Question 1

Find the domain of x in the expression $\sqrt { 16 - x ^ { 2 } }$ .

Accepted Answer

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

Question 2

Find the interval(s)for b such that the equation has at least one real solution and write a conjecture about the interval(s)based on the values of the coefficients​ $4 x ^ { 2 } + b x + 7 = 0$ . ​

Accepted Answer

A) $( - \infty , - 2 \sqrt { 28 } ] \cap [ 2 \sqrt { 28 } , \infty )$ If $a > 0$ and $c 0$ , $b \leq - 2 \sqrt { a c }$ or $b \leq 2 \sqrt { a c }$ C) $( - \infty , - 2 \sqrt { 28 } ] \cup [ 2 \sqrt { 28 } , \infty )$ If $a > 0$ and $c > 0$ , $b \leq - 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$ D) $( - \infty , 2 \sqrt { 28 } ] \cup [ 2 \sqrt { 28 } , \infty )$ If $a > 0$ and $c > 0$ , $b \leq 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$ E) $( - \infty , - 2 \sqrt { 28 } ] \cap [ 2 \sqrt { 28 } , \infty )$ If $a < 0$ and $c < 0$ , $b \leq 2 \sqrt { a c }$ or $b \leq 2 \sqrt { a c }$ A) $( - \infty , - 2 \sqrt { 28 } ] \cap [ 2 \sqrt { 28 } , \infty )$ If $a > 0$ and $c 0$ , $b \leq - 2 \sqrt { a c }$ or $b \leq 2 \sqrt { a c }$ C) $( - \infty , - 2 \sqrt { 28 } ] \cup [ 2 \sqrt { 28 } , \infty )$ If $a > 0$ and $c > 0$ , $b \leq - 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$ D) $( - \infty , 2 \sqrt { 28 } ] \cup [ 2 \sqrt { 28 } , \infty )$ If $a > 0$ and $c > 0$ , $b \leq 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$ E) $( - \infty , - 2 \sqrt { 28 } ] \cap [ 2 \sqrt { 28 } , \infty )$ If $a < 0$ and $c < 0$ , $b \leq 2 \sqrt { a c }$ or $b \leq 2 \sqrt { a c }$

Question 3

Solve the inequality and write the solution set in interval notation.​ $6 x ^ { 2 } - 10 x < 0$ ​

Accepted Answer

A)  $$( - \infty , 0 ) ] \cup [$$ $\frac { 5 } { 3 }$ $, \infty )$ 
B)  $$\varnothing$$ 
C)  $$( - \infty , 0 )  \cup($$ $\frac { 5 } { 3 }$ $, \infty )$ 
D)  $( \infty , 0 ) \cup [ -$ $\frac { 5 } { 3 }$ $, \infty )$ 
E)  $( 0 ,$ $\frac { 5 } { 3 }$ ) ​ 
A)  $$( - \infty , 0 ) ] \cup [$$ $\frac { 5 } { 3 }$ $, \infty )$ 
B)  $$\varnothing$$ 
C)  $$( - \infty , 0 )  \cup($$ $\frac { 5 } { 3 }$ $, \infty )$ 
D)  $( \infty , 0 ) \cup [ -$ $\frac { 5 } { 3 }$ $, \infty )$ 
E)  $( 0 ,$ $\frac { 5 } { 3 }$ ) ​

Question 4

Solve the inequality and graph the solution on the real number line.​ $$\frac { 2 } { x + 4 } > \frac { 1 } { x - 2 }$$ ​

Accepted Answer

A)  $$( - 4,2 ) \cup ( 8 , \infty )$$   
B)  $$( - 4,2 ) \cap ( 8 , \infty )$$   
C)  $$( - 4 , - 2 ) \cup ( 8 , \infty )$$   
D)  $$( - 4,2 ) \cap ( - 8 , \infty )$$   
E)  $$( 4,2 ) \cup ( 8 , \infty )$$   
A)  $$( - 4,2 ) \cup ( 8 , \infty )$$   
B)  $$( - 4,2 ) \cap ( 8 , \infty )$$   
C)  $$( - 4 , - 2 ) \cup ( 8 , \infty )$$   
D)  $$( - 4,2 ) \cap ( - 8 , \infty )$$   
E)  $$( 4,2 ) \cup ( 8 , \infty )$$

Question 5

A rectangular playing field with a perimeter of 98 meters is to have an area of at least 444 square meters.Within what bounds must the length of the rectangle lie?
​

Accepted Answer

A)  $444 m \leq L \leq 13 m$ 
B)  $37 m \leq L \leq 98 m$ 
C)  $12 m \leq L \leq 37 m$ 
D)  $39 m \leq L \leq 14 m$ 
E)  $444 m < L < 13 m$ 
A)  $444 m \leq L \leq 13 m$ 
B)  $37 m \leq L \leq 98 m$ 
C)  $12 m \leq L \leq 37 m$ 
D)  $39 m \leq L \leq 14 m$ 
E)  $444 m < L < 13 m$

Question 6

Solve the inequality and write the solution set in interval notation.​ $5 x ^ { 3 } - 20 x ^ { 2 } > 0$ ​

Accepted Answer

A)  $( 4 , \infty )$ 
B)  $( - 4 , - \infty )$ 
C)  $( - 4 , \infty )$ 
D)  $( 4 , - \infty )$ 
E)  $( - \infty , 5 )$ 
A)  $( 4 , \infty )$ 
B)  $( - 4 , - \infty )$ 
C)  $( - 4 , \infty )$ 
D)  $( 4 , - \infty )$ 
E)  $( - \infty , 5 )$

Question 7

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

Accepted Answer

A)  $( - 3,3 )$   
B) ​ $[ - 3,3 ]$   
C)  $[ - 3,3 ]$   
D)  $[ 3 , - 3 ]$   
E)  $( - 3,3 )$   
A)  $( - 3,3 )$   
B) ​ $[ - 3,3 ]$   
C)  $[ - 3,3 ]$   
D)  $[ 3 , - 3 ]$   
E)  $( - 3,3 )$

Question 8

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 176 feet per second.At what instant will it be back at ground level?
​

Accepted Answer

A)  $t = 11$ Sec 
B)  $t = 16$ Sec 
C)  $t = 13$ Sec 
D)  $t = 12$ Sec 
E)  $t = 10$ Sec 
A)  $t = 11$ Sec 
B)  $t = 16$ Sec 
C)  $t = 13$ Sec 
D)  $t = 12$ Sec 
E)  $t = 10$ Sec

Question 9

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. ​
Equation: $y = \frac { 6 ( x - 6 ) } { x + 5 }$ ​
Inequality: $y \leq 0$ ​

Accepted Answer

A) ​ ​   $$- 5 \leq x \leq 6$$ 
B) ​   $$- 5  6$$ 
C) ​   $$- 5 < x \leq 6$$ ​ 
D)    $$- 5 < x \leq 6$$ 
E) ​   $$- 5 < x < 6$$ 
A) ​ ​   $$- 5 \leq x \leq 6$$ 
B) ​   $$- 5  6$$ 
C) ​   $$- 5 < x \leq 6$$ ​ 
D)    $$- 5 < x \leq 6$$ 
E) ​   $$- 5 < x < 6$$

Question 10

Determine whether the value of $x = - 6$ is a solution of the inequality.​ $x ^ { 2 } - x - 14 \geq 0$ ​

Accepted Answer

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

Question 11

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

Accepted Answer

A)  $[ - 2,2 ]$   
B)  $[ - 2,2 ]$   
C)  $( - 2,2 )$ ​   
D)  $( - 2,2 )$ ​   
E)  $( - 2,2 )$ ​   
A)  $[ - 2,2 ]$   
B)  $[ - 2,2 ]$   
C)  $( - 2,2 )$ ​   
D)  $( - 2,2 )$ ​   
E)  $( - 2,2 )$ ​

Question 12

Solve the inequality and write the solution set in interval notation.​ $x ^ { 8 } ( x - 2 ) \leq 0$ ​ ​

Accepted Answer

A)  $( - \infty , 2 ]$ 
B)  $( - \infty , - 2 ) ]$ 
C)  $( - \infty , 2 ]$ 
D)  $( - 2,2 ]$ 
E)  $( - \infty , 2 )$ 
A)  $( - \infty , 2 ]$ 
B)  $( - \infty , - 2 ) ]$ 
C)  $( - \infty , 2 ]$ 
D)  $( - 2,2 ]$ 
E)  $( - \infty , 2 )$

Question 13

Solve the inequality and graph the solution on the real number line.​ $x ^ { 2 } - 10 x + 8 < 19$ ​

Accepted Answer

A)  $( - 1,11 )$   
B)  $( - 1 , - 11 )$   ​ 
C)  $( 1 , - 11 )$ ​   
D)  $( - 1 , - 11 )$   
E)  $( - 1,11 )$   
A)  $( - 1,11 )$   
B)  $( - 1 , - 11 )$   ​ 
C)  $( 1 , - 11 )$ ​   
D)  $( - 1 , - 11 )$   
E)  $( - 1,11 )$

Question 14

Solve: $x ^ { 2 } - 2 x - 15 < 0$

Accepted Answer

A)  $( - \infty , - 2 )$ 
B)  $( - 3 , \infty )$ 
C)  $( - 3,5 )$ 
D)  $( - \infty , 5 )$ 
E)  $( 5 , \infty )$ 
A)  $( - \infty , - 2 )$ 
B)  $( - 3 , \infty )$ 
C)  $( - 3,5 )$ 
D)  $( - \infty , 5 )$ 
E)  $( 5 , \infty )$

Question 15

Solve the inequality and graph the solution on the real number line.​ $$\frac { x ^ { 2 } + 4 x } { x ^ { 2 } - 25 } \leq 0$$ ​

Accepted Answer

A)  $$( - 5 , - 4 ] \cup [ 0,5 )$$   
B)  $$( - 5,4 ] \cup [ 0 , - 5 )$$   
C)  $$( - 5,4 ] \cup [ 0,5 )$$   
D)  $$( 5 , - 4 ] \cup [ 0,5 )$$   
E)  $$( 5,4 ] \cup [ 0,5 )$$   
A)  $$( - 5 , - 4 ] \cup [ 0,5 )$$   
B)  $$( - 5,4 ] \cup [ 0 , - 5 )$$   
C)  $$( - 5,4 ] \cup [ 0,5 )$$   
D)  $$( 5 , - 4 ] \cup [ 0,5 )$$   
E)  $$( 5,4 ] \cup [ 0,5 )$$

Question 16

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

Accepted Answer

A)  $( - \infty , 2 ] \cap [ 2 , \infty )$ 
B)  $( - \infty , - 2 ] \cup [ 2 , \infty )$ 
C)  $( - \infty , - 2 ] \cap [ 2 , \infty )$ 
D)  $( - \infty , 2 ] \cup [ 2 , \infty )$ 
E)  $( - \infty , - 2 ) \cup [ 2 , \infty )$ 
A)  $( - \infty , 2 ] \cap [ 2 , \infty )$ 
B)  $( - \infty , - 2 ] \cup [ 2 , \infty )$ 
C)  $( - \infty , - 2 ] \cap [ 2 , \infty )$ 
D)  $( - \infty , 2 ] \cup [ 2 , \infty )$ 
E)  $( - \infty , - 2 ) \cup [ 2 , \infty )$

Exam 17: Nonlinear Inequalities

Find the domain of x in the expression 16−x2\sqrt { 16 - x ^ { 2 } }16−x2​ .

Find the interval(s)for b such that the equation has at least one real solution and write a conjecture about the interval(s)based on the values of the coefficients​ 4x2+bx+7=04 x ^ { 2 } + b x + 7 = 04x2+bx+7=0 . ​

Solve the inequality and write the solution set in interval notation.​ 6x2−10x<06 x ^ { 2 } - 10 x < 06x2−10x<0 ​

Solve the inequality and graph the solution on the real number line.​ 2x+4>1x−2\frac { 2 } { x + 4 } > \frac { 1 } { x - 2 }x+42​>x−21​ ​

A rectangular playing field with a perimeter of 98 meters is to have an area of at least 444 square meters.Within what bounds must the length of the rectangle lie? ​

Solve the inequality and write the solution set in interval notation.​ 5x3−20x2>05 x ^ { 3 } - 20 x ^ { 2 } > 05x3−20x2>0 ​

Solve the inequality and graph the solution on the real number line​ x2≤9x ^ { 2 } \leq 9x2≤9 ​

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. ​ Equation: y=6(x−6)x+5y = \frac { 6 ( x - 6 ) } { x + 5 }y=x+56(x−6)​ ​ Inequality: y≤0y \leq 0y≤0 ​

Determine whether the value of x=−6x = - 6x=−6 is a solution of the inequality.​ x2−x−14≥0x ^ { 2 } - x - 14 \geq 0x2−x−14≥0 ​

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

Solve the inequality and write the solution set in interval notation.​ x8(x−2)≤0x ^ { 8 } ( x - 2 ) \leq 0x8(x−2)≤0 ​ ​

Solve the inequality and graph the solution on the real number line.​ x2−10x+8<19x ^ { 2 } - 10 x + 8 < 19x2−10x+8<19 ​

Solve: x2−2x−15<0x ^ { 2 } - 2 x - 15 < 0x2−2x−15<0

Solve the inequality and graph the solution on the real number line.​ x2+4xx2−25≤0\frac { x ^ { 2 } + 4 x } { x ^ { 2 } - 25 } \leq 0x2−25x2+4x​≤0 ​

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

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

Rotation of Conics

Parametric Equations

Polar Coordinates

Find the domain of x in the expression $\sqrt { 16 - x ^ { 2 } }$ .

Find the interval(s)for b such that the equation has at least one real solution and write a conjecture about the interval(s)based on the values of the coefficients $4 x ^ { 2 } + b x + 7 = 0$ .

Solve the inequality and write the solution set in interval notation. $6 x ^ { 2 } - 10 x < 0$

Solve the inequality and graph the solution on the real number line. $\frac { 2 } { x + 4 } > \frac { 1 } { x - 2 }$

A rectangular playing field with a perimeter of 98 meters is to have an area of at least 444 square meters.Within what bounds must the length of the rectangle lie?

Solve the inequality and write the solution set in interval notation. $5 x ^ { 3 } - 20 x ^ { 2 } > 0$

Solve the inequality and graph the solution on the real number line $x ^ { 2 } \leq 9$

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. Equation: $y = \frac { 6 ( x - 6 ) } { x + 5 }$ Inequality: $y \leq 0$

Determine whether the value of $x = - 6$ is a solution of the inequality. $x ^ { 2 } - x - 14 \geq 0$

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

Solve the inequality and write the solution set in interval notation. $x ^ { 8 } ( x - 2 ) \leq 0$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } - 10 x + 8 < 19$

Solve: $x ^ { 2 } - 2 x - 15 < 0$

Solve the inequality and graph the solution on the real number line. $\frac { x ^ { 2 } + 4 x } { x ^ { 2 } - 25 } \leq 0$

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