Question 1

Solve the inequality. $\frac { 3 x } { x + 4 } > 6$ Please enter your answer in interval notation.

Accepted Answer

The answer of Solve the inequality. \(\frac { 3 x...

Question 2

Solve the inequality. $2 x ^ { 2 } + 9 x - 5 \leq 0$ Please enter your answer in interval notation.

Accepted Answer

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

Question 3

The number $b ^ { 2 } - 4 a c$ is called the discriminant of the quadratic equation.

Accepted Answer

A) True 
 B)False

Question 4

Solve the inequality. $\frac { 4 x } { x + 2 } > 6$

Accepted Answer

A)  $( - 6 , - 2 )$ 
B)  $( - \infty , - 6 ) \cup ( - 2 , \infty )$ 
C)  $( 2,6 )$ 
A)  $( - 6 , - 2 )$ 
B)  $( - \infty , - 6 ) \cup ( - 2 , \infty )$ 
C)  $( 2,6 )$

Question 5

To multiply factors in the form $\sqrt { - b }$ , rewrite $\sqrt { - b }$ in the form $i \sqrt { b }$ .

Accepted Answer

A) True 
 B)False

Question 6

Use the method of completing the square to solve the quadratic equation. 2 x 2 + 6 x $-$ 5 = 0

Accepted Answer

A)  $x = \frac { - 6 + \sqrt { 19 } } { 2 } , x = \frac { 6 + \sqrt { 19 } } { 2 }$ 
B)  $x = \frac { - 3 + \sqrt { 19 } } { 2 } , x = \frac { - 3 - \sqrt { 19 } } { 2 }$ 
C)  $x = \frac { 6 + \sqrt { 19 } } { 2 } , x = \frac { - 6 - \sqrt { 19 } } { 2 }$ 
A)  $x = \frac { - 6 + \sqrt { 19 } } { 2 } , x = \frac { 6 + \sqrt { 19 } } { 2 }$ 
B)  $x = \frac { - 3 + \sqrt { 19 } } { 2 } , x = \frac { - 3 - \sqrt { 19 } } { 2 }$ 
C)  $x = \frac { 6 + \sqrt { 19 } } { 2 } , x = \frac { - 6 - \sqrt { 19 } } { 2 }$

Question 7

Solve the equation for the variable t . Assume that all letters represent positive numbers. $A = P t ^ { 2 }$

Accepted Answer

The answer of Solve the equation for the variable t...

Question 8

Use the quadratic formula to solve the quadratic equation. Check your solutions by using the sum and product relationships. Match each of the equations with the number to obtain a true statement.
-$\frac { 1 \pm i \sqrt { 62 } } { 7 }$

Accepted Answer

A)  $- y ^ { 2 } + 17 y = 8$ 
B)  $8 x ^ { 2 } + x - 4 = 0$ 
C)  $16 x ^ { 2 } + 2 x + 1 = 0$ 
D)  $7 x ^ { 2 } - 2 x + 9 = 0$ 
A)  $- y ^ { 2 } + 17 y = 8$ 
B)  $8 x ^ { 2 } + x - 4 = 0$ 
C)  $16 x ^ { 2 } + 2 x + 1 = 0$ 
D)  $7 x ^ { 2 } - 2 x + 9 = 0$

Question 9

Solve the quadratic equation using the method that seems most appropriate to you. $x ^ { 4 } - 153 x ^ { 2 } + 450 = 0$

Accepted Answer

A)  $\{ \sqrt { 3 } , 5 \sqrt { 6 } \}$ 
B)  $\{ \pm \sqrt { 3 } , 5 \sqrt { 6 } \}$ 
C)  $\{ \pm \sqrt { 3 } , \pm 5 \sqrt { 6 } \}$ 
D)  $\{ - \sqrt { 3 } , \pm 5 \sqrt { 6 } \}$ 
E)  $\{ \sqrt { 3 } , \pm 5 \sqrt { 6 } \}$ 
A)  $\{ \sqrt { 3 } , 5 \sqrt { 6 } \}$ 
B)  $\{ \pm \sqrt { 3 } , 5 \sqrt { 6 } \}$ 
C)  $\{ \pm \sqrt { 3 } , \pm 5 \sqrt { 6 } \}$ 
D)  $\{ - \sqrt { 3 } , \pm 5 \sqrt { 6 } \}$ 
E)  $\{ \sqrt { 3 } , \pm 5 \sqrt { 6 } \}$

Question 10

Solve each quadratic equation by using the method of completing the square. x 2 $-$ 18 x = $-$ 80

Accepted Answer

A)  x = 8, x = 10 
B)  x = 8, x = -10 
C)  x = -8, x = 10 
A)  x = 8, x = 10 
B)  x = 8, x = -10 
C)  x = -8, x = 10

Question 11

A 93-foot guy-wire makes an angle of 60 o with the ground and is attached to a telephone pole (see the figure). Find the distance from the base of the pole to the point on the pole where the wire is attached. __________ feet

Accepted Answer

The answer of A 93-foot guy-wire makes an angle of...

Question 12

Write $\sqrt { - 16 }$ in terms of i and simplify.

Accepted Answer

A)  $-$ 4 i 
B)  $-$ 4 
C)  4 i 
A)  $-$ 4 i 
B)  $-$ 4 
C)  4 i

Question 13

Solve the inequality. ( x + 2 )( x $-$ 2 )( x $-$ 7 ) 0 Please enter your answer in interval notation.

Accepted Answer

The answer of Solve the inequality. ( x + 2...

Question 14

Write $\frac { \sqrt { - 169 } } { \sqrt { - 16 } }$ in terms of i , perform the indicated operations, and simplify.

Accepted Answer

A)  $\frac { 13 } { 4 } i$ 
B)  $- \frac { 13 } { 4 }$ 
C)  $\frac { 13 } { 4 }$ 
A)  $\frac { 13 } { 4 } i$ 
B)  $- \frac { 13 } { 4 }$ 
C)  $\frac { 13 } { 4 }$

Question 15

Solve the inequality. $4 x ^ { 2 } + 17 x - 15 \leq 0$

Accepted Answer

A)  $[ - 3,5 ]$ 
B)  $\left[ - 5 , \frac { 3 } { 4 } \right]$ 
C)  $[ - 5,3 ]$ 
A)  $[ - 3,5 ]$ 
B)  $\left[ - 5 , \frac { 3 } { 4 } \right]$ 
C)  $[ - 5,3 ]$

Question 16

Solve the quadratic equation by using the factoring method. x 2 $-$ 4 x $-$ 60 = 0

Accepted Answer

A)  x = 6, x = 10 
B)  x = -6, x = 10 
C)  x = 6, x = -10 
A)  x = 6, x = 10 
B)  x = -6, x = 10 
C)  x = 6, x = -10

Question 17

For this problem use the isosceles right triangle in the figure. If c = 16 meters find a and b . Express the answers in simplest radical form.

Accepted Answer

A)  $a = 8 \sqrt { 2 } \text { meters, } b = 16 \sqrt { 2 } \text { meters }$ 
B)  $a = 16 \sqrt { 2 } \text { meters, } b = 16 \sqrt { 2 } \text { meters }$ 
C)  $a = 8 \text { meters, } b = 8 \text { meters }$ 
D)  $a = 8 \sqrt { 2 } \text { meters, } b = 8 \sqrt { 2 } \text { meters }$ 
A)  $a = 8 \sqrt { 2 } \text { meters, } b = 16 \sqrt { 2 } \text { meters }$ 
B)  $a = 16 \sqrt { 2 } \text { meters, } b = 16 \sqrt { 2 } \text { meters }$ 
C)  $a = 8 \text { meters, } b = 8 \text { meters }$ 
D)  $a = 8 \sqrt { 2 } \text { meters, } b = 8 \sqrt { 2 } \text { meters }$

Question 18

Solve the inequality. $( x + 11 ) ^ { 2 } \geq 0$

Accepted Answer

A)  $( - 11 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , 11 )$ 
A)  $( - 11 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , 11 )$

Question 19

Solve each quadratic equation by using the factoring method. Match each equation with the corresponding solution.
-$x = - 1 , x = 7$

Accepted Answer

A)  $x ^ { 2 } - 6 x - 40 = 0$ 
B)  $x ^ { 2 } - 2 x - 63 = 0$ 
C)  $x ^ { 2 } - 6 x - 7 = 0$ 
A)  $x ^ { 2 } - 6 x - 40 = 0$ 
B)  $x ^ { 2 } - 2 x - 63 = 0$ 
C)  $x ^ { 2 } - 6 x - 7 = 0$

Question 20

Solve the quadratic equation using the method that seems most appropriate to you. $35 - 9 x - 2 x ^ { 2 } = 0$ Please enter your answer as two numbers, separated by a comma. Please enter one of the numbers as a fraction.

Accepted Answer

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

Solve the inequality. $\frac { 3 x } { x + 4 } > 6$ Please enter your answer in interval notation.

Solve the inequality. $2 x ^ { 2 } + 9 x - 5 \leq 0$ Please enter your answer in interval notation.

The number $b ^ { 2 } - 4 a c$ is called the discriminant of the quadratic equation.

Solve the inequality. $\frac { 4 x } { x + 2 } > 6$

To multiply factors in the form $\sqrt { - b }$ , rewrite $\sqrt { - b }$ in the form $i \sqrt { b }$ .

Use the method of completing the square to solve the quadratic equation. 2 x 2 + 6 x $-$ 5 = 0

Solve the equation for the variable t . Assume that all letters represent positive numbers. $A = P t ^ { 2 }$

Use the quadratic formula to solve the quadratic equation. Check your solutions by using the sum and product relationships. Match each of the equations with the number to obtain a true statement. - $\frac { 1 \pm i \sqrt { 62 } } { 7 }$

Solve the quadratic equation using the method that seems most appropriate to you. $x ^ { 4 } - 153 x ^ { 2 } + 450 = 0$

Solve each quadratic equation by using the method of completing the square. x 2 $-$ 18 x = $-$ 80

A 93-foot guy-wire makes an angle of 60 o with the ground and is attached to a telephone pole (see the figure). Find the distance from the base of the pole to the point on the pole where the wire is attached. __________ feet

Write $\sqrt { - 16 }$ in terms of i and simplify.

Solve the inequality. ( x + 2 )( x $-$ 2 )( x $-$ 7 ) 0 Please enter your answer in interval notation.

Write $\frac { \sqrt { - 169 } } { \sqrt { - 16 } }$ in terms of i , perform the indicated operations, and simplify.

Solve the inequality. $4 x ^ { 2 } + 17 x - 15 \leq 0$

Solve the quadratic equation by using the factoring method. x 2 $-$ 4 x $-$ 60 = 0

For this problem use the isosceles right triangle in the figure. If c = 16 meters find a and b . Express the answers in simplest radical form.

Solve the inequality. $( x + 11 ) ^ { 2 } \geq 0$

Solve each quadratic equation by using the factoring method. Match each equation with the corresponding solution. - $x = - 1 , x = 7$

Solve the quadratic equation using the method that seems most appropriate to you. $35 - 9 x - 2 x ^ { 2 } = 0$ Please enter your answer as two numbers, separated by a comma. Please enter one of the numbers as a fraction.

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 inequality. 3xx+4>6\frac { 3 x } { x + 4 } > 6x+43x​>6 Please enter your answer in interval notation.

Solve the inequality. 2x2+9x−5≤02 x ^ { 2 } + 9 x - 5 \leq 02x2+9x−5≤0 Please enter your answer in interval notation.

The number b2−4acb ^ { 2 } - 4 a cb2−4ac is called the discriminant of the quadratic equation.

Solve the inequality. 4xx+2>6\frac { 4 x } { x + 2 } > 6x+24x​>6

To multiply factors in the form −b\sqrt { - b }−b​ , rewrite −b\sqrt { - b }−b​ in the form ibi \sqrt { b }ib​ .

Use the method of completing the square to solve the quadratic equation. 2 x 2 + 6 x −-− 5 = 0

Solve the equation for the variable t . Assume that all letters represent positive numbers. A=Pt2A = P t ^ { 2 }A=Pt2

Use the quadratic formula to solve the quadratic equation. Check your solutions by using the sum and product relationships. Match each of the equations with the number to obtain a true statement. - 1±i627\frac { 1 \pm i \sqrt { 62 } } { 7 }71±i62​​

Solve the quadratic equation using the method that seems most appropriate to you. x4−153x2+450=0x ^ { 4 } - 153 x ^ { 2 } + 450 = 0x4−153x2+450=0

Solve each quadratic equation by using the method of completing the square. x 2 −-− 18 x = −-− 80

A 93-foot guy-wire makes an angle of 60 o with the ground and is attached to a telephone pole (see the figure). Find the distance from the base of the pole to the point on the pole where the wire is attached. __________ feet

Write −16\sqrt { - 16 }−16​ in terms of i and simplify.

Solve the inequality. ( x + 2 )( x −-− 2 )( x −-− 7 ) 0 Please enter your answer in interval notation.

Write −169−16\frac { \sqrt { - 169 } } { \sqrt { - 16 } }−16​−169​​ in terms of i , perform the indicated operations, and simplify.

Solve the inequality. 4x2+17x−15≤04 x ^ { 2 } + 17 x - 15 \leq 04x2+17x−15≤0

Solve the quadratic equation by using the factoring method. x 2 −-− 4 x −-− 60 = 0

For this problem use the isosceles right triangle in the figure. If c = 16 meters find a and b . Express the answers in simplest radical form.

Solve the inequality. (x+11)2≥0( x + 11 ) ^ { 2 } \geq 0(x+11)2≥0

Solve each quadratic equation by using the factoring method. Match each equation with the corresponding solution. - x=−1,x=7x = - 1 , x = 7x=−1,x=7

Solve the quadratic equation using the method that seems most appropriate to you. 35−9x−2x2=035 - 9 x - 2 x ^ { 2 } = 035−9x−2x2=0 Please enter your answer as two numbers, separated by a comma. Please enter one of the numbers as a fraction.

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 inequality. $\frac { 3 x } { x + 4 } > 6$ Please enter your answer in interval notation.

Solve the inequality. $2 x ^ { 2 } + 9 x - 5 \leq 0$ Please enter your answer in interval notation.

The number $b ^ { 2 } - 4 a c$ is called the discriminant of the quadratic equation.

Solve the inequality. $\frac { 4 x } { x + 2 } > 6$

To multiply factors in the form $\sqrt { - b }$ , rewrite $\sqrt { - b }$ in the form $i \sqrt { b }$ .

Use the method of completing the square to solve the quadratic equation. 2 x 2 + 6 x $-$ 5 = 0

Solve the equation for the variable t . Assume that all letters represent positive numbers. $A = P t ^ { 2 }$

Use the quadratic formula to solve the quadratic equation. Check your solutions by using the sum and product relationships. Match each of the equations with the number to obtain a true statement. - $\frac { 1 \pm i \sqrt { 62 } } { 7 }$

Solve the quadratic equation using the method that seems most appropriate to you. $x ^ { 4 } - 153 x ^ { 2 } + 450 = 0$

Solve each quadratic equation by using the method of completing the square. x 2 $-$ 18 x = $-$ 80

Write $\sqrt { - 16 }$ in terms of i and simplify.

Solve the inequality. ( x + 2 )( x $-$ 2 )( x $-$ 7 ) 0 Please enter your answer in interval notation.

Write $\frac { \sqrt { - 169 } } { \sqrt { - 16 } }$ in terms of i , perform the indicated operations, and simplify.

Solve the inequality. $4 x ^ { 2 } + 17 x - 15 \leq 0$

Solve the quadratic equation by using the factoring method. x 2 $-$ 4 x $-$ 60 = 0

Solve the inequality. $( x + 11 ) ^ { 2 } \geq 0$

Solve each quadratic equation by using the factoring method. Match each equation with the corresponding solution. - $x = - 1 , x = 7$

Solve the quadratic equation using the method that seems most appropriate to you. $35 - 9 x - 2 x ^ { 2 } = 0$ Please enter your answer as two numbers, separated by a comma. Please enter one of the numbers as a fraction.