Question 1

Find the domain of x in the expression.​ $\sqrt { 9 - 4 x ^ { 2 } }$ ​

Accepted Answer

A)  $\left[ \frac { 3 } { 2 } , \frac { 3 } { 2 } \right]$ 
B)  $\left[ - \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right]$ 
C)  $\left[ - \frac { 3 } { 2 } , \frac { 3 } { 2 } \right]$ 
D)  $\left[ - \frac { 2 } { 3 } , \frac { 2 } { 3 } \right]$ 
E)  $\left[ - \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right]$ 
A)  $\left[ \frac { 3 } { 2 } , \frac { 3 } { 2 } \right]$ 
B)  $\left[ - \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right]$ 
C)  $\left[ - \frac { 3 } { 2 } , \frac { 3 } { 2 } \right]$ 
D)  $\left[ - \frac { 2 } { 3 } , \frac { 2 } { 3 } \right]$ 
E)  $\left[ - \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right]$

Question 2

Find the domain of x in the expression $\sqrt [ 4 ] { x ^ { 3 } - 3 x }$ . ​

Accepted Answer

A)  $( - \infty , - \sqrt { 3 } ] , [ \sqrt { 3 } , \infty )$ 
B)  $( - \infty , \sqrt { 3 } ] , [ \sqrt { 3 } , \infty )$ 
C)  $[ - \sqrt { 3 } , 0 ] , [ \sqrt { 3 } , \infty )$ 
D)  $[ - \sqrt { 3 } , \sqrt { 3 } ]$ 
E)  $( - \infty , - \sqrt { 3 } ) , ( 0 , \sqrt { 3 } )$ 
A)  $( - \infty , - \sqrt { 3 } ] , [ \sqrt { 3 } , \infty )$ 
B)  $( - \infty , \sqrt { 3 } ] , [ \sqrt { 3 } , \infty )$ 
C)  $[ - \sqrt { 3 } , 0 ] , [ \sqrt { 3 } , \infty )$ 
D)  $[ - \sqrt { 3 } , \sqrt { 3 } ]$ 
E)  $( - \infty , - \sqrt { 3 } ) , ( 0 , \sqrt { 3 } )$

Question 3

Find the domain of x in the expression.​ $\sqrt { x ^ { 2 } - 7 x + 12 }$ ​

Accepted Answer

A)  $( - \infty , 3 ] \cup [ 4 , \infty )$ 
B)  $( - \infty , 3 ] \cap [ 4 , \infty )$ 
C)  $( \infty , - 3 ] \cup [ 4 , \infty )$ 
D)  $( \infty , 3 ] \cap [ 4 , \infty )$ 
E)  $( \infty , - 3 ] \cap [ 4 , \infty )$ 
A)  $( - \infty , 3 ] \cup [ 4 , \infty )$ 
B)  $( - \infty , 3 ] \cap [ 4 , \infty )$ 
C)  $( \infty , - 3 ] \cup [ 4 , \infty )$ 
D)  $( \infty , 3 ] \cap [ 4 , \infty )$ 
E)  $( \infty , - 3 ] \cap [ 4 , \infty )$

Question 4

Determine whether the value of $$x = \frac { 2 } { 7 }$$ is a solution of the inequality. $x ^ { 2 } - 2 < 0$ ​

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 5

Solve the inequality and graph the solution on the real number line.​ $$\frac { 3 x - 5 } { x - 5 } \geq 0$$ ​

Accepted Answer

A) ( $$- \infty , \frac { 5 } { 3 }$$ ​] $$\cup( 5 , \infty )$$   
B) ( $$- \infty , \frac { 5 } { 3 }$$ ​] $$\cup ( - 5 , \infty )$$   
C) ( $$- \infty , - \frac { 5 } { 3 }$$ ​] $$\cup( 5 , \infty )$$   
D) ( $$- \infty , - \frac { 5 } { 3 }$$ ​] $$\cup ( - 5 , \infty )$$   
E) ( $$- \infty , \frac { 5 } { 3 }$$ ​] $$\cap ( 5 , \infty )$$   
A) ( $$- \infty , \frac { 5 } { 3 }$$ ​] $$\cup( 5 , \infty )$$   
B) ( $$- \infty , \frac { 5 } { 3 }$$ ​] $$\cup ( - 5 , \infty )$$   
C) ( $$- \infty , - \frac { 5 } { 3 }$$ ​] $$\cup( 5 , \infty )$$   
D) ( $$- \infty , - \frac { 5 } { 3 }$$ ​] $$\cup ( - 5 , \infty )$$   
E) ( $$- \infty , \frac { 5 } { 3 }$$ ​] $$\cap ( 5 , \infty )$$

Question 6

Solve the inequality and graph the solution on the real number line.​ $$\frac { x + 9 } { x + 1 } - 2 < 0$$ ​

Accepted Answer

A)  $$( - \infty , - 1 ) \cup ( 7 , \infty )$$   
B)  $$( - \infty , - 1 ) \cap ( - 7 , \infty )$$   
C)  $$( - \infty , 1 ) \cap ( 7 , \infty )$$   
D)  $$( - \infty , - 1 ) \cup ( - 7 , \infty )$$   
E)  $$( - \infty , - 1 ) \cap ( 7 , \infty )$$   
A)  $$( - \infty , - 1 ) \cup ( 7 , \infty )$$   
B)  $$( - \infty , - 1 ) \cap ( - 7 , \infty )$$   
C)  $$( - \infty , 1 ) \cap ( 7 , \infty )$$   
D)  $$( - \infty , - 1 ) \cup ( - 7 , \infty )$$   
E)  $$( - \infty , - 1 ) \cap ( 7 , \infty )$$

Question 7

Find the domain of x in the expression.​ $\sqrt { 25 - x ^ { 2 } }$ ​

Accepted Answer

A)  $( - 25,25 )$ 
B)  $$[ - 25,25 ]$$ 
C)  $$( - 5,5 )$$ 
D)  $[ - 5,25 )$ 
E)  $[ - 5,5 ]$ 
A)  $( - 25,25 )$ 
B)  $$[ - 25,25 ]$$ 
C)  $$( - 5,5 )$$ 
D)  $[ - 5,25 )$ 
E)  $[ - 5,5 ]$

Question 8

Find the domain of x in the expression.​ $\sqrt { \frac { x } { x ^ { 2 } - 2 x - 24 } }$ ​

Accepted Answer

A)  $( - 4,0 ] \cap ( 6 , \infty )$ 
B)  $( - 6,0 ] \cup ( 4 , \infty )$ 
C)  $( - 4,0 ] \cup ( 6 , \infty )$ 
D)  $( - 4,0 ] \cup ( - 6 , \infty )$ 
E)  $( - 6,0 ] \cap ( - 4 , \infty )$ 
A)  $( - 4,0 ] \cap ( 6 , \infty )$ 
B)  $( - 6,0 ] \cup ( 4 , \infty )$ 
C)  $( - 4,0 ] \cup ( 6 , \infty )$ 
D)  $( - 4,0 ] \cup ( - 6 , \infty )$ 
E)  $( - 6,0 ] \cap ( - 4 , \infty )$

Question 9

Solve the inequality and graph the solution on the real number line.​ $$x ^ { 2 } > 2 x + 48$$ ​

Accepted Answer

A)  $$( - \infty , - 6 ) \cup ( 8 , \infty )$$   
B)  $$( - \infty , 6 ) \cup ( 8 , \infty )$$   
C)  $$( - \infty , - 6 ) \cup ( - 8 , - \infty )$$   
D)  $$( - \infty , - 6 ) \cup ( - 8 , \infty )$$   
E)  $$( - \infty , 6 ) \cup ( 8 , \infty )$$   
A)  $$( - \infty , - 6 ) \cup ( 8 , \infty )$$   
B)  $$( - \infty , 6 ) \cup ( 8 , \infty )$$   
C)  $$( - \infty , - 6 ) \cup ( - 8 , - \infty )$$   
D)  $$( - \infty , - 6 ) \cup ( - 8 , \infty )$$   
E)  $$( - \infty , 6 ) \cup ( 8 , \infty )$$

Question 10

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy the following inequality. ​
Equation: $y = \frac { 7 x } { x ^ { 2 } + 6 }$ ​
Inequality: $y \geq 1$ ​

Accepted Answer

A) ​   $$1 \leq x \leq 6$$ 
B) ​   $$1 \leq x < 6$$ 
C) ​   $$1 < x < 6$$ 
D) ​   $$1 < x \leq 6$$ 
E) ​   $$1 < x \leq 6$$ 
A) ​   $$1 \leq x \leq 6$$ 
B) ​   $$1 \leq x < 6$$ 
C) ​   $$1 < x < 6$$ 
D) ​   $$1 < x \leq 6$$ 
E) ​   $$1 < x \leq 6$$

Question 11

Solve the inequality and graph the solution on the real number line.​ $$x ^ { 2 } + 3 x > 4$$ ​

Accepted Answer

A)  $$( - \infty , - 4 ) \cup ( 1 , \infty )$$   
B)  $$( - \infty , - 4 ) \cup ( - 1 , \infty )$$   
C)  $$( - \infty , - 4 ) \cup ( 1 , \infty )$$   
D)  $$( - \infty , - 4 ) \cup ( - 1 , \infty )$$   
E)  $$( - \infty , - 4 ) \cup ( 1 , - \infty )$$   
A)  $$( - \infty , - 4 ) \cup ( 1 , \infty )$$   
B)  $$( - \infty , - 4 ) \cup ( - 1 , \infty )$$   
C)  $$( - \infty , - 4 ) \cup ( 1 , \infty )$$   
D)  $$( - \infty , - 4 ) \cup ( - 1 , \infty )$$   
E)  $$( - \infty , - 4 ) \cup ( 1 , - \infty )$$

Question 12

The numbers N (in millions)of students enrolled in schools in the United States from 1995 through 1997 are shown in the table. ​
$$\begin{array} { | c | c | } 
\hline \text { Year } & \text { Number, } N \
\hline 1995 & 71.2 \
\hline 1996 & 72.3 \
\hline 1997 & 74 \
\hline
\end{array}$$
Use a graphing utility to create a scatter plot of the data.Let t represent the year,with t = 5 corresponding to 1995.

Accepted Answer

A) ​ ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​ ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 13

Find the domain of x in the following expression. $\sqrt [ 3 ] { x ^ { 4 } - 625 }$

Accepted Answer

A)  $[ - 5,5 ]$ 
B)  $( - \infty , 5 ) \cup ( 5 , \infty )$ 
C)  $[ 5 , \infty )$ 
D)  $( 5 , \infty )$ 
E) all real numbers 
A)  $[ - 5,5 ]$ 
B)  $( - \infty , 5 ) \cup ( 5 , \infty )$ 
C)  $[ 5 , \infty )$ 
D)  $( 5 , \infty )$ 
E) all real numbers

Question 14

Solve the inequality and graph the solution on the real number line.​ $9 x ^ { 2 } - 6 x + 1 \leq 0$ ​

Accepted Answer

A) ​ $x = 3$   
B)  $x = \frac { 1 } { 3 }$   
C)  $x = \frac { 1 } { 9 }$   
D)  $x = - \frac { 1 } { 3 }$   
E)  $x = - 3$   
A) ​ $x = 3$   
B)  $x = \frac { 1 } { 3 }$   
C)  $x = \frac { 1 } { 9 }$   
D)  $x = - \frac { 1 } { 3 }$   
E)  $x = - 3$

Question 15

Find the key numbers of the expression.​ $16 x ^ { 3 } - 49 x ^ { 2 }$ ​

Accepted Answer

A) 0, $\frac { 16 } { 49 }$ 
B) 0,49 
C) 0,51 
D) 0,-49 
E) 0, $\frac { 49 } { 16 }$ 
A) 0, $\frac { 16 } { 49 }$ 
B) 0,49 
C) 0,51 
D) 0,-49 
E) 0, $\frac { 49 } { 16 }$

Question 16

Find the domain of x in the expression.​ $\sqrt { \frac { x } { x ^ { 2 } - 36 } }$ ​

Accepted Answer

A)  $( - 36,0 ] \cup ( 36 , \infty )$ 
B)  $( - 36,0 ] \cap ( 36 , \infty )$ 
C)  $( - 36,0 ] \cap ( 6 , \infty )$ 
D)  $( - 6,0 ] \cup ( 6 , \infty )$ 
E)  $( - 36,0 ] \cap ( - 6 , \infty )$ 
A)  $( - 36,0 ] \cup ( 36 , \infty )$ 
B)  $( - 36,0 ] \cap ( 36 , \infty )$ 
C)  $( - 36,0 ] \cap ( 6 , \infty )$ 
D)  $( - 6,0 ] \cup ( 6 , \infty )$ 
E)  $( - 36,0 ] \cap ( - 6 , \infty )$

Question 17

Use the position equation $s = - 16 t ^ { 2 } + v _ { 0 } t + s _ { 0 }$ ,where s represents the height of an object (in feet), $v _ { 0 }$ represents the initial velocity of the object (in feet per second), $s_0$ represents the initial height of the object (in feet),and t represents the time (in seconds). A projectile is fired straight upward from ground level $\left( s _ { 0 } = 0 \right)$ with an initial velocity of 160 feet per second.At what instant will it be back at ground level?
​

Accepted Answer

A)  $t = 8$ Sec 
B)  $t = 10$ Sec 
C)  $t = 12$ Sec 
D)  $t = 11$ Sec 
E)  $t = 9$ Sec 
A)  $t = 8$ Sec 
B)  $t = 10$ Sec 
C)  $t = 12$ Sec 
D)  $t = 11$ Sec 
E)  $t = 9$ Sec

Question 18

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. ​
Equation: $$y = \frac { 5 x ^ { 2 } } { x ^ { 2 } + 25 }$$ ​
Inequality: $$y \leq 2$$ ​

Accepted Answer

A) ​   $$- \infty < x \leq \frac { 5 \sqrt { 3 } } { 3 }$$ 
B) ​   $$- \infty < x < \infty$$ 
C) ​   $$- \frac { 5 \sqrt { 3 } } { 3 } \leq x \leq \frac { 5 \sqrt { 3 } } { 3 }$$ 
D) ​   $$- \infty < x \leq \frac { \sqrt { 3 } } { 3 }$$ 
E) ​   $$- \infty < x \leq 5 \sqrt { 3 }$$ 
A) ​   $$- \infty < x \leq \frac { 5 \sqrt { 3 } } { 3 }$$ 
B) ​   $$- \infty < x < \infty$$ 
C) ​   $$- \frac { 5 \sqrt { 3 } } { 3 } \leq x \leq \frac { 5 \sqrt { 3 } } { 3 }$$ 
D) ​   $$- \infty < x \leq \frac { \sqrt { 3 } } { 3 }$$ 
E) ​   $$- \infty < x \leq 5 \sqrt { 3 }$$

Question 19

When two resistors of resistances $R _ { 1 }$ and $R _ { 2 }$ are connected in parallel (see figure),the total resistance $R$ satisfies the equation​ $\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }$ .   Find $R _ { 1 }$ for a parallel circuit in which $R _ { 2 } = 7$ ohms and R must be at least 1 ohm. ​

Accepted Answer

A)  $R _ { 1 } \leq 7 \text { ohms }$ 
B)  $R _ { 1 }  7 \mathrm { ohms }$ 
E)  $R _ { 1 } =$ $\frac { 7 } { 6 }$ $\text { ohms }$ 
A)  $R _ { 1 } \leq 7 \text { ohms }$ 
B)  $R _ { 1 }  7 \mathrm { ohms }$ 
E)  $R _ { 1 } =$ $\frac { 7 } { 6 }$ $\text { ohms }$

Question 20

Solve the inequality and graph the solution on the real number line​ $$x ^ { 3 } + 3 x ^ { 2 } - 9 x - 27 \leq 0$$ ​

Accepted Answer

A)  $$( - \infty , 3 ]$$   
B)  $$( - \infty , 3 )$$   
C)  $$( - \infty , 3 ]$$   
D)  $$( - \infty , - 3 ]$$   
E)  $$( - \infty , - 3 )$$   
A)  $$( - \infty , 3 ]$$   
B)  $$( - \infty , 3 )$$   
C)  $$( - \infty , 3 ]$$   
D)  $$( - \infty , - 3 ]$$   
E)  $$( - \infty , - 3 )$$

Exam 17: Nonlinear Inequalities

Find the domain of x in the expression.​ 9−4x2\sqrt { 9 - 4 x ^ { 2 } }9−4x2​ ​

Find the domain of x in the expression x3−3x4\sqrt [ 4 ] { x ^ { 3 } - 3 x }4x3−3x​ . ​

Find the domain of x in the expression.​ x2−7x+12\sqrt { x ^ { 2 } - 7 x + 12 }x2−7x+12​ ​

Determine whether the value of x=27x = \frac { 2 } { 7 }x=72​ is a solution of the inequality. x2−2<0x ^ { 2 } - 2 < 0x2−2<0 ​

Solve the inequality and graph the solution on the real number line.​ 3x−5x−5≥0\frac { 3 x - 5 } { x - 5 } \geq 0x−53x−5​≥0 ​

Solve the inequality and graph the solution on the real number line.​ x+9x+1−2<0\frac { x + 9 } { x + 1 } - 2 < 0x+1x+9​−2<0 ​

Find the domain of x in the expression.​ 25−x2\sqrt { 25 - x ^ { 2 } }25−x2​ ​

Find the domain of x in the expression.​ xx2−2x−24\sqrt { \frac { x } { x ^ { 2 } - 2 x - 24 } }x2−2x−24x​​ ​

Solve the inequality and graph the solution on the real number line.​ x2>2x+48x ^ { 2 } > 2 x + 48x2>2x+48 ​

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy the following inequality. ​ Equation: y=7xx2+6y = \frac { 7 x } { x ^ { 2 } + 6 }y=x2+67x​ ​ Inequality: y≥1y \geq 1y≥1 ​

Solve the inequality and graph the solution on the real number line.​ x2+3x>4x ^ { 2 } + 3 x > 4x2+3x>4 ​

The numbers N (in millions)of students enrolled in schools in the United States from 1995 through 1997 are shown in the table. ​ Year Number, N 1995 71.2 1996 72.3 1997 74 Use a graphing utility to create a scatter plot of the data.Let t represent the year,with t = 5 corresponding to 1995.

Find the domain of x in the following expression. x4−6253\sqrt [ 3 ] { x ^ { 4 } - 625 }3x4−625​

Solve the inequality and graph the solution on the real number line.​ 9x2−6x+1≤09 x ^ { 2 } - 6 x + 1 \leq 09x2−6x+1≤0 ​

Find the key numbers of the expression.​ 16x3−49x216 x ^ { 3 } - 49 x ^ { 2 }16x3−49x2 ​

Find the domain of x in the expression.​ xx2−36\sqrt { \frac { x } { x ^ { 2 } - 36 } }x2−36x​​ ​

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. ​ Equation: y=5x2x2+25y = \frac { 5 x ^ { 2 } } { x ^ { 2 } + 25 }y=x2+255x2​ ​ Inequality: y≤2y \leq 2y≤2 ​

Solve the inequality and graph the solution on the real number line​ x3+3x2−9x−27≤0x ^ { 3 } + 3 x ^ { 2 } - 9 x - 27 \leq 0x3+3x2−9x−27≤0 ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Find the domain of x in the expression. $\sqrt { 9 - 4 x ^ { 2 } }$

Find the domain of x in the expression $\sqrt [ 4 ] { x ^ { 3 } - 3 x }$ .

Find the domain of x in the expression. $\sqrt { x ^ { 2 } - 7 x + 12 }$

Determine whether the value of $x = \frac { 2 } { 7 }$ is a solution of the inequality. $x ^ { 2 } - 2 < 0$

Solve the inequality and graph the solution on the real number line. $\frac { 3 x - 5 } { x - 5 } \geq 0$

Solve the inequality and graph the solution on the real number line. $\frac { x + 9 } { x + 1 } - 2 < 0$

Find the domain of x in the expression. $\sqrt { 25 - x ^ { 2 } }$

Find the domain of x in the expression. $\sqrt { \frac { x } { x ^ { 2 } - 2 x - 24 } }$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } > 2 x + 48$

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy the following inequality. Equation: $y = \frac { 7 x } { x ^ { 2 } + 6 }$ Inequality: $y \geq 1$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } + 3 x > 4$

The numbers N (in millions)of students enrolled in schools in the United States from 1995 through 1997 are shown in the table. Year Number, N 1995 71.2 1996 72.3 1997 74 Use a graphing utility to create a scatter plot of the data.Let t represent the year,with t = 5 corresponding to 1995.

Find the domain of x in the following expression. $\sqrt [ 3 ] { x ^ { 4 } - 625 }$

Solve the inequality and graph the solution on the real number line. $9 x ^ { 2 } - 6 x + 1 \leq 0$

Find the key numbers of the expression. $16 x ^ { 3 } - 49 x ^ { 2 }$

Find the domain of x in the expression. $\sqrt { \frac { x } { x ^ { 2 } - 36 } }$

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. Equation: $y = \frac { 5 x ^ { 2 } } { x ^ { 2 } + 25 }$ Inequality: $y \leq 2$

Solve the inequality and graph the solution on the real number line $x ^ { 3 } + 3 x ^ { 2 } - 9 x - 27 \leq 0$