Question 1

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 seniorsE) A) and D)
F) None of the above

Question 2

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

Accepted Answer

A)  
B)  
C)  
D)   E) A) and D)
F) All of the above

Question 3

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 4

Use a graphing utility to approximate the solution(s)  to the system of equations. Round the coordinates to 3 decimal places.
- y=x2−12x+43y=7log⁡x\begin{array} { l } y = x ^ { 2 } - 12 x + 43 \y = 7 \log x\end{array}y=x2−12x+43y=7logx​

Accepted Answer

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

Question 5

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

Accepted Answer

A)   No
B)   Yes C) A) and B)
D) undefined

Question 6

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.E) All of the above
F) A) and B)

Question 7

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

Accepted Answer

substituti...

Question 8

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.E) A) and B)
F) A) and C)

Question 9

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)

Accepted Answer

A)    y=−5x2−2x+13y = - 5 x ^ { 2 } - 2 x + 13y=−5x2−2x+13 
B)    y=2x2−3xy = 2 x ^ { 2 } - 3 xy=2x2−3x 
C)    y=5x2+2x−5y = 5 x ^ { 2 } + 2 x - 5y=5x2+2x−5 
D)    y=2x2+5x−5y = 2 x ^ { 2 } + 5 x - 5y=2x2+5x−5E) A) and B)
F) B) and D)

Question 10

Graph the solution set. If there is no solution, indicate that the solution set is the empty set.
- x2+y2≤16x2+y2≥49\begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 16 \x ^ { 2 } + y ^ { 2 } \geq 49\end{array}x2+y2≤16x2+y2≥49​

Accepted Answer

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

Question 11

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) - \frac { 2 } { 5 } x + \frac { 9 } { 5 }">y>−25x+95y > - \frac { 2 } { 5 } x + \frac { 9 } { 5 }y>−52x+59 \frac{1}{2} x+0 \y>5 x+18\end{array}">y>12x+0y>5x+18\begin{array}{l}y>\frac{1}{2} x+0 \y>5 x+18\end{array}y>21x+0y>5x+18 B) y<−25x+95y < - \frac { 2 } { 5 } x + \frac { 9 } { 5 }y<−52x+59 y<12x+0y<−5x−12\begin{array}{l}y<\frac{1}{2} x+0 \y<-5 x-12\end{array}y<21x+0y<−5x−12 C) - \frac { 2 } { 5 } x + \frac { 9 } { 5 }">y>−25x+95y > - \frac { 2 } { 5 } x + \frac { 9 } { 5 }y>−52x+59 \frac{1}{2} x+0 \y>-5 x-12\end{array}">y>12x+0y>−5x−12\begin{array}{l}y>\frac{1}{2} x+0 \y>-5 x-12\end{array}y>21x+0y>−5x−12 D) y<−25x+95y < - \frac { 2 } { 5 } x + \frac { 9 } { 5 }y<−52x+59 \frac{1}{2} x+0 \yy>12x+0y<5x+18\begin{array}{l}y>\frac{1}{2} x+0 \y<5 x+18\end{array}y>21x+0y<5x+18 E) A) and C) F) A) and B)

Question 12

Solve the system of equations by using the addition method.
- 5x2+3y2=95x2+5y2=129\begin{array} { l } 5 x ^ { 2 } + 3 y ^ { 2 } = 95 \x ^ { 2 } + 5 y ^ { 2 } = 129\end{array}5x2+3y2=95x2+5y2=129​

Accepted Answer

A)    {(2,5) ,(2,−5) ,(−2,5) ,(−2,−5) }\{ ( 2,5 )  , ( 2 , - 5 )  , ( - 2,5 )  , ( - 2 , - 5 )  \}{(2,5) ,(2,−5) ,(−2,5) ,(−2,−5) } 
B)    {(2,5) ,(2,−5) }\{ ( 2,5 )  , ( 2 , - 5 )  \}{(2,5) ,(2,−5) } 
C)   {  }
D)    {(2,5) ,(−2,5) }\{ ( 2,5 )  , ( - 2,5 )  \}{(2,5) ,(−2,5) }E) B) and C)
F) C) and D)

Question 13

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

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

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	ext { Maximize: } z = 300 x + 150 y Maximize: z=300x+150y

Accepted Answer

A)    x=20,y=20x = 20 , y = 20x=20,y=20 
B)    x=20,y=40x = 20 , y = 40x=20,y=40 
C)    x=0,y=0x = 0 , y = 0x=0,y=0 
D)    x=60,y=0x = 60 , y = 0x=60,y=0E) A) and D)
F) All of the above

Question 16

Solve the system by using any method.
- 2x+2y=184x−2y=−12\begin{array} { l } 2 ^ { x } + 2 ^ { y } = 18 \4 ^ { x } - 2 ^ { y } = - 12\end{array}2x+2y=184x−2y=−12​

Accepted Answer

A)    {(1,4) }\{ ( 1,4 )  \}{(1,4) } 
B)    {(4,1) }\{ ( 4,1 )  \}{(4,1) } 
C)    {(0,log⁡218) }\left\{ \left( 0 , \log _ { 2 } 18 \right)  \right\}{(0,log2​18) } 
D)    {(log⁡218,0) }\left\{ \left( \log _ { 2 } 18,0 \right)  \right\}{(log2​18,0) }E) A) and B)
F) All of the above

Question 17

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=87x+59yz = 87 x + 59 yz=87x+59y 
B)    z=73(x+y) z = 73 ( x + y ) z=73(x+y)  
C)    z=59x+87yz = 59 x + 87 yz=59x+87y 
D)    z=28(x+y) z = 28 ( x + y ) z=28(x+y) E) None of the above
F) B) and C)

Question 18

Solve the system by substitution.
- y=−6x−145x−3y=19\begin{aligned}y & = - 6 x - 14 \5 x - 3 y & = 19\end{aligned}y5x−3y​=−6x−14=19​

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

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=x2−2y=−x−2\begin{array} { l } y = x ^ { 2 } - 2 \y = - x - 2\end{array}y=x2−2y=−x−2​

Accepted Answer

A)    {(0,−2) ,(2,2) }\{ ( 0 , - 2 )  , ( 2,2 )  \}{(0,−2) ,(2,2) } 
B)    {(0,−2) ,(1,−1) }\{ ( 0 , - 2 )  , ( 1 , - 1 )  \}{(0,−2) ,(1,−1) } 
C)    {(0,−2) ,(−1,−1) }\{ ( 0 , - 2 )  , ( - 1 , - 1 )  \}{(0,−2) ,(−1,−1) } 
D)    {(0,−2) ,(−2,2) }\{ ( 0 , - 2 )  , ( - 2,2 )  \}{(0,−2) ,(−2,2) }  E) B) and C)
F) A) and B)

Exam 5: Systems of Equations and Inequalities

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

Correct Answer
verified

Correct Answer
verified

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

Correct Answer
verified

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) .

Correct Answer
verified

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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. - $\begin{array} { l } y = x ^ { 2 } - 2 \\y = - x - 2\end{array}$

Correct Answer
verified

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

Correct Answer
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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.

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

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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.

Correct Answer
verified
triple; in...
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Solve the system by substitution. - $\begin{aligned}y & = - 6 x - 14 \\5 x - 3 y & = 19\end{aligned}$

Correct Answer
verified

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

Correct Answer
verified
substituti...
View Answer

Exam 5: Systems of Equations and Inequalities

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

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Solve the system by using any method. - 2x+2y=184x−2y=−12\begin{array} { l } 2 ^ { x } + 2 ^ { y } = 18 \\4 ^ { x } - 2 ^ { y } = - 12\end{array}2x+2y=184x−2y=−12​

Correct AnswerverifiedShow Answer

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) .

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Solve the system of equations by using the addition method. - 5x2+3y2=95x2+5y2=129\begin{array} { l } 5 x ^ { 2 } + 3 y ^ { 2 } = 95 \\x ^ { 2 } + 5 y ^ { 2 } = 129\end{array}5x2+3y2=95x2+5y2=129​

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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=x2−2y=−x−2\begin{array} { l } y = x ^ { 2 } - 2 \\y = - x - 2\end{array}y=x2−2y=−x−2​

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

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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.

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

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)

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Use a graphing utility to approximate the solution(s) to the system of equations. Round the coordinates to 3 decimal places. - y=x2−12x+43y=7log⁡x\begin{array} { l } y = x ^ { 2 } - 12 x + 43 \\y = 7 \log x\end{array}y=x2−12x+43y=7logx​

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Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - x2+y2≤16x2+y2≥49\begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 16 \\x ^ { 2 } + y ^ { 2 } \geq 49\end{array}x2+y2≤16x2+y2≥49​

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Correct Answerverifiedtriple; in...View AnswerShow Answer

Solve the system by substitution. - y=−6x−145x−3y=19\begin{aligned}y & = - 6 x - 14 \\5 x - 3 y & = 19\end{aligned}y5x−3y​=−6x−14=19​

Correct AnswerverifiedShow Answer

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

Correct Answerverifiedsubstituti...View AnswerShow Answer

Correct Answer
verified

Correct Answer
verified

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

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

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

Correct Answer
verified

Correct Answer
verified

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. - $\begin{array} { l } y = x ^ { 2 } - 2 \\y = - x - 2\end{array}$

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

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

Correct Answer
verified

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

Correct Answer
verified
triple; in...
View Answer

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

Correct Answer
verified

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

Correct Answer
verified
substituti...
View Answer