Question 1

What are the critical numbers for each inequality?
 a. $\log _ { 5 } 3$ b. $\frac { \log 3 } { \log 5 }$

Accepted Answer

The answer of What are the critical numbers for each...

Question 2

If one number in an interval satisfies the inequality, ________ numbers in that interval will satisfy the inequality.

Accepted Answer

The answer of If one number in an interval satisfies...

Question 3

The following is a student s solution for solving $2 x ^ { 2 } = 1 - 5 x$ . What error did the student make?
 $\begin{array} { l } 
2 x ^ { 2 } = 1 - 5 x \
2 x ^ { 2 } - 1 + 5 x = 0 \
x = \frac { 1 \pm \sqrt { ( - 1 ) ^ { 2 } - 4 ( 2 ) ( 5 ) } } { 4 } \
x = \frac { 1 \pm \sqrt { 1 - 40 } } { 4 } \
x = \frac { 1 \pm \sqrt { - 39 } } { 4 } \
x = \frac { 1 } { 4 } \pm \frac { \sqrt { 39 } } { 4 } i
\end{array}$

Accepted Answer

Since the student di

Question 4

Simplify: $\frac { 6 \pm 2 \sqrt { 3 } } { 8 }$

Accepted Answer

The answer of Simplify: \(\frac { 6 \pm 2 \sqrt...

Question 5

Solve: $x ^ { 2 } - x - 2 < 0$

Accepted Answer

A)  $( - \infty , - 1 ) \cup ( 2 , \infty )$ 
B)  $( - \infty , - 1 )$ 
C)  $( - 2,1 )$ 
D)  $( - 1,2 )$ 
A)  $( - \infty , - 1 ) \cup ( 2 , \infty )$ 
B)  $( - \infty , - 1 )$ 
C)  $( - 2,1 )$ 
D)  $( - 1,2 )$

Question 6

Use the square root property to solve the equation. $z ^ { 2 } = 25$

Accepted Answer

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

Question 7

Use completing the square to solve the equation. $x ^ { 2 } - 2 x - 3 = 0$

Accepted Answer

The answer of Use completing the square to solve the...

Question 8

Solve $x ^ { 2 } - 10 x - 4 = 0$ by completing the square.

Accepted Answer

A)  $\{ 5 \pm \sqrt { 89 } \}$ 
B)  $\{ - 5 \pm \sqrt { 89 } \}$ 
C)  $\{ 5 \pm \sqrt { 29 } \}$ 
D)  $\{ - 5 \pm \sqrt { 29 } \}$ 
A)  $\{ 5 \pm \sqrt { 89 } \}$ 
B)  $\{ - 5 \pm \sqrt { 89 } \}$ 
C)  $\{ 5 \pm \sqrt { 29 } \}$ 
D)  $\{ - 5 \pm \sqrt { 29 } \}$

Question 9

Use the quadratic formula to solve the equation. $9 t ^ { 2 } - 9 t - 28 = 0$

Accepted Answer

The answer of Use the quadratic formula to solve the...

Question 10

Solve $x ^ { 2 } + \sqrt { 19 } x + \frac { 15 } { 4 } = 0$ by completing the square.

Accepted Answer

The answer of Solve \(x ^ { 2 } +...

Question 11

Which of the following equations has a parabola as its graph?

Accepted Answer

A)  $f ( x ) = | x - 3 |$ 
B)  $f ( x ) = 3 x - 5$ 
C)  $f ( x ) = x ^ { 2 } - 3 x + 5$ 
D)  $f ( x ) = x ^ { 3 } + 5$ 
A)  $f ( x ) = | x - 3 |$ 
B)  $f ( x ) = 3 x - 5$ 
C)  $f ( x ) = x ^ { 2 } - 3 x + 5$ 
D)  $f ( x ) = x ^ { 3 } + 5$

Question 12

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 13

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 14

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 15

Use completing the square to solve the equation. $x ^ { 2 } - 6 x + 10 = 0$

Accepted Answer

The answer of Use completing the square to solve the...

Question 16

Tickets to a dance cost $5.00 and the projected attendance is 350 people. It is further projected that for every $0.50 increase in ticket price, the average attendance will decrease by 5. At what ticket price will the receipts from the dance be $3,360?

Accepted Answer

A)  $9.50 
B)  $11.00 
C)  $19.00 
D)  $12.00 
A)  $9.50 
B)  $11.00 
C)  $19.00 
D)  $12.00

Question 17

Refer to the graph. Fill in the blanks.   $f ( x ) = 2 x ^ { 2 } - 12 x + 17$ is called a __________ function. Its graph is a cup-shaped figure called a __________.

Accepted Answer

The answer of Refer to the graph. Fill in the...

Question 18

Which of the following equations would be obtained when solving $4 x ^ { 2 } + 8 x + 8 = 0$ by completing the square?

Accepted Answer

A)  $\left( x ^ { 2 } + 1 \right) ^ { 2 } = - 1$ 
B)  $( x + 1 ) ^ { 2 } = 3$ 
C)  $( x + 1 ) ^ { 2 } = - 3$ 
D)  $( x + 1 ) ^ { 2 } = - 1$ 
A)  $\left( x ^ { 2 } + 1 \right) ^ { 2 } = - 1$ 
B)  $( x + 1 ) ^ { 2 } = 3$ 
C)  $( x + 1 ) ^ { 2 } = - 3$ 
D)  $( x + 1 ) ^ { 2 } = - 1$

Question 19

Graph $f(x)=2 x^{2}$
 and $g ( x ) = 2 ( x - 3 ) ^ { 2 }$ on the same coordinate system. Then describe how the graphs are similar and how they are different.

Accepted Answer

@#IMG-DLM&
 The two graphs have the same

Question 20

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...

What are the critical numbers for each inequality? a. $\log _ { 5 } 3$ b. $\frac { \log 3 } { \log 5 }$

If one number in an interval satisfies the inequality, ________ numbers in that interval will satisfy the inequality.

The following is a student s solution for solving $2 x ^ { 2 } = 1 - 5 x$ . What error did the student make? 2=1-5x 2-1+5x=0 x= x= x= x=\pmi

Simplify: $\frac { 6 \pm 2 \sqrt { 3 } } { 8 }$

Solve: $x ^ { 2 } - x - 2 < 0$

Use the square root property to solve the equation. $z ^ { 2 } = 25$

Use completing the square to solve the equation. $x ^ { 2 } - 2 x - 3 = 0$

Solve $x ^ { 2 } - 10 x - 4 = 0$ by completing the square.

Use the quadratic formula to solve the equation. $9 t ^ { 2 } - 9 t - 28 = 0$

Solve $x ^ { 2 } + \sqrt { 19 } x + \frac { 15 } { 4 } = 0$ by completing the square.

Which of the following equations has a parabola as its graph?

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

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

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

Use completing the square to solve the equation. $x ^ { 2 } - 6 x + 10 = 0$

Tickets to a dance cost $5.00 and the projected attendance is 350 people. It is further projected that for every $0.50 increase in ticket price, the average attendance will decrease by 5. At what ticket price will the receipts from the dance be $3,360?

Refer to the graph. Fill in the blanks. $Refer to the graph. Fill in the blanks. f ( x ) = 2 x ^ { 2 } - 12 x + 17 is called a function. Its graph is a cup-shaped figure called a .$ $f ( x ) = 2 x ^ { 2 } - 12 x + 17$ is called a function. Its graph is a cup-shaped figure called a .

Which of the following equations would be obtained when solving $4 x ^ { 2 } + 8 x + 8 = 0$ by completing the square?

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

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

What are the critical numbers for each inequality? a. log⁡53\log _ { 5 } 3log5​3 b. log⁡3log⁡5\frac { \log 3 } { \log 5 }log5log3​

If one number in an interval satisfies the inequality, ________ numbers in that interval will satisfy the inequality.

The following is a student s solution for solving 2x2=1−5x2 x ^ { 2 } = 1 - 5 x2x2=1−5x . What error did the student make? 2=1-5x 2-1+5x=0 x= x= x= x=\pmi

Simplify: 6±238\frac { 6 \pm 2 \sqrt { 3 } } { 8 }86±23​​

Solve: x2−x−2<0x ^ { 2 } - x - 2 < 0x2−x−2<0

Use the square root property to solve the equation. z2=25z ^ { 2 } = 25z2=25

Use completing the square to solve the equation. x2−2x−3=0x ^ { 2 } - 2 x - 3 = 0x2−2x−3=0

Solve x2−10x−4=0x ^ { 2 } - 10 x - 4 = 0x2−10x−4=0 by completing the square.

Use the quadratic formula to solve the equation. 9t2−9t−28=09 t ^ { 2 } - 9 t - 28 = 09t2−9t−28=0

Solve x2+19x+154=0x ^ { 2 } + \sqrt { 19 } x + \frac { 15 } { 4 } = 0x2+19​x+415​=0 by completing the square.

Which of the following equations has a parabola as its graph?

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

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

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

Use completing the square to solve the equation. x2−6x+10=0x ^ { 2 } - 6 x + 10 = 0x2−6x+10=0

Tickets to a dance cost $5.00 and the projected attendance is 350 people. It is further projected that for every $0.50 increase in ticket price, the average attendance will decrease by 5. At what ticket price will the receipts from the dance be $3,360?

Refer to the graph. Fill in the blanks. f(x)=2x2−12x+17f ( x ) = 2 x ^ { 2 } - 12 x + 17f(x)=2x2−12x+17 is called a __________ function. Its graph is a cup-shaped figure called a __________.

Which of the following equations would be obtained when solving 4x2+8x+8=04 x ^ { 2 } + 8 x + 8 = 04x2+8x+8=0 by completing the square?

Graph f(x)=2x2f(x)=2 x^{2}f(x)=2x2 and g(x)=2(x−3)2g ( x ) = 2 ( x - 3 ) ^ { 2 }g(x)=2(x−3)2 on the same coordinate system. Then describe how the graphs are similar and how they are different.

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

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

What are the critical numbers for each inequality? a. $\log _ { 5 } 3$ b. $\frac { \log 3 } { \log 5 }$

The following is a student s solution for solving $2 x ^ { 2 } = 1 - 5 x$ . What error did the student make? 2=1-5x 2-1+5x=0 x= x= x= x=\pmi

Simplify: $\frac { 6 \pm 2 \sqrt { 3 } } { 8 }$

Solve: $x ^ { 2 } - x - 2 < 0$

Use the square root property to solve the equation. $z ^ { 2 } = 25$

Use completing the square to solve the equation. $x ^ { 2 } - 2 x - 3 = 0$

Solve $x ^ { 2 } - 10 x - 4 = 0$ by completing the square.

Use the quadratic formula to solve the equation. $9 t ^ { 2 } - 9 t - 28 = 0$

Solve $x ^ { 2 } + \sqrt { 19 } x + \frac { 15 } { 4 } = 0$ by completing the square.

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

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

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

Use completing the square to solve the equation. $x ^ { 2 } - 6 x + 10 = 0$

Refer to the graph. Fill in the blanks. $Refer to the graph. Fill in the blanks. f ( x ) = 2 x ^ { 2 } - 12 x + 17 is called a function. Its graph is a cup-shaped figure called a .$ $f ( x ) = 2 x ^ { 2 } - 12 x + 17$ is called a function. Its graph is a cup-shaped figure called a .

Which of the following equations would be obtained when solving $4 x ^ { 2 } + 8 x + 8 = 0$ by completing the square?

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