Question 1

Determine whether the ordered pair is a solution to the system of inequalities.
-$\begin{array} { l } 
x + y < - 2  ; (-3,5 )

\y \leq - 2 x - 5
\end{array}$

Accepted Answer

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

Question 2

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-The cost for an animal shelter to spay a female cat is $87 and the cost to neuter a male cat is $59. Write an objective function z = f (x, y) that represents the total cost for spaying x female cats and Neutering y male cats.

Accepted Answer

A)  $z = 87 x + 59 y$ 
B)  $z = 73 ( x + y )$ 
C)  $z = 59 x + 87 y$ 
D)  $z = 28 ( x + y )$ 
A)  $z = 87 x + 59 y$ 
B)  $z = 73 ( x + y )$ 
C)  $z = 59 x + 87 y$ 
D)  $z = 28 ( x + y )$

Question 3

Solve the problem.
-The small zoo at Nichols Park charges $8 for adult admission, $5 for child admission (18 years old and under), and $3 for senior admission (60 years old and over). For one day, the zoo collected $539
And admitted 96 visitors. If the adult admission is 9 more than the senior admission, how many
Persons of each category were admitted on this particular day?

Accepted Answer

A)  41 adults; 23 children; 32 seniors 
B)  38 adults; 24 children; 34 seniors 
C)  41 adults; 18 children; 37 seniors 
D)  38 adults; 26 children; 32 seniors 
A)  41 adults; 23 children; 32 seniors 
B)  38 adults; 24 children; 34 seniors 
C)  41 adults; 18 children; 37 seniors 
D)  38 adults; 26 children; 32 seniors

Question 4

Solve the problem.
-The perimeter of a triangle is 55 in. The shortest side is 16 in. less than the longest side. The middle side is 13 in. less than the combined lengths of the shortest and longest sides. Find the lengths of the
Three sides.

Accepted Answer

A)  The sides are 9 in., 21 in., and 25 in. 
B)  The sides are 9 in., 23 in., and 27 in. 
C)  The sides are 11 in., 21 in., and 27 in. 
D)  The sides are 11 in., 23 in., and 25 in. 
A)  The sides are 9 in., 21 in., and 25 in. 
B)  The sides are 9 in., 23 in., and 27 in. 
C)  The sides are 11 in., 21 in., and 27 in. 
D)  The sides are 11 in., 23 in., and 25 in.

Question 5

Solve the system by substitution.
-9x - 5y = 16 y = - 12 x + 6

Accepted Answer

A)  2023, 12823 
B)  { } 
C)  {(-4, -4)} 
D)  {(4, 4)} 
A)  2023, 12823 
B)  { } 
C)  {(-4, -4)} 
D)  {(4, 4)}

Question 6

Graph the solution set. If there is no solution, indicate that the solution set is the empty set.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } \leq 16 \
x ^ { 2 } + y ^ { 2 } \geq 49
\end{array}$$

Accepted Answer

A) 
  
B)  The solution set is {   } . 
C) 
  
D) 
  
A) 
  
B)  The solution set is {   } . 
C) 
  
D)

Question 7

Use a graphing utility to approximate the solution(s) to the system of equations. Round the coordinates to 3 decimal places.
-$$\begin{array} { l } 
y = x ^ { 2 } - 12 x + 43 \
y = 7 \log x
\end{array}$$

Accepted Answer

A)  $\{ ( 4.846,4.798 \} , \{ 7.154,4.798 \} )$ 
B)  {   } 
C)  $\{ ( 4.846,11.047 \} , \{ 7.154,13.774 \} )$ 
D)  $\{ ( 6,5.447 ) \}$ 
A)  $\{ ( 4.846,4.798 \} , \{ 7.154,4.798 \} )$ 
B)  {   } 
C)  $\{ ( 4.846,11.047 \} , \{ 7.154,13.774 \} )$ 
D)  $\{ ( 6,5.447 ) \}$

Question 8

Solve the system of equations by using the addition method.
-$$\begin{array} { l } 
5 x ^ { 2 } + 3 y ^ { 2 } = 95 \
x ^ { 2 } + 5 y ^ { 2 } = 129
\end{array}$$

Accepted Answer

A)  $\{ ( 2,5 ) , ( 2 , - 5 ) , ( - 2,5 ) , ( - 2 , - 5 ) \}$ 
B)  $\{ ( 2,5 ) , ( 2 , - 5 ) \}$ 
C)  {  } 
D)  $\{ ( 2,5 ) , ( - 2,5 ) \}$ 
A)  $\{ ( 2,5 ) , ( 2 , - 5 ) , ( - 2,5 ) , ( - 2 , - 5 ) \}$ 
B)  $\{ ( 2,5 ) , ( 2 , - 5 ) \}$ 
C)  {  } 
D)  $\{ ( 2,5 ) , ( - 2,5 ) \}$

Question 9

Choose the one alternative that best completes the statement or answers the question.
Determine whether the ordered pair is a solution to the inequality.
-$$- \frac { 1 } { 2 } x + 2 < 1$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 10

Two algebraic methods to solve a system of linear equations in two variables are the________ method and the ________method.

Accepted Answer

substituti

Question 11

Solve the problem.
-A package in the shape of a rectangular solid is to be mailed. The combination of the girth (perimeter of a cross section defined by w and h) and the length of the package is 60 in. The width is
4 in. greater than the height, and the length is 13 in. greater than the width. Find the dimensions of the
Package.

Accepted Answer

A)  $w = 11$ in., $h = 7$ in., $l = 24$ in 
B)  $w = 11$ in., $h = 7$ in., $l = 13$ in 
C)  $w = 10$ in., $h = 6$ in., $l = 28$ in 
D)  $w = 10$ in., $h = 6$ in. $l = 23$ in 
A)  $w = 11$ in., $h = 7$ in., $l = 24$ in 
B)  $w = 11$ in., $h = 7$ in., $l = 13$ in 
C)  $w = 10$ in., $h = 6$ in., $l = 28$ in 
D)  $w = 10$ in., $h = 6$ in. $l = 23$ in

Question 12

Solve the problem.
-The average weekly salary of two employees is $1,200. One makes $200 more than the other. Find their salaries.

Accepted Answer

A)  One makes $700 and the other makes $900. 
B)  One makes $500 and the other makes $700. 
C)  One makes $1,100 and the other makes $1,300. 
D)  One makes $1,300 and the other makes $1,500. 
A)  One makes $700 and the other makes $900. 
B)  One makes $500 and the other makes $700. 
C)  One makes $1,100 and the other makes $1,300. 
D)  One makes $1,300 and the other makes $1,500.

Question 13

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-A solution to a system of linear equations in three variables is an ordered________ that satisfies each equation in the system. Graphically, this is the point of ________of three planes.

Accepted Answer

triple; in

Question 14

Two or more linear equations taken together is called a________ of linear equations.

Accepted Answer

The answer of Two or more linear equations taken together...

Question 15

Find the indicated system of inequalities.
-Write a system of inequalities that represents the points inside the triangle with vertices (2, 1), (-3, 3), and (-4, -2).

Accepted Answer

A) $y > - \frac { 2 } { 5 } x + \frac { 9 } { 5 }$ $\begin{array}{l} y>\frac{1}{2} x+0 \ y>5 x+18 \end{array}$ B) $y - \frac { 2 } { 5 } x + \frac { 9 } { 5 }$ $\begin{array}{l} y>\frac{1}{2} x+0 \ y>-5 x-12 \end{array}$ D) $y \frac{1}{2} x+0 \ y<5 x+18 \end{array}$ A) $y > - \frac { 2 } { 5 } x + \frac { 9 } { 5 }$ $\begin{array}{l} y>\frac{1}{2} x+0 \ y>5 x+18 \end{array}$ B) $y - \frac { 2 } { 5 } x + \frac { 9 } { 5 }$ $\begin{array}{l} y>\frac{1}{2} x+0 \ y>-5 x-12 \end{array}$ D) $y \frac{1}{2} x+0 \ y<5 x+18 \end{array}$

Question 16

Solve the system by using any method.
-$$\begin{array} { l } 
2 ^ { x } + 2 ^ { y } = 18 \
4 ^ { x } - 2 ^ { y } = - 12
\end{array}$$

Accepted Answer

A)  $\{ ( 1,4 ) \}$ 
B)  $\{ ( 4,1 ) \}$ 
C)  $\left\{ \left( 0 , \log _ { 2 } 18 \right) \right\}$ 
D)  $\left\{ \left( \log _ { 2 } 18,0 \right) \right\}$ 
A)  $\{ ( 1,4 ) \}$ 
B)  $\{ ( 4,1 ) \}$ 
C)  $\left\{ \left( 0 , \log _ { 2 } 18 \right) \right\}$ 
D)  $\left\{ \left( \log _ { 2 } 18,0 \right) \right\}$

Question 17

Solve the system by substitution.
-$$\begin{aligned}
y & = - 6 x - 14 \
5 x - 3 y & = 19
\end{aligned}$$

Accepted Answer

A)  $\{ ( - 6,22 ) \}$ 
B)  $\{ ( 4 , - 38 ) \}$ 
C)  $\{ ( - 1 , - 8 ) \}$ 
D)  No solution; \{ \} ; inconsistent system 
A)  $\{ ( - 6,22 ) \}$ 
B)  $\{ ( 4 , - 38 ) \}$ 
C)  $\{ ( - 1 , - 8 ) \}$ 
D)  No solution; \{ \} ; inconsistent system

Question 18

Determine the values of x and y that produce the maximum value of the objective function on the given
feasible region.
-$\text { Maximize: } z = 300 x + 150 y$

Accepted Answer

A)  $x = 20 , y = 20$ 
B)  $x = 20 , y = 40$ 
C)  $x = 0 , y = 0$ 
D)  $x = 60 , y = 0$ 
A)  $x = 20 , y = 20$ 
B)  $x = 20 , y = 40$ 
C)  $x = 0 , y = 0$ 
D)  $x = 60 , y = 0$

Question 19

Choose the one alternative that best completes the statement or answers the question.
a. Graph the equations in the system.
b. Solve the system by using the substitution method.
-$$\begin{array} { l } 
y = x ^ { 2 } - 2 \
y = - x - 2
\end{array}$$

Accepted Answer

A)  $\{ ( 0 , - 2 ) , ( 2,2 ) \}$
  
B)  $\{ ( 0 , - 2 ) , ( 1 , - 1 ) \}$
  
C)  $\{ ( 0 , - 2 ) , ( - 1 , - 1 ) \}$
  
D)  $\{ ( 0 , - 2 ) , ( - 2,2 ) \}$
  
A)  $\{ ( 0 , - 2 ) , ( 2,2 ) \}$
  
B)  $\{ ( 0 , - 2 ) , ( 1 , - 1 ) \}$
  
C)  $\{ ( 0 , - 2 ) , ( - 1 , - 1 ) \}$
  
D)  $\{ ( 0 , - 2 ) , ( - 2,2 ) \}$

Question 20

Find an equation of the form $y = a x ^ { 2 } + b x + c$ that defines the parabola through the three noncollinear
points given.
-$$( 0 , - 5 ) , ( - 3 , - 2 ) , ( 2,13 )$$

Accepted Answer

A)  $y = - 5 x ^ { 2 } - 2 x + 13$ 
B)  $y = 2 x ^ { 2 } - 3 x$ 
C)  $y = 5 x ^ { 2 } + 2 x - 5$ 
D)  $y = 2 x ^ { 2 } + 5 x - 5$ 
A)  $y = - 5 x ^ { 2 } - 2 x + 13$ 
B)  $y = 2 x ^ { 2 } - 3 x$ 
C)  $y = 5 x ^ { 2 } + 2 x - 5$ 
D)  $y = 2 x ^ { 2 } + 5 x - 5$

Determine whether the ordered pair is a solution to the system of inequalities. - x+y<-2;(-3,5) y\leq-2x-5

Solve the problem. -The perimeter of a triangle is 55 in. The shortest side is 16 in. less than the longest side. The middle side is 13 in. less than the combined lengths of the shortest and longest sides. Find the lengths of the Three sides.

Solve the system by substitution. -9x - 5y = 16 y = - 12 x + 6

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - +\leq16 +\geq49

Use a graphing utility to approximate the solution(s) to the system of equations. Round the coordinates to 3 decimal places. - y=-12x+43 y=7x

Solve the system of equations by using the addition method. - 5+3=95 +5=129

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - $- \frac { 1 } { 2 } x + 2 < 1$

Two algebraic methods to solve a system of linear equations in two variables are the method and the method.

Solve the problem. -The average weekly salary of two employees is $1,200. One makes $200 more than the other. Find their salaries.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A solution to a system of linear equations in three variables is an ordered that satisfies each equation in the system. Graphically, this is the point of of three planes.

Two or more linear equations taken together is called a________ of linear equations.

Find the indicated system of inequalities. -Write a system of inequalities that represents the points inside the triangle with vertices (2, 1), (-3, 3), and (-4, -2).

Solve the system by using any method. - +=18 -=-12

Solve the system by substitution. - y =-6x-14 5x-3y =19

Choose the one alternative that best completes the statement or answers the question. a. Graph the equations in the system. b. Solve the system by using the substitution method. - y=-2 y=-x-2

Find an equation of the form $y = a x ^ { 2 } + b x + c$ that defines the parabola through the three noncollinear points given. - $( 0 , - 5 ) , ( - 3 , - 2 ) , ( 2,13 )$

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Exam 5: Systems of Equations and Inequalities

Determine whether the ordered pair is a solution to the system of inequalities. - x+y<-2;(-3,5) y\leq-2x-5

Solve the problem. -The perimeter of a triangle is 55 in. The shortest side is 16 in. less than the longest side. The middle side is 13 in. less than the combined lengths of the shortest and longest sides. Find the lengths of the Three sides.

Solve the system by substitution. -9x - 5y = 16 y = - 12 x + 6

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - +\leq16 +\geq49

Use a graphing utility to approximate the solution(s) to the system of equations. Round the coordinates to 3 decimal places. - y=-12x+43 y=7x

Solve the system of equations by using the addition method. - 5+3=95 +5=129

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - −12x+2<1- \frac { 1 } { 2 } x + 2 < 1−21​x+2<1

Two algebraic methods to solve a system of linear equations in two variables are the________ method and the ________method.

Solve the problem. -The average weekly salary of two employees is $1,200. One makes $200 more than the other. Find their salaries.

Two or more linear equations taken together is called a________ of linear equations.

Find the indicated system of inequalities. -Write a system of inequalities that represents the points inside the triangle with vertices (2, 1), (-3, 3), and (-4, -2).

Solve the system by using any method. - +=18 -=-12

Solve the system by substitution. - y =-6x-14 5x-3y =19

Determine the values of x and y that produce the maximum value of the objective function on the given feasible region. - Maximize: z=300x+150y\text { Maximize: } z = 300 x + 150 y Maximize: z=300x+150y

Choose the one alternative that best completes the statement or answers the question. a. Graph the equations in the system. b. Solve the system by using the substitution method. - y=-2 y=-x-2

Find an equation of the form y=ax2+bx+cy = a x ^ { 2 } + b x + cy=ax2+bx+c that defines the parabola through the three noncollinear points given. - (0,−5),(−3,−2),(2,13)( 0 , - 5 ) , ( - 3 , - 2 ) , ( 2,13 )(0,−5),(−3,−2),(2,13)

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - $- \frac { 1 } { 2 } x + 2 < 1$

Two algebraic methods to solve a system of linear equations in two variables are the method and the method.

Find an equation of the form $y = a x ^ { 2 } + b x + c$ that defines the parabola through the three noncollinear points given. - $( 0 , - 5 ) , ( - 3 , - 2 ) , ( 2,13 )$