Question 1

Solve the equation. $7 x ^ { 2 } - 3 x - 1 = 0$

Accepted Answer

The answer of Solve the equation. \(7 x ^ {...

Question 2

Solve $( x + 1 ) ^ { 2 } - 7 = 0$ by square root property.

Accepted Answer

A)  $\{ - 1 \pm 4 \sqrt { 5 } \}$ 
B)  $\{ 1 \pm 4 \sqrt { 5 } \}$ 
C)  $\{ 1 \pm \sqrt { 7 } \}$ 
D)  $\{ - 1 \pm \sqrt { 7 } \}$ 
A)  $\{ - 1 \pm 4 \sqrt { 5 } \}$ 
B)  $\{ 1 \pm 4 \sqrt { 5 } \}$ 
C)  $\{ 1 \pm \sqrt { 7 } \}$ 
D)  $\{ - 1 \pm \sqrt { 7 } \}$

Question 3

A box with no top is to be made by cutting a 2-inch square from each corner of the square sheet of metal. After bending up the sides, the volume of the box is to be 512 cubic inches. What are the dimensions of the square sheet?

Accepted Answer

A)  17 inches by 17 inches 
B)  6 inches by 6 inches 
C)  19 inches by 19 inches 
D)  20 inches by 20 inches 
A)  17 inches by 17 inches 
B)  6 inches by 6 inches 
C)  19 inches by 19 inches 
D)  20 inches by 20 inches

Question 4

Solve: $\frac { x ^ { 2 } } { 3 } - \frac { x } { 2 } = \frac { 3 } { 8 }$

Accepted Answer

A)  $\left\{ \frac { 3 } { 2 } \right\}$ 
B)  $\left\{ \frac { 3 } { 4 } \pm \frac { 3 \sqrt { 3 } } { 4 } i \right\}$ 
C)  none of these 
D)  $\left\{ \frac { 3 \pm 3 \sqrt { 3 } } { 4 } \right\}$ 
A)  $\left\{ \frac { 3 } { 2 } \right\}$ 
B)  $\left\{ \frac { 3 } { 4 } \pm \frac { 3 \sqrt { 3 } } { 4 } i \right\}$ 
C)  none of these 
D)  $\left\{ \frac { 3 \pm 3 \sqrt { 3 } } { 4 } \right\}$

Question 5

Use the quadratic formula to solve $x ^ { 2 } - 4 i x - 3 = 0$ .

Accepted Answer

The answer of Use the quadratic formula to solve \(x...

Question 6

Use the square root property to solve the equation. $( a + 1 ) ^ { 2 } = 8$

Accepted Answer

The answer of Use the square root property to solve...

Question 7

Solve the inequality. Write the solution set in interval notation and graph it. $\log _ { 5 } 3$

Accepted Answer

The answer of Solve the inequality. Write the solution set...

Question 8

Which of the following is an example of a quadratic equation?

Accepted Answer

A)  $5 x - 6 = 0$ 
B)  $2 x ^ { 2 } - 6 x - 6 = 0$ 
C)  $9 x ^ { 3 } + 3 x ^ { 2 } - 5 x + 8 = 0$ 
D)  $\left| x ^ { 2 } - 1 \right| = 0$ 
A)  $5 x - 6 = 0$ 
B)  $2 x ^ { 2 } - 6 x - 6 = 0$ 
C)  $9 x ^ { 3 } + 3 x ^ { 2 } - 5 x + 8 = 0$ 
D)  $\left| x ^ { 2 } - 1 \right| = 0$

Question 9

Graph the inequality. $\log _ { 5 } 3$

Accepted Answer

The answer of Graph the inequality. \(\log _ { 5...

Question 10

The hypotenuse of a right triangle is 6.1 units long. The longer leg is 4.9 units longer than the shorter leg. Find the lengths of the sides of the triangle. longer leg __________ units shorter leg __________ units

Accepted Answer

The answer of The hypotenuse of a right triangle is...

Question 11

Solve $6 x ^ { 2 } + 12 x + 5 = 0$ by the quadratic formula.

Accepted Answer

A)  $\left\{ \frac { - 6 \pm \sqrt { 6 } } { 6 } \right\}$ 
B)  $\{ - 1 \pm \sqrt { 6 } \}$ 
C)  $\left\{ \frac { 6 \pm \sqrt { 6 } } { 6 } \right\}$ 
D)  $\{ \pm \sqrt { 6 } \}$ 
A)  $\left\{ \frac { - 6 \pm \sqrt { 6 } } { 6 } \right\}$ 
B)  $\{ - 1 \pm \sqrt { 6 } \}$ 
C)  $\left\{ \frac { 6 \pm \sqrt { 6 } } { 6 } \right\}$ 
D)  $\{ \pm \sqrt { 6 } \}$

Question 12

Solve $( x - 7 ) ^ { 2 } = 96$ by the square root property.

Accepted Answer

A)  $\{ - 11 \sqrt { 6 } , \sqrt { 6 } \}$ 
B)  $\{ - \sqrt { 6 } , 11 \sqrt { 6 } \}$ 
C)  $\{ - 7 \pm 4 \sqrt { 6 } \}$ 
D)  $\{ 7 \pm 4 \sqrt { 6 } \}$ 
A)  $\{ - 11 \sqrt { 6 } , \sqrt { 6 } \}$ 
B)  $\{ - \sqrt { 6 } , 11 \sqrt { 6 } \}$ 
C)  $\{ - 7 \pm 4 \sqrt { 6 } \}$ 
D)  $\{ 7 \pm 4 \sqrt { 6 } \}$

Question 13

Use the quadratic formula to solve $x ^ { 2 } - 8 \sqrt { 5 } x - 45 = 0$ .

Accepted Answer

The answer of Use the quadratic formula to solve \(x...

Question 14

The graph of $f ( x ) = x ^ { 2 } - 6 x + 5$ is a _________.

Accepted Answer

The answer of The graph of \(f ( x )...

Question 15

Tickets to a school dance cost $4, and the projected attendance is 300 persons. It is further projected that for every $0.1 increase in ticket price, the average attendance will decrease by 5. At what ticket price will the receipts from the dance be $1,242?

Accepted Answer

The answer of Tickets to a school dance cost $4,...

Question 16

What is the next step in solving $4 x ^ { 2 } - 12 x = 9$ by completing the square?

Accepted Answer

A)  Add -9 to each side of the equation. 
B)  Take one-half of -12 and add to each side of the equation. 
C)  Take one-half of 4 and square it and then add this number to each side of the equation. 
D)  Divide each side of the equation by 4 . 
A)  Add -9 to each side of the equation. 
B)  Take one-half of -12 and add to each side of the equation. 
C)  Take one-half of 4 and square it and then add this number to each side of the equation. 
D)  Divide each side of the equation by 4 .

Question 17

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

Accepted Answer

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

Question 18

The graph of $f ( x ) = x ^ { 2 } - 7 x + 2$ is

Accepted Answer

A)  a parabola that opens upward 
B)  a parabola that opens downward 
C)  a parabola that opens to the right 
D)  a parabola that opens to the left 
A)  a parabola that opens upward 
B)  a parabola that opens downward 
C)  a parabola that opens to the right 
D)  a parabola that opens to the left

Question 19

Solve the equation. $\frac { x ^ { 2 } } { 7 } + \frac { 9 } { 7 } x = - 1$

Accepted Answer

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

Question 20

Graph: $y > x ^ { 2 } - 2 x - 2$

Accepted Answer

The answer of Graph: \(y > x ^ { 2...

Solve the equation. $7 x ^ { 2 } - 3 x - 1 = 0$

Solve $( x + 1 ) ^ { 2 } - 7 = 0$ by square root property.

A box with no top is to be made by cutting a 2-inch square from each corner of the square sheet of metal. After bending up the sides, the volume of the box is to be 512 cubic inches. What are the dimensions of the square sheet?

Solve: $\frac { x ^ { 2 } } { 3 } - \frac { x } { 2 } = \frac { 3 } { 8 }$

Use the quadratic formula to solve $x ^ { 2 } - 4 i x - 3 = 0$ .

Use the square root property to solve the equation. $( a + 1 ) ^ { 2 } = 8$

Solve the inequality. Write the solution set in interval notation and graph it. $\log _ { 5 } 3$

Which of the following is an example of a quadratic equation?

Graph the inequality. $\log _ { 5 } 3$

The hypotenuse of a right triangle is 6.1 units long. The longer leg is 4.9 units longer than the shorter leg. Find the lengths of the sides of the triangle. longer leg units shorter leg units

Solve $6 x ^ { 2 } + 12 x + 5 = 0$ by the quadratic formula.

Solve $( x - 7 ) ^ { 2 } = 96$ by the square root property.

Use the quadratic formula to solve $x ^ { 2 } - 8 \sqrt { 5 } x - 45 = 0$ .

The graph of $f ( x ) = x ^ { 2 } - 6 x + 5$ is a _________.

Tickets to a school dance cost $4, and the projected attendance is 300 persons. It is further projected that for every $0.1 increase in ticket price, the average attendance will decrease by 5. At what ticket price will the receipts from the dance be $1,242?

What is the next step in solving $4 x ^ { 2 } - 12 x = 9$ by completing the square?

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

The graph of $f ( x ) = x ^ { 2 } - 7 x + 2$ is

Solve the equation. $\frac { x ^ { 2 } } { 7 } + \frac { 9 } { 7 } x = - 1$

Graph: $y > x ^ { 2 } - 2 x - 2$ $Graph: y > x ^ { 2 } - 2 x - 2$

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 8: Quadratic Equations, Functions, and Inequalities

Solve the equation. 7x2−3x−1=07 x ^ { 2 } - 3 x - 1 = 07x2−3x−1=0

Solve (x+1)2−7=0( x + 1 ) ^ { 2 } - 7 = 0(x+1)2−7=0 by square root property.

A box with no top is to be made by cutting a 2-inch square from each corner of the square sheet of metal. After bending up the sides, the volume of the box is to be 512 cubic inches. What are the dimensions of the square sheet?

Solve: x23−x2=38\frac { x ^ { 2 } } { 3 } - \frac { x } { 2 } = \frac { 3 } { 8 }3x2​−2x​=83​

Use the quadratic formula to solve x2−4ix−3=0x ^ { 2 } - 4 i x - 3 = 0x2−4ix−3=0 .

Use the square root property to solve the equation. (a+1)2=8( a + 1 ) ^ { 2 } = 8(a+1)2=8

Solve the inequality. Write the solution set in interval notation and graph it. log⁡53\log _ { 5 } 3log5​3

Which of the following is an example of a quadratic equation?

Graph the inequality. log⁡53\log _ { 5 } 3log5​3

The hypotenuse of a right triangle is 6.1 units long. The longer leg is 4.9 units longer than the shorter leg. Find the lengths of the sides of the triangle. longer leg __________ units shorter leg __________ units

Solve 6x2+12x+5=06 x ^ { 2 } + 12 x + 5 = 06x2+12x+5=0 by the quadratic formula.

Solve (x−7)2=96( x - 7 ) ^ { 2 } = 96(x−7)2=96 by the square root property.

Use the quadratic formula to solve x2−85x−45=0x ^ { 2 } - 8 \sqrt { 5 } x - 45 = 0x2−85​x−45=0 .

The graph of f(x)=x2−6x+5f ( x ) = x ^ { 2 } - 6 x + 5f(x)=x2−6x+5 is a _________.

Tickets to a school dance cost $4, and the projected attendance is 300 persons. It is further projected that for every $0.1 increase in ticket price, the average attendance will decrease by 5. At what ticket price will the receipts from the dance be $1,242?

What is the next step in solving 4x2−12x=94 x ^ { 2 } - 12 x = 94x2−12x=9 by completing the square?

Solve the equation. x2+2x=7x ^ { 2 } + 2 x = 7x2+2x=7

The graph of f(x)=x2−7x+2f ( x ) = x ^ { 2 } - 7 x + 2f(x)=x2−7x+2 is

Solve the equation. x27+97x=−1\frac { x ^ { 2 } } { 7 } + \frac { 9 } { 7 } x = - 17x2​+79​x=−1

Graph: y>x2−2x−2y > x ^ { 2 } - 2 x - 2y>x2−2x−2

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Solve the equation. $7 x ^ { 2 } - 3 x - 1 = 0$

Solve $( x + 1 ) ^ { 2 } - 7 = 0$ by square root property.

Solve: $\frac { x ^ { 2 } } { 3 } - \frac { x } { 2 } = \frac { 3 } { 8 }$

Use the quadratic formula to solve $x ^ { 2 } - 4 i x - 3 = 0$ .

Use the square root property to solve the equation. $( a + 1 ) ^ { 2 } = 8$

Solve the inequality. Write the solution set in interval notation and graph it. $\log _ { 5 } 3$

Graph the inequality. $\log _ { 5 } 3$

The hypotenuse of a right triangle is 6.1 units long. The longer leg is 4.9 units longer than the shorter leg. Find the lengths of the sides of the triangle. longer leg units shorter leg units

Solve $6 x ^ { 2 } + 12 x + 5 = 0$ by the quadratic formula.

Solve $( x - 7 ) ^ { 2 } = 96$ by the square root property.

Use the quadratic formula to solve $x ^ { 2 } - 8 \sqrt { 5 } x - 45 = 0$ .

The graph of $f ( x ) = x ^ { 2 } - 6 x + 5$ is a _________.

What is the next step in solving $4 x ^ { 2 } - 12 x = 9$ by completing the square?

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

The graph of $f ( x ) = x ^ { 2 } - 7 x + 2$ is

Solve the equation. $\frac { x ^ { 2 } } { 7 } + \frac { 9 } { 7 } x = - 1$

Graph: $y > x ^ { 2 } - 2 x - 2$ $Graph: y > x ^ { 2 } - 2 x - 2$