Question 1

Select the correct graph of the inequality.​ $$3 y - x \geq 6$$ ​

Accepted Answer

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

Question 2

Select the correct graph of the inequality.​ $$6 \geq y$$ ​

Accepted Answer

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

Question 3

For the given supply and demand equations,find the consumer surplus. Demand
Supply $p = 100 - 0.00006 x$ $p = 80 + 0.00002 x$ ​
​

Accepted Answer

A) $1,875,000 
B) $2,812,500 
C) $2,062,500 
D) $2,250,000 
E) $625,000 
A) $1,875,000 
B) $2,812,500 
C) $2,062,500 
D) $2,250,000 
E) $625,000 A

Question 4

Select the correct graph of the inequality.​ $$y < \ln 13 x$$ ​

Accepted Answer

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

Question 5

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

Accepted Answer

A)  $$\left\{ \begin{array} { c } 
y < 3 - 2 x \
y \geq x - 4 \
x \geq 1
\end{array} \right.$$ 
B)  $$\left\{ \begin{array} { c } 
y < 6 - 2 x \
y \geq x - 2 \
x \geq 1
\end{array} \right.$$ 
C)  $$\left\{ \begin{array} { c } 
y < 4 - 2 x \
y \geq x - 5 \
x \geq 1
\end{array} \right.$$ 
D)  $$\left\{ \begin{array} { c } 
y < 7 - 2 x \
y \geq x - 3 \
x \geq 1
\end{array} \right.$$ 
E)  $$\left\{ \begin{array} { c } 
y < 5 - 2 x \
y \geq x - 6 \
x \geq 1
\end{array} \right.$$ 
A)  $$\left\{ \begin{array} { c } 
y < 3 - 2 x \
y \geq x - 4 \
x \geq 1
\end{array} \right.$$ 
B)  $$\left\{ \begin{array} { c } 
y < 6 - 2 x \
y \geq x - 2 \
x \geq 1
\end{array} \right.$$ 
C)  $$\left\{ \begin{array} { c } 
y < 4 - 2 x \
y \geq x - 5 \
x \geq 1
\end{array} \right.$$ 
D)  $$\left\{ \begin{array} { c } 
y < 7 - 2 x \
y \geq x - 3 \
x \geq 1
\end{array} \right.$$ 
E)  $$\left\{ \begin{array} { c } 
y < 5 - 2 x \
y \geq x - 6 \
x \geq 1
\end{array} \right.$$

Question 6

Determine which one of the ordered pairs below is a solution of the system of linear inequalities.​ $$\left\{ \begin{array} { c } 
2 x + 3 y > 2 \
- y - \frac { 1 } { 3 } x \leq - 3 \
13 x - 6 y > 0
\end{array} \right.$$ ​

Accepted Answer

A) (2,8) 
B) (6,1) 
C) (0,0) 
D) (-1,4) 
E) (3,-3) 
A) (2,8) 
B) (6,1) 
C) (0,0) 
D) (-1,4) 
E) (3,-3)

Question 7

A dietitian is asked to design a special dietary supplement using two different foods.Each ounce of food X contains 20 units of calcium,15 units of iron,and 10 units of vitamin B.Each ounce of food Y contains 10 units of calcium,10 units of iron,and 20 units of vitamin B.The minimum daily requirements of the diet are 350 units of calcium,300 units of iron,and 400 units of vitamin B.Write a system of inequalities describing the different amounts of food X and food Y that can be used. ​

Accepted Answer

A)  $$\left\{ \begin{array} { c } 
20 x + 10 y \geq 350 \
15 x + 10 y \geq 300 \
10 x + 20 y \geq 400 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ 
B)  $$\left\{ \begin{array} { c } 
20 x + 10 y \geq 400 \
15 x + 10 y \geq 350 \
10 x + 20 y \geq 300 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ 
C)  $$\left\{ \begin{array} { c } 
20 x + 10 y \geq 300 \
15 x + 10 y \geq 350 \
10 x + 20 y \geq 400 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ 
D)  $$\left\{ \begin{array} { c } 
20 x + 10 y \geq 400 \
15 x + 10 y \geq 300 \
10 x + 20 y \geq 350 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ 
E)  $$\left\{ \begin{array} { c } 
20 x + 10 y \geq 300 \
15 x + 10 y \geq 400 \
10 x + 20 y \geq 350 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ 
A)  $$\left\{ \begin{array} { c } 
20 x + 10 y \geq 350 \
15 x + 10 y \geq 300 \
10 x + 20 y \geq 400 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ 
B)  $$\left\{ \begin{array} { c } 
20 x + 10 y \geq 400 \
15 x + 10 y \geq 350 \
10 x + 20 y \geq 300 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ 
C)  $$\left\{ \begin{array} { c } 
20 x + 10 y \geq 300 \
15 x + 10 y \geq 350 \
10 x + 20 y \geq 400 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ 
D)  $$\left\{ \begin{array} { c } 
20 x + 10 y \geq 400 \
15 x + 10 y \geq 300 \
10 x + 20 y \geq 350 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ 
E)  $$\left\{ \begin{array} { c } 
20 x + 10 y \geq 300 \
15 x + 10 y \geq 400 \
10 x + 20 y \geq 350 \
x \geq 0 \
y \geq 0
\end{array} \right.$$

Question 8

Use a graphing utility to graph the inequality.Shade the region representing the solution.​ $$y$$ ≤ $$2 ^ { 1 - x }$$

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 9

Select the correct graph of the inequality.​ $$y < 2 - x ^ { 2 }$$ ​

Accepted Answer

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

Question 10

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

Accepted Answer

A)  $y < 6 x + 7$ 
B)  $y < 4 x + 5$ 
C)  $y < 5 x + 6$ 
D)  $y < 2 x + 3$ 
E)  $y < 3 x + 4$ 
A)  $y < 6 x + 7$ 
B)  $y < 4 x + 5$ 
C)  $y < 5 x + 6$ 
D)  $y < 2 x + 3$ 
E)  $y < 3 x + 4$

Question 11

Sketch the graph and label the vertices of the solution set of the system of inequalities.Shade the solution set. $$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } < 16 \
x ^ { 2 } + y ^ { 2 } \geq 25
\end{array} \right.$$

Accepted Answer

A)    ​ 
B) ​   ​ 
C)  $$\text { no solution }$$ 
D) ​   ​ 
E) ​   
A)    ​ 
B) ​   ​ 
C)  $$\text { no solution }$$ 
D) ​   ​ 
E) ​

Question 12

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

Accepted Answer

A)  $y \geq$ $( x - 2 ) ^ { 2 }$ 
B) y ≥ $x ^ { 2 } - 2$ 
C) y ≤ $2 - x ^ { 2 }$ 
D) y ≥ $2 - x ^ { 2 }$ 
E) y ≥ $x ^ { 2 } + 2$ 
A)  $y \geq$ $( x - 2 ) ^ { 2 }$ 
B) y ≥ $x ^ { 2 } - 2$ 
C) y ≤ $2 - x ^ { 2 }$ 
D) y ≥ $2 - x ^ { 2 }$ 
E) y ≥ $x ^ { 2 } + 2$

Question 13

Select the correct graph of the inequality.​ $$4 x + 4 y \geq - 16$$ ​

Accepted Answer

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

Question 14

Find the consumer surplus and producer surplus. ​
Demand $p = 100 - 0.00006 x$ ​
Supply $p = 90 + 0.00004 x$ ​

Accepted Answer

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

Question 15

Select the correct graph of the inequality.​ $$( x - 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } > 4$$ ​

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

Select the correct graph of the inequality.​ $$y < 4 ^ { - x - 5 }$$ ​

Accepted Answer

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

Question 18

Select the correct graph of the inequality.​ $$4 y ^ { 2 } - x < 0$$ ​

Accepted Answer

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

Question 19

Select the correct graph of the inequality.​ $$y \geq - 4 - \ln ( x + 5 )$$ ​

Accepted Answer

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

Question 20

A dietitian is asked to design a special dietary supplement using two different foods.Each ounce of food X contains 20 units of calcium,15 units of iron,and 10 units of vitamin B.Each ounce of food Y contains 10 units of calcium,10 units of iron,and 20 units of vitamin B.The minimum daily requirements of the diet are 350 units of calcium,300 units of iron,and 400 units of vitamin B.Sketch a graph of the region corresponding to the system inequalities describing the different amounts of food X and food Y that can be used.​ $$\left\{ \begin{array} { c } 
20 x + 10 y \geq 350 \
15 x + 10 y \geq 300 \
10 x + 20 y \geq 400 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​

Accepted Answer

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

Exam 45: Systems of Inequalities

Select the correct graph of the inequality.​ 3y−x≥63 y - x \geq 63y−x≥6 ​

Select the correct graph of the inequality.​ 6≥y6 \geq y6≥y ​

For the given supply and demand equations,find the consumer surplus. Demand Supply p=100−0.00006xp = 100 - 0.00006 xp=100−0.00006x p=80+0.00002xp = 80 + 0.00002 xp=80+0.00002x ​ ​

Select the correct graph of the inequality.​ y<ln⁡13xy < \ln 13 xy<ln13x ​

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

Use a graphing utility to graph the inequality.Shade the region representing the solution.​ yyy ≤ 21−x2 ^ { 1 - x }21−x

Select the correct graph of the inequality.​ y<2−x2y < 2 - x ^ { 2 }y<2−x2 ​

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

Sketch the graph and label the vertices of the solution set of the system of inequalities.Shade the solution set. {x2+y2<16x2+y2≥25\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } < 16 \\x ^ { 2 } + y ^ { 2 } \geq 25\end{array} \right.{x2+y2<16x2+y2≥25​

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

Select the correct graph of the inequality.​ 4x+4y≥−164 x + 4 y \geq - 164x+4y≥−16 ​

Find the consumer surplus and producer surplus. ​ Demand p=100−0.00006xp = 100 - 0.00006 xp=100−0.00006x ​ Supply p=90+0.00004xp = 90 + 0.00004 xp=90+0.00004x ​

Select the correct graph of the inequality.​ (x−1)2+(y−4)2>4( x - 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } > 4(x−1)2+(y−4)2>4 ​

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

Select the correct graph of the inequality.​ y<4−x−5y < 4 ^ { - x - 5 }y<4−x−5 ​

Select the correct graph of the inequality.​ 4y2−x<04 y ^ { 2 } - x < 04y2−x<0 ​

Select the correct graph of the inequality.​ y≥−4−ln⁡(x+5)y \geq - 4 - \ln ( x + 5 )y≥−4−ln(x+5) ​

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. $3 y - x \geq 6$

Select the correct graph of the inequality. $6 \geq y$

For the given supply and demand equations,find the consumer surplus. Demand Supply $p = 100 - 0.00006 x$ $p = 80 + 0.00002 x$

Select the correct graph of the inequality. $y < \ln 13 x$

Select a set of inequalities to describe the region.

Use a graphing utility to graph the inequality.Shade the region representing the solution. $y$ ≤ $2 ^ { 1 - x }$

Select the correct graph of the inequality. $y < 2 - x ^ { 2 }$

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

Select the correct graph of the inequality. $4 x + 4 y \geq - 16$

Find the consumer surplus and producer surplus. Demand $p = 100 - 0.00006 x$ Supply $p = 90 + 0.00004 x$

Select the correct graph of the inequality. $( x - 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } > 4$

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

Select the correct graph of the inequality. $y < 4 ^ { - x - 5 }$

Select the correct graph of the inequality. $4 y ^ { 2 } - x < 0$

Select the correct graph of the inequality. $y \geq - 4 - \ln ( x + 5 )$