problem a and b represent the lengths of the legs of a right triangle, and c represents the length of the hypotenuse. Find a if $c = 21$ and $b = 11$ inches. Express the answer in simplest radical form.

Accepted Answer

The answer of For this problem a and b represent...

Question 13

Solve the quadratic equation. ( n $-$ 2) 2 = 7

Accepted Answer

A)  $n = \sqrt { 7 } - 2 \text { or } n = - \sqrt { 7 } - 2$ 
B)  $n = \sqrt { 7 } + 2 \text { or } n = \sqrt { 7 } - 2$ 
C)  n = 51 or n = 47 
D)  $n = \sqrt { 7 } + 2 \text { or } n = - \sqrt { 7 } + 2$ 
A)  $n = \sqrt { 7 } - 2 \text { or } n = - \sqrt { 7 } - 2$ 
B)  $n = \sqrt { 7 } + 2 \text { or } n = \sqrt { 7 } - 2$ 
C)  n = 51 or n = 47 
D)  $n = \sqrt { 7 } + 2 \text { or } n = - \sqrt { 7 } + 2$

Question 14

Solve the quadratic equation. $12 n ^ { 2 } = 15$

Accepted Answer

A)  $x = - \frac { \sqrt { 5 } } { 2 } \text { or } x = \frac { \sqrt { 5 } } { 2 }$ 
B)  $x = - \frac { \sqrt { 2 } } { 5 } \text { or } x = \frac { \sqrt { 2 } } { 5 }$ 
C)  $x = - \frac { \sqrt { 10 } } { 2 } \text { or } x = \frac { \sqrt { 10 } } { 2 }$ 
D)  $x = - \frac { \sqrt { 5 } } { 10 } \text { or } x = \frac { \sqrt { 5 } } { 10 }$ 
A)  $x = - \frac { \sqrt { 5 } } { 2 } \text { or } x = \frac { \sqrt { 5 } } { 2 }$ 
B)  $x = - \frac { \sqrt { 2 } } { 5 } \text { or } x = \frac { \sqrt { 2 } } { 5 }$ 
C)  $x = - \frac { \sqrt { 10 } } { 2 } \text { or } x = \frac { \sqrt { 10 } } { 2 }$ 
D)  $x = - \frac { \sqrt { 5 } } { 10 } \text { or } x = \frac { \sqrt { 5 } } { 10 }$

Question 15

Solve the quadratic equation. (4 x + 1) 2 = 16

Accepted Answer

A)  $n = \frac { 3 } { 4 } \text { or } n = - \frac { 5 } { 4 }$ 
B)  x = 3 or x = $-$ 3 
C)  $n = \frac { 3 } { 4 } \text { or } n = - \frac { 3 } { 4 }$ 
D)  x = 3 or x = 5 
A)  $n = \frac { 3 } { 4 } \text { or } n = - \frac { 5 } { 4 }$ 
B)  x = 3 or x = $-$ 3 
C)  $n = \frac { 3 } { 4 } \text { or } n = - \frac { 3 } { 4 }$ 
D)  x = 3 or x = 5

Question 16

Solve the quadratic equation by factoring and applying the property " ab = 0 if and only if a = 0 or b = 0." x  2 + 4 kx = 0 Enter your answer as two numbers, separated by a comma.

Accepted Answer

Question 17

Write $\frac { \sqrt { - 640 } } { \sqrt { 10 } }$ in terms of i , perform the indicated operations, and simplify.

Accepted Answer

The answer of Write \(\frac { \sqrt { - 640...

Question 18

Write $\sqrt { 11 } \sqrt { - 25 }$ in terms of i , perform the indicated operations, and simplify.

Accepted Answer

The answer of Write \(\sqrt { 11 } \sqrt {...

Question 19

Solve each quadratic equation using the method that seems most appropriate. 2 n 2 $-$ 6 n = 3

Accepted Answer

A)  $n = \frac { 3 + \sqrt { 3 } } { 2 } , n = \frac { 3 - \sqrt { 3 } } { 2 }$ 
B)  $n = \frac { 6 + \sqrt { 3 } } { 2 } , n = \frac { - 6 - \sqrt { 3 } } { 2 }$ 
C)  $n = \frac { - 6 + \sqrt { 3 } } { 2 } , n = \frac { 6 + \sqrt { 3 } } { 2 }$ 
A)  $n = \frac { 3 + \sqrt { 3 } } { 2 } , n = \frac { 3 - \sqrt { 3 } } { 2 }$ 
B)  $n = \frac { 6 + \sqrt { 3 } } { 2 } , n = \frac { - 6 - \sqrt { 3 } } { 2 }$ 
C)  $n = \frac { - 6 + \sqrt { 3 } } { 2 } , n = \frac { 6 + \sqrt { 3 } } { 2 }$

Question 20

Solve the quadratic equation by using the factoring method. 2 n 2 + 9 n $-$ 5 = 0

Accepted Answer

A)  $n = - 5 , n = - \frac { 1 } { 2 }$ 
B)  $n = - 5 , n = \frac { 1 } { 2 }$ 
C)  $n = 5 , n = \frac { 1 } { 2 }$ 
A)  $n = - 5 , n = - \frac { 1 } { 2 }$ 
B)  $n = - 5 , n = \frac { 1 } { 2 }$ 
C)  $n = 5 , n = \frac { 1 } { 2 }$

Solve the radical equation. Don t forget, you must check potential solutions. $7 \sqrt { x } = x + 12$ Enter your answer as two numbers, separated by a comma.

Find two consecutive whole numbers such that the sum of their squares is 41.

Find each of the products and match each expression with the corresponding answer. - $60 - 32 i$

Use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. $x ^ { 2 } - 8 x + 17 = 0$

The method of completing the square will solve any linear equation.

Solve the inequality. $\frac { x - 1 } { x - 5 } \leq 5$

Solve the quadratic equation by factoring and applying the property ab = 0 if and only if a = 0 or b = 0. x 2 + 3 kx $-$ 28 k 2 = 0 Enter your answer as two numbers, separated by a comma.

Solve the quadratic equation using the method that seems most appropriate to you. $\frac { 49 } { x + 12 } - \frac { 19 } { x } = - 6$

The quadratic formula is $\frac { - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$ , where $a \neq 0$ .

Write $\sqrt { - 108 }$ in terms of i and simplify.

Solve the quadratic equation using the method that seems most appropriate to you. $16 x ^ { 4 } + 55 x ^ { 2 } - 125 = 0$ Please separate your answers with commas.

For this problem a and b represent the lengths of the legs of a right triangle, and c represents the length of the hypotenuse. Find a if $c = 21$ and $b = 11$ inches. Express the answer in simplest radical form.

Solve the quadratic equation. ( n $-$ 2) 2 = 7

Solve the quadratic equation. $12 n ^ { 2 } = 15$

Solve the quadratic equation. (4 x + 1)² = 16

Solve the quadratic equation by factoring and applying the property " ab = 0 if and only if a = 0 or b = 0." x ² + 4 kx = 0 Enter your answer as two numbers, separated by a comma.

Write $\frac { \sqrt { - 640 } } { \sqrt { 10 } }$ in terms of i , perform the indicated operations, and simplify.

Write $\sqrt { 11 } \sqrt { - 25 }$ in terms of i , perform the indicated operations, and simplify.

Solve each quadratic equation using the method that seems most appropriate. 2 n 2 $-$ 6 n = 3

Solve the quadratic equation by using the factoring method. 2 n 2 + 9 n $-$ 5 = 0

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Exam 11: Quadratic Equations and Inequalities

Solve the radical equation. Don t forget, you must check potential solutions. 7x=x+127 \sqrt { x } = x + 127x​=x+12 Enter your answer as two numbers, separated by a comma.

Find two consecutive whole numbers such that the sum of their squares is 41.

Find each of the products and match each expression with the corresponding answer. - 60−32i60 - 32 i60−32i

Use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. x2−8x+17=0x ^ { 2 } - 8 x + 17 = 0x2−8x+17=0

The method of completing the square will solve any linear equation.

Solve the inequality. x−1x−5≤5\frac { x - 1 } { x - 5 } \leq 5x−5x−1​≤5

Solve the quadratic equation by factoring and applying the property ab = 0 if and only if a = 0 or b = 0. x 2 + 3 kx −-− 28 k 2 = 0 Enter your answer as two numbers, separated by a comma.

Solve the quadratic equation using the method that seems most appropriate to you. 49x+12−19x=−6\frac { 49 } { x + 12 } - \frac { 19 } { x } = - 6x+1249​−x19​=−6

The quadratic formula is −b±b2−4ac2a\frac { - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }2a−b±b2−4ac​​ , where a≠0a \neq 0a=0 .

Write −108\sqrt { - 108 }−108​ in terms of i and simplify.

Solve the quadratic equation using the method that seems most appropriate to you. 16x4+55x2−125=016 x ^ { 4 } + 55 x ^ { 2 } - 125 = 016x4+55x2−125=0 Please separate your answers with commas.

For this problem a and b represent the lengths of the legs of a right triangle, and c represents the length of the hypotenuse. Find a if c=21c = 21c=21 and b=11b = 11b=11 inches. Express the answer in simplest radical form.

Solve the quadratic equation. ( n −-− 2) 2 = 7

Solve the quadratic equation. 12n2=1512 n ^ { 2 } = 1512n2=15

Solve the quadratic equation. (4 x + 1) 2 = 16

Solve the quadratic equation by factoring and applying the property " ab = 0 if and only if a = 0 or b = 0." x 2 + 4 kx = 0 Enter your answer as two numbers, separated by a comma.

Write −64010\frac { \sqrt { - 640 } } { \sqrt { 10 } }10​−640​​ in terms of i , perform the indicated operations, and simplify.

Write 11−25\sqrt { 11 } \sqrt { - 25 }11​−25​ in terms of i , perform the indicated operations, and simplify.

Solve each quadratic equation using the method that seems most appropriate. 2 n 2 −-− 6 n = 3

Solve the quadratic equation by using the factoring method. 2 n 2 + 9 n −-− 5 = 0

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Solve the radical equation. Don t forget, you must check potential solutions. $7 \sqrt { x } = x + 12$ Enter your answer as two numbers, separated by a comma.

Find each of the products and match each expression with the corresponding answer. - $60 - 32 i$

Use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. $x ^ { 2 } - 8 x + 17 = 0$

Solve the inequality. $\frac { x - 1 } { x - 5 } \leq 5$

Solve the quadratic equation by factoring and applying the property ab = 0 if and only if a = 0 or b = 0. x 2 + 3 kx $-$ 28 k 2 = 0 Enter your answer as two numbers, separated by a comma.

Solve the quadratic equation using the method that seems most appropriate to you. $\frac { 49 } { x + 12 } - \frac { 19 } { x } = - 6$

The quadratic formula is $\frac { - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$ , where $a \neq 0$ .

Write $\sqrt { - 108 }$ in terms of i and simplify.

Solve the quadratic equation using the method that seems most appropriate to you. $16 x ^ { 4 } + 55 x ^ { 2 } - 125 = 0$ Please separate your answers with commas.

For this problem a and b represent the lengths of the legs of a right triangle, and c represents the length of the hypotenuse. Find a if $c = 21$ and $b = 11$ inches. Express the answer in simplest radical form.

Solve the quadratic equation. ( n $-$ 2) 2 = 7

Solve the quadratic equation. $12 n ^ { 2 } = 15$

Solve the quadratic equation. (4 x + 1)² = 16

Solve the quadratic equation by factoring and applying the property " ab = 0 if and only if a = 0 or b = 0." x ² + 4 kx = 0 Enter your answer as two numbers, separated by a comma.

Write $\frac { \sqrt { - 640 } } { \sqrt { 10 } }$ in terms of i , perform the indicated operations, and simplify.

Write $\sqrt { 11 } \sqrt { - 25 }$ in terms of i , perform the indicated operations, and simplify.

Solve each quadratic equation using the method that seems most appropriate. 2 n 2 $-$ 6 n = 3

Solve the quadratic equation by using the factoring method. 2 n 2 + 9 n $-$ 5 = 0