Question 1

Select the correct graph of the inequality.​ $$y > \frac { - 21 } { x ^ { 2 } + x + 3 }$$ ​

Accepted Answer

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

Question 2

Derive a set of inequalities to describe the region.​

Accepted Answer

A) ​ $$\left\{ \begin{array} { c } 
x ^ { 2 } + y ^ { 2 } \leq 9 \
x ^ { 2 } + y ^ { 2 } \geq 16 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ 
B) ​ $$\left\{ \begin{array} { c } 
x ^ { 2 } + y ^ { 2 } \geq 3 \
x ^ { 2 } + y ^ { 2 } \leq 4 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ 
C) ​ $$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } \geq 3 \
x ^ { 2 } + y ^ { 2 } \leq 4
\end{array} \right.$$ 
D) ​ $$\left\{ \begin{array} { c } 
x ^ { 2 } + y ^ { 2 } \geq 9 \
x ^ { 2 } + y ^ { 2 } \leq 16
\end{array} \right.$$ 
E)  $$\left\{ \begin{array} { c } 
x ^ { 2 } + y ^ { 2 } \geq 9 \
x ^ { 2 } + y ^ { 2 } \leq 16 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ 
A) ​ $$\left\{ \begin{array} { c } 
x ^ { 2 } + y ^ { 2 } \leq 9 \
x ^ { 2 } + y ^ { 2 } \geq 16 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ 
B) ​ $$\left\{ \begin{array} { c } 
x ^ { 2 } + y ^ { 2 } \geq 3 \
x ^ { 2 } + y ^ { 2 } \leq 4 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ 
C) ​ $$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } \geq 3 \
x ^ { 2 } + y ^ { 2 } \leq 4
\end{array} \right.$$ 
D) ​ $$\left\{ \begin{array} { c } 
x ^ { 2 } + y ^ { 2 } \geq 9 \
x ^ { 2 } + y ^ { 2 } \leq 16
\end{array} \right.$$ 
E)  $$\left\{ \begin{array} { c } 
x ^ { 2 } + y ^ { 2 } \geq 9 \
x ^ { 2 } + y ^ { 2 } \leq 16 \
x \geq 0 \
y \geq 0
\end{array} \right.$$

Question 3

Select an inequality for the shaded region shown in the figure.​   ​

Accepted Answer

A)  $y \geq x ^ { 2 } - 3$ 
B)  $y \geq x ^ { 2 } - 4$ 
C)  $y \geq x ^ { 2 } - 2$ 
D)  $y \geq x ^ { 2 } - 5$ 
E)  $y \geq x ^ { 2 } - 6$ 
A)  $y \geq x ^ { 2 } - 3$ 
B)  $y \geq x ^ { 2 } - 4$ 
C)  $y \geq x ^ { 2 } - 2$ 
D)  $y \geq x ^ { 2 } - 5$ 
E)  $y \geq x ^ { 2 } - 6$

Question 4

A person plans to invest up to $26,000 in two different interest-bearing accounts.Each account is to contain at least $5000.Moreover,the amount in one account should be at least twice the amount in the other account.Find and graph a system of inequalities to describe the various amounts that can be deposited in each account. ​

Accepted Answer

A) ​ $$\left\{ \begin{array} { c } 
x + y = 25,000 \
y \geq 2 x \
x \geq 5000 \
y \geq 5000
\end{array} \right.$$   
B)  $$\left\{ \begin{array} { c } 
x + y \leq 26,000 \
y \geq 2 x \
x \geq 5000 \
y \geq 5000
\end{array} \right.$$ ​   
C)  $$\left\{ \begin{array} { c } 
x + y = 22,000 \
y \geq 2 x \
x \geq 5000 \
y \geq 5000
\end{array} \right.$$ ​   
D)  $$\left\{ \begin{array} { c } 
x + y \geq 30,000 \
y \geq 2 x \
x \geq 5000 \
y \geq 5000
\end{array} \right.$$ ​   
E)  $$\left\{ \begin{array} { c } 
x + y \geq 23,000 \
y \geq 2 x \
x \geq 5000 \
y \geq 5000
\end{array} \right.$$ ​   
A) ​ $$\left\{ \begin{array} { c } 
x + y = 25,000 \
y \geq 2 x \
x \geq 5000 \
y \geq 5000
\end{array} \right.$$   
B)  $$\left\{ \begin{array} { c } 
x + y \leq 26,000 \
y \geq 2 x \
x \geq 5000 \
y \geq 5000
\end{array} \right.$$ ​   
C)  $$\left\{ \begin{array} { c } 
x + y = 22,000 \
y \geq 2 x \
x \geq 5000 \
y \geq 5000
\end{array} \right.$$ ​   
D)  $$\left\{ \begin{array} { c } 
x + y \geq 30,000 \
y \geq 2 x \
x \geq 5000 \
y \geq 5000
\end{array} \right.$$ ​   
E)  $$\left\{ \begin{array} { c } 
x + y \geq 23,000 \
y \geq 2 x \
x \geq 5000 \
y \geq 5000
\end{array} \right.$$ ​

Question 5

Select the correct graph of the inequality.​ $$y < 4 - x$$ ​

Accepted Answer

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

Question 6

Find the consumer surplus and producer surplus. ​
Demand $p = 600 - 0.0002 x$ ​
Supply $p = 450 + 0.0001 x$ ​

Accepted Answer

A) Consumer surplus: $25,000,150 Producer surplus: $12,500,400 
B) Consumer surplus: $25,000,200 Producer surplus: $12,500,300 
C) Consumer surplus: $25,000,100 Producer surplus: $12,500,100 
D) Consumer surplus: $25,000,050 Producer surplus: $12,500,200 
E) Consumer surplus: $25,000,000 Producer surplus: $12,500,000 
A) Consumer surplus: $25,000,150 Producer surplus: $12,500,400 
B) Consumer surplus: $25,000,200 Producer surplus: $12,500,300 
C) Consumer surplus: $25,000,100 Producer surplus: $12,500,100 
D) Consumer surplus: $25,000,050 Producer surplus: $12,500,200 
E) Consumer surplus: $25,000,000 Producer surplus: $12,500,000

Question 7

Select an inequality to describe the region.​   ​

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } \geq 4$ 
B)  $x ^ { 2 } + y ^ { 2 } \geq 9$ 
C)  $x ^ { 2 } + y ^ { 2 } \geq 1$ 
D)  $x ^ { 2 } + y ^ { 2 } \geq 16$ 
E)  $x ^ { 2 } + y ^ { 2 } \geq 25$ 
A)  $x ^ { 2 } + y ^ { 2 } \geq 4$ 
B)  $x ^ { 2 } + y ^ { 2 } \geq 9$ 
C)  $x ^ { 2 } + y ^ { 2 } \geq 1$ 
D)  $x ^ { 2 } + y ^ { 2 } \geq 16$ 
E)  $x ^ { 2 } + y ^ { 2 } \geq 25$

Question 8

Sketch the graph of the inequality. $$( x - 3 ) ^ { 2 } + ( y + 1 ) ^ { 2 }$$ < 4

Accepted Answer

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

Question 9

Select a set of inequalities to describe the region.​   ​

Accepted Answer

A)  $$\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 9
\end{array} \right.$$ 
B)  $$\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 1
\end{array} \right.$$ 
C)  $$\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 4
\end{array} \right.$$ 
D)  $$\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 25
\end{array} \right.$$ 
E)  $$\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 16
\end{array} \right.$$ 
A)  $$\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 9
\end{array} \right.$$ 
B)  $$\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 1
\end{array} \right.$$ 
C)  $$\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 4
\end{array} \right.$$ 
D)  $$\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 25
\end{array} \right.$$ 
E)  $$\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 16
\end{array} \right.$$

Question 10

Select the correct graph of the inequality.​ $$x ^ { 2 } + 4 y - 8 \leq 0$$ ​

Accepted Answer

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

Question 11

Use a graphing utility to graph the inequalities.Shade the region representing the solution set of the system. ​​ $$\left\{ \begin{array} { l } 
y > x ^ { 2 } - 5 x + 2 \
y < - x ^ { 2 } + x + 2
\end{array} \right.$$ ​

Accepted Answer

A) ​ 10   -10​ 
B) 10   -10​ 
C) ​10   ​ -10 
D) ​ 10   -10​ 
E) 10​   ​ -10 
A) ​ 10   -10​ 
B) 10   -10​ 
C) ​10   ​ -10 
D) ​ 10   -10​ 
E) 10​   ​ -10

Question 12

For a concert event,there are $30 reserved seat tickets and $20 general admission tickets.There are 2000 reserved seats available,and fire regulations limit the number of paid ticket holders to 3000.The promoter must take in at least $65,000 in ticket sales.Find and graph a system of inequalities describing the different numbers of tickets that can be sold. ​

Accepted Answer

A)  $$\left\{ \begin{array} { c } 
x + y \leq 3000 \
30 x + 20 y \geq 72,000 \
x \leq 2000 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​   
B)  $$\left\{ \begin{array} { c } 
x + y \leq 3000 \
30 x + 20 y \geq 68,000 \
x \leq 2000 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​   
C) ​ $$\left\{ \begin{array} { c } 
x + y \leq 3000 \
30 x + 20 y \geq 66,000 \
x \leq 2000 \
x \geq 0 \
y \geq 0
\end{array} \right.$$   
D)  $$\left\{ \begin{array} { c } 
x + y \leq 3000 \
30 x + 20 y \geq 73,000 \
x \leq 2000 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​   
E)  $$\left\{ \begin{array} { c } 
x + y \leq 3000 \
30 x + 20 y \geq 65,000 \
x \leq 2000 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​   
A)  $$\left\{ \begin{array} { c } 
x + y \leq 3000 \
30 x + 20 y \geq 72,000 \
x \leq 2000 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​   
B)  $$\left\{ \begin{array} { c } 
x + y \leq 3000 \
30 x + 20 y \geq 68,000 \
x \leq 2000 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​   
C) ​ $$\left\{ \begin{array} { c } 
x + y \leq 3000 \
30 x + 20 y \geq 66,000 \
x \leq 2000 \
x \geq 0 \
y \geq 0
\end{array} \right.$$   
D)  $$\left\{ \begin{array} { c } 
x + y \leq 3000 \
30 x + 20 y \geq 73,000 \
x \leq 2000 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​   
E)  $$\left\{ \begin{array} { c } 
x + y \leq 3000 \
30 x + 20 y \geq 65,000 \
x \leq 2000 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​

Question 13

A store sells two models of laptop computers.Because of the demand,the store stocks at least twice as many units of model A as of model B.The costs to the store for the two models are $800 and $1200,respectively.The management does not want more than $29,000 in computer inventory at any one time,and it wants at least four model A laptop computers and two model B laptop computers in inventory at all times.Find and graph a system of inequalities describing all possible inventory levels.
​

Accepted Answer

A)  $$\left\{\begin{array} { c } 
x \geq 2 y \
8 x + 12 y \leq 310 \
x \geq 4 \
y \geq 2
\end{array}\right.$$   
B)  $$\left\{\begin{array} { c } 
x \geq 2 y \
8 x + 12 y \leq 290 \
x \geq 4 \
y \geq 2
\end{array}\right.$$ ​   
C)  $$\left\{ \begin{array} { c } 
x \geq y \
8 x + 12 y \leq 290 \
x \geq 4 \
y \geq 2
\end{array} \right.$$ ​   
D) ​ $$\left\{\begin{array} { c } 
x \geq 2 y \
8 x + 12 y \leq 290 \
x \geq 2 \
y \geq 2
\end{array}\right.$$   
E)  $$\left\{ \begin{array} { c } 
x \geq 3 y \
8 x + 12 y \leq 290 \
x \geq 4 \
y \geq 2
\end{array} \right.$$ ​   
A)  $$\left\{\begin{array} { c } 
x \geq 2 y \
8 x + 12 y \leq 310 \
x \geq 4 \
y \geq 2
\end{array}\right.$$   
B)  $$\left\{\begin{array} { c } 
x \geq 2 y \
8 x + 12 y \leq 290 \
x \geq 4 \
y \geq 2
\end{array}\right.$$ ​   
C)  $$\left\{ \begin{array} { c } 
x \geq y \
8 x + 12 y \leq 290 \
x \geq 4 \
y \geq 2
\end{array} \right.$$ ​   
D) ​ $$\left\{\begin{array} { c } 
x \geq 2 y \
8 x + 12 y \leq 290 \
x \geq 2 \
y \geq 2
\end{array}\right.$$   
E)  $$\left\{ \begin{array} { c } 
x \geq 3 y \
8 x + 12 y \leq 290 \
x \geq 4 \
y \geq 2
\end{array} \right.$$ ​

Question 14

Select the correct graph of the inequality.​ $$x \geq 3$$ ​

Accepted Answer

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

Question 15

Select the correct graph of the inequality.​ $$y > - 4$$ ​

Accepted Answer

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

Question 16

Select the correct graph of the inequality.​ $$y < - 1.8 x + 1.1$$ ​

Accepted Answer

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

Question 17

​Derive a set of inequalities to describe the region. ​
Triangle: vertices at (0,0), (4,0), (4,5)
​

Accepted Answer

A) ​ $$\left\{ \begin{array} { c } 
y \geq \frac { 5 } { 4 } x \
y \geq 0 \
x \leq 4
\end{array} \right.$$ 
B) ​ $$\left\{ \begin{array} { c } 
y \leq \frac { 5 } { 4 } x \
x \geq 4
\end{array} \right.$$ 
C) ​ $$\left\{ \begin{array} { c } 
y \geq \frac { 4 } { 5 } x \
y \geq 0 \
x \leq 4
\end{array} \right.$$ 
D) ​ $$\left\{ \begin{array} { c } 
y \leq \frac { 5 } { 4 } x \
y \geq 0 \
x \leq 4
\end{array} \right.$$ 
E) ​ $$\left\{ \begin{array} { c } 
y \leq \frac { 5 } { 4 } x \
x \leq 4
\end{array} \right.$$ 
A) ​ $$\left\{ \begin{array} { c } 
y \geq \frac { 5 } { 4 } x \
y \geq 0 \
x \leq 4
\end{array} \right.$$ 
B) ​ $$\left\{ \begin{array} { c } 
y \leq \frac { 5 } { 4 } x \
x \geq 4
\end{array} \right.$$ 
C) ​ $$\left\{ \begin{array} { c } 
y \geq \frac { 4 } { 5 } x \
y \geq 0 \
x \leq 4
\end{array} \right.$$ 
D) ​ $$\left\{ \begin{array} { c } 
y \leq \frac { 5 } { 4 } x \
y \geq 0 \
x \leq 4
\end{array} \right.$$ 
E) ​ $$\left\{ \begin{array} { c } 
y \leq \frac { 5 } { 4 } x \
x \leq 4
\end{array} \right.$$

Question 18

Use a graphing utility to graph the inequality.​ $$y \geq \frac { 5 } { 9 } x - 4$$ ​

Accepted Answer

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

Question 19

Select the correct graph of the inequality.​ $$y \geq - 16.74 + 5.66 x$$ ​

Accepted Answer

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

Question 20

Select the correct graph of the inequality.​ $$y \leq \frac { 5 } { 1 + x ^ { 2 } }$$ ​

Accepted Answer

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

Exam 45: Systems of Inequalities

Select the correct graph of the inequality.​ y>−21x2+x+3y > \frac { - 21 } { x ^ { 2 } + x + 3 }y>x2+x+3−21​ ​

Derive a set of inequalities to describe the region.​

Select an inequality for the shaded region shown in the figure.​ ​

Select the correct graph of the inequality.​ y<4−xy < 4 - xy<4−x ​

Find the consumer surplus and producer surplus. ​ Demand p=600−0.0002xp = 600 - 0.0002 xp=600−0.0002x ​ Supply p=450+0.0001xp = 450 + 0.0001 xp=450+0.0001x ​

Select an inequality to describe the region.​ ​

Sketch the graph of the inequality. (x−3)2+(y+1)2( x - 3 ) ^ { 2 } + ( y + 1 ) ^ { 2 }(x−3)2+(y+1)2 < 4

Select a set of inequalities to describe the region.​ ​

Select the correct graph of the inequality.​ x2+4y−8≤0x ^ { 2 } + 4 y - 8 \leq 0x2+4y−8≤0 ​

Use a graphing utility to graph the inequalities.Shade the region representing the solution set of the system. ​​ {y>x2−5x+2y<−x2+x+2\left\{ \begin{array} { l } y > x ^ { 2 } - 5 x + 2 \\y < - x ^ { 2 } + x + 2\end{array} \right.{y>x2−5x+2y<−x2+x+2​ ​

Select the correct graph of the inequality.​ x≥3x \geq 3x≥3 ​

Select the correct graph of the inequality.​ y>−4y > - 4y>−4 ​

Select the correct graph of the inequality.​ y<−1.8x+1.1y < - 1.8 x + 1.1y<−1.8x+1.1 ​

​Derive a set of inequalities to describe the region. ​ Triangle: vertices at (0,0), (4,0), (4,5) ​

Use a graphing utility to graph the inequality.​ y≥59x−4y \geq \frac { 5 } { 9 } x - 4y≥95​x−4 ​

Select the correct graph of the inequality.​ y≥−16.74+5.66xy \geq - 16.74 + 5.66 xy≥−16.74+5.66x ​

Select the correct graph of the inequality.​ y≤51+x2y \leq \frac { 5 } { 1 + x ^ { 2 } }y≤1+x25​ ​

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

Nonlinear Inequalities

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

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

Select the correct graph of the inequality. $y > \frac { - 21 } { x ^ { 2 } + x + 3 }$

Derive a set of inequalities to describe the region.

Select an inequality for the shaded region shown in the figure.

Select the correct graph of the inequality. $y < 4 - x$

Find the consumer surplus and producer surplus. Demand $p = 600 - 0.0002 x$ Supply $p = 450 + 0.0001 x$

Select an inequality to describe the region.

Sketch the graph of the inequality. $( x - 3 ) ^ { 2 } + ( y + 1 ) ^ { 2 }$ < 4 $Sketch the graph of the inequality. ( x - 3 ) ^ { 2 } + ( y + 1 ) ^ { 2 } < 4$

Select a set of inequalities to describe the region.

Select the correct graph of the inequality. $x ^ { 2 } + 4 y - 8 \leq 0$

Use a graphing utility to graph the inequalities.Shade the region representing the solution set of the system. $\left\{ \begin{array} { l } y > x ^ { 2 } - 5 x + 2 \\y < - x ^ { 2 } + x + 2\end{array} \right.$

Select the correct graph of the inequality. $x \geq 3$

Select the correct graph of the inequality. $y > - 4$

Select the correct graph of the inequality. $y < - 1.8 x + 1.1$

Derive a set of inequalities to describe the region. Triangle: vertices at (0,0), (4,0), (4,5)

Use a graphing utility to graph the inequality. $y \geq \frac { 5 } { 9 } x - 4$

Select the correct graph of the inequality. $y \geq - 16.74 + 5.66 x$

Select the correct graph of the inequality. $y \leq \frac { 5 } { 1 + x ^ { 2 } }$