Question 1

Solve the system by using any method.
-$\begin{array} { l } 
( x + 2 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 25 \
( x - 3 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 8
\end{array}$

Accepted Answer

A)  $\left\{ ( 1,1 ) , \left( \frac { 85 } { 61 } , \frac { 41 } { 61 } \right) \right\}$ 
B)  $\left\{ \left( \frac { 85 } { 61 } , \frac { 41 } { 61 } \right) , \left( - \frac { 85 } { 61 } , - \frac { 41 } { 61 } \right) \right\}$ 
C)  $\{ ( 1,1 ) , ( - 1 , - 1 ) \}$ 
D)  $\{ ( 1,1 ) \}$ 
A)  $\left\{ ( 1,1 ) , \left( \frac { 85 } { 61 } , \frac { 41 } { 61 } \right) \right\}$ 
B)  $\left\{ \left( \frac { 85 } { 61 } , \frac { 41 } { 61 } \right) , \left( - \frac { 85 } { 61 } , - \frac { 41 } { 61 } \right) \right\}$ 
C)  $\{ ( 1,1 ) , ( - 1 , - 1 ) \}$ 
D)  $\{ ( 1,1 ) \}$

Question 2

Solve the system.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 10 \
3 y ^ { 2 } - x ^ { 2 } = 14
\end{array}$$

Accepted Answer

A)  $\{ ( 2 , \sqrt { 6 } ) , ( 2 , - \sqrt { 6 } ) , ( - 2 , \sqrt { 6 } ) , ( - 2 , - \sqrt { 6 } ) \}$ 
B)  $\{ ( 2 , \sqrt { 6 } ) \}$ 
C) {  } 
D)  $\{ ( 2 , \sqrt { 6 } ) , ( - 2 , - \sqrt { 6 } ) \}$ 
A)  $\{ ( 2 , \sqrt { 6 } ) , ( 2 , - \sqrt { 6 } ) , ( - 2 , \sqrt { 6 } ) , ( - 2 , - \sqrt { 6 } ) \}$ 
B)  $\{ ( 2 , \sqrt { 6 } ) \}$ 
C) {  } 
D)  $\{ ( 2 , \sqrt { 6 } ) , ( - 2 , - \sqrt { 6 } ) \}$

Question 3

Choose the one alternative that best completes the statement or answers the question.
Determine whether the ordered pair is a solution of the system.
-$$\begin{aligned}
\left( \frac { 4 } { 9 } , - 5 \right) \
36 x + 5 y & = - 9 \
- 27 x - 4 y & = 12
\end{aligned}$$

Accepted Answer

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

Question 4

Graph the solution set. If there is no solution, indicate that the solution set is the empty set.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } \leq 64 \
y \geq x \
y \geq 1
\end{array}$$

Accepted Answer

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

Question 5

Find the measure of angles x and y.
-(The figure is not necessarily drawn to scale.)

Accepted Answer

A)  $x = 61 ^ { \circ } ; y = 84 ^ { \circ }$ 
B)  $x = 82 ^ { \circ } ; y = 86 ^ { \circ }$ 
C)  $x = 84 ^ { \circ } ; y = 61 ^ { \circ }$ 
D)  $x = 86 ^ { \circ } ; y = 82 ^ { \circ }$ 
A)  $x = 61 ^ { \circ } ; y = 84 ^ { \circ }$ 
B)  $x = 82 ^ { \circ } ; y = 86 ^ { \circ }$ 
C)  $x = 84 ^ { \circ } ; y = 61 ^ { \circ }$ 
D)  $x = 86 ^ { \circ } ; y = 82 ^ { \circ }$

Question 6

Solve the system of equations by using the substitution method.
-$$\begin{array} { l } 
y = - 2 x ^ { 2 } \
x = \sqrt { y }
\end{array}$$

Accepted Answer

A)  $\{ ( 3 , \sqrt { 3 } ) \}$ 
B)  $\{ ( \sqrt { 3 } , 3 ) \}$ 
C)  $\{ ( 0,1 ) , ( 0,3 ) \}$ 
D)  $\{ ( 0,0 ) , ( \sqrt { 3 } , 3 ) \}$ 
A)  $\{ ( 3 , \sqrt { 3 } ) \}$ 
B)  $\{ ( \sqrt { 3 } , 3 ) \}$ 
C)  $\{ ( 0,1 ) , ( 0,3 ) \}$ 
D)  $\{ ( 0,0 ) , ( \sqrt { 3 } , 3 ) \}$

Question 7

Solve the system of equations by using the substitution method.
-$$\begin{array} { l } 
y = x ^ { 3 } \
y = 25 x
\end{array}$$

Accepted Answer

A)  $\{ ( 0,0 ) , ( 5,125 ) \}$ 
B)  $\{ ( 0,0 ) , ( 5,125 ) , ( - 5 , - 125 ) \}$ 
C)  {  } 
D)  $\{ ( 0,0 ) \}$ 
A)  $\{ ( 0,0 ) , ( 5,125 ) \}$ 
B)  $\{ ( 0,0 ) , ( 5,125 ) , ( - 5 , - 125 ) \}$ 
C)  {  } 
D)  $\{ ( 0,0 ) \}$

Question 8

Solve the system by using any method. If a system does not have one unique solution, state whether the
system is inconsistent or whether the equations are dependent.
-$$\begin{array} { l } 
3 ( 4 x - 3 ) = - 15 y - 1 \
\frac { 2 } { 3 } x + \frac { 5 } { 6 } y = - \frac { 1 } { 6 }
\end{array}$$

Accepted Answer

A)  $\left\{ \left( 2 , - \frac { 16 } { 15 } \right) \right\}$ 
B)  No solution; \{ \} ; inconsistent system 
C)  $\left\{ \left( 0 , - \frac { 1 } { 5 } \right) \right\}$ 
D)  $\left\{ \left( - 1 , \frac { 4 } { 3 } \right) \right\}$ 
A)  $\left\{ \left( 2 , - \frac { 16 } { 15 } \right) \right\}$ 
B)  No solution; \{ \} ; inconsistent system 
C)  $\left\{ \left( 0 , - \frac { 1 } { 5 } \right) \right\}$ 
D)  $\left\{ \left( - 1 , \frac { 4 } { 3 } \right) \right\}$

Question 9

Solve the problem.
-A vendor at a carnival sells cotton candy and caramel apples for $2.00 each. The vendor is charged $60 to set up his booth. Furthermore, the vendor's average cost for each product he produces is Approximately $0.80.

a.Write a linear cost function representing the cost C(x) (in $) to produce x products.
b. Write a linear revenue function representing the revenue R(x) (in $) for selling x products.
c. Determine the number of products to be produced and sold for the vendor to break even.

Accepted Answer

A)  a. $C ( x ) = 60$
b. $R ( x ) = 1.2 x$
c. products $= 75$ 
B)  a. $C ( x ) = 60$
b. $R ( x ) = 1.2 x$
c. products $= 50$ 
C)  a. $C ( x ) = 0.8 x + 60$
b. $R ( x ) = 2 x$
c. products $= 75$ 
D)  a. $C ( x ) = 0.8 x + 60$
b. $R ( x ) = 2 x$
c. products $= 50$ 
A)  a. $C ( x ) = 60$
b. $R ( x ) = 1.2 x$
c. products $= 75$ 
B)  a. $C ( x ) = 60$
b. $R ( x ) = 1.2 x$
c. products $= 50$ 
C)  a. $C ( x ) = 0.8 x + 60$
b. $R ( x ) = 2 x$
c. products $= 75$ 
D)  a. $C ( x ) = 0.8 x + 60$
b. $R ( x ) = 2 x$
c. products $= 50$

Question 10

Choose the one alternative that best completes the statement or answers the question.
Find three ordered triples that are solutions to the linear equation in three variables.
-$$4 x - 4 y - 2 z = 32$$

Accepted Answer

A)  $\{ ( - 4,0,0 ) , ( 0,4,0 ) , ( 0,0,2 ) \}$ 
B)  $\{ ( 8,0,0 ) , ( 0 , - 8,0 ) , ( 0,0 , - 16 ) \}$ 
C)  $\{ ( 4,0,0 ) , ( 0 , - 4,0 ) , ( 0,0 , - 2 ) \}$ 
D)  $\{ ( 28,0,0 ) , ( 0,36,0 ) , ( 0,0,34 ) \}$ 
A)  $\{ ( - 4,0,0 ) , ( 0,4,0 ) , ( 0,0,2 ) \}$ 
B)  $\{ ( 8,0,0 ) , ( 0 , - 8,0 ) , ( 0,0 , - 16 ) \}$ 
C)  $\{ ( 4,0,0 ) , ( 0 , - 4,0 ) , ( 0,0 , - 2 ) \}$ 
D)  $\{ ( 28,0,0 ) , ( 0,36,0 ) , ( 0,0,34 ) \}$

Question 11

Determine the values of x and y that produce the maximum value of the objective function on the given feasible region.
-Maximize $z = 40 x + 50 y$

Accepted Answer

A)  $x = 10 , y = 4$ 
B)  $x = 0 , y = 8$ 
C)  $x = 10 , y = 0$ 
D)  $x = 6 , y = 8$ 
A)  $x = 10 , y = 4$ 
B)  $x = 0 , y = 8$ 
C)  $x = 10 , y = 0$ 
D)  $x = 6 , y = 8$

Question 12

Find the partial fraction decomposition.
-$$\frac { - 4 x - 2 } { x ^ { 2 } + 2 x }$$

Accepted Answer

A)  $\frac { - 3 } { x } + \frac { - 1 } { x + 2 }$ 
B)  $\frac { - 3 } { x ^ { 2 } } + \frac { - 1 } { 2 x }$ 
C)  $\frac { - 1 } { x ^ { 2 } } + \frac { - 3 } { 2 x }$ 
D)  $\frac { - 1 } { x } + \frac { - 3 } { x + 2 }$ 
A)  $\frac { - 3 } { x } + \frac { - 1 } { x + 2 }$ 
B)  $\frac { - 3 } { x ^ { 2 } } + \frac { - 1 } { 2 x }$ 
C)  $\frac { - 1 } { x ^ { 2 } } + \frac { - 3 } { 2 x }$ 
D)  $\frac { - 1 } { x } + \frac { - 3 } { x + 2 }$

Question 13

Choose the one alternative that best completes the statement or answers the question.
Determine whether the ordered pair is a solution of the system.
-$$\begin{array} { l } 
5 x - 7 y = - 21 ; \quad ( 7,8 ) \
4 x + 9 y = 97
\end{array}$$

Accepted Answer

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

Question 14

Find the partial fraction decomposition.
-$$\frac { - 13 x - 8 } { ( x + 4 ) ( 5 x - 2 ) }$$

Accepted Answer

A)  $\frac { - 8 } { x + 4 } + \frac { - 13 x } { 5 x - 2 }$ 
B)  $\frac { - 2 } { x + 4 } + \frac { - 3 } { 5 x - 2 }$ 
C)  $\frac { - 13 x } { x + 4 } + \frac { - 8 } { 5 x - 2 }$ 
D)  $\frac { - 3 } { x + 4 } + \frac { - 2 } { 5 x - 2 }$ 
A)  $\frac { - 8 } { x + 4 } + \frac { - 13 x } { 5 x - 2 }$ 
B)  $\frac { - 2 } { x + 4 } + \frac { - 3 } { 5 x - 2 }$ 
C)  $\frac { - 13 x } { x + 4 } + \frac { - 8 } { 5 x - 2 }$ 
D)  $\frac { - 3 } { x + 4 } + \frac { - 2 } { 5 x - 2 }$

Question 15

Solve the problem.
-A ball is kicked off the side of a hill at an angle of elevation of 30°. The hill slopes downward 30° from the horizontal. Consider a coordinate system in which the origin is the point on the edge of the hill from
Which the ball is kicked. The path of the ball and the line of declination of the hill can be approximated by $y = - \frac { x ^ { 2 } } { 231 } + \frac { \sqrt { 3 } } { 3 } x \quad$ Path of the ball
$y = - \frac { \sqrt { 3 } } { 3 } x \quad$ Line of declination of the hill
Solve the system to determine where the ball will hit the ground.

Accepted Answer

A)  The ball will hit the ground at the point $( 77 \sqrt { 3 } , - 77 )$ 
B)  The ball will hit the ground at the point $( 154 , - 154 \sqrt { 3 } )$ 
C)  The ball will hit the ground at the point $( 77 , - 77 \sqrt { 3 } ) \mathrm { r }$ 
D)  The ball will hit the ground at the point $( 154 \sqrt { 3 } , - 154 )$ 
A)  The ball will hit the ground at the point $( 77 \sqrt { 3 } , - 77 )$ 
B)  The ball will hit the ground at the point $( 154 , - 154 \sqrt { 3 } )$ 
C)  The ball will hit the ground at the point $( 77 , - 77 \sqrt { 3 } ) \mathrm { r }$ 
D)  The ball will hit the ground at the point $( 154 \sqrt { 3 } , - 154 )$

Question 16

Solve the problem.
-The measure of the largest angle in a triangle is 6° more than the sum of the measures of the other two angles. The measure of the smallest angle is one-half the measure of the middle angle. Find the
Measure of each angle.

Accepted Answer

A)  The angles are 27°, 54°, and 99°. 
B)  The angles are 31°, 62°, and 87°. 
C)  The angles are 33°, 66°, and 81°. 
D)  The angles are 29°, 58°, and 93°. 
A)  The angles are 27°, 54°, and 99°. 
B)  The angles are 31°, 62°, and 87°. 
C)  The angles are 33°, 66°, and 81°. 
D)  The angles are 29°, 58°, and 93°.

Question 17

Find the partial fraction decomposition.
-$$\frac { - 4 x ^ { 2 } - 33 x - 54 } { x ^ { 3 } + 6 x ^ { 2 } + 9 x }$$

Accepted Answer

A)  $\frac { - 6 } { x } + \frac { - 3 } { ( x + 3 ) ^ { 2 } }$ 
B)  $\frac { - 6 } { x } + \frac { 2 } { x + 3 } + \frac { - 3 x } { ( x + 3 ) ^ { 2 } }$ 
C)  $\frac { - 6 } { x } + \frac { 2 x - 3 } { ( x + 3 ) ^ { 2 } }$ 
D)  $\frac { - 6 } { x } + \frac { 2 } { x + 3 } + \frac { - 3 } { ( x + 3 ) ^ { 2 } }$ 
A)  $\frac { - 6 } { x } + \frac { - 3 } { ( x + 3 ) ^ { 2 } }$ 
B)  $\frac { - 6 } { x } + \frac { 2 } { x + 3 } + \frac { - 3 x } { ( x + 3 ) ^ { 2 } }$ 
C)  $\frac { - 6 } { x } + \frac { 2 x - 3 } { ( x + 3 ) ^ { 2 } }$ 
D)  $\frac { - 6 } { x } + \frac { 2 } { x + 3 } + \frac { - 3 } { ( x + 3 ) ^ { 2 } }$

Question 18

Choose the one alternative that best completes the statement or answers the question.
Determine whether the ordered pair is a solution of the system.
-$$\left( \begin{array} { r l } 
\left( \frac { 3 } { 4 } , - \frac { 6 } { 5 } \right) \
12 x + 5 y & = 3 \
4 x + 15 y & = - 15
\end{array} \right.$$

Accepted Answer

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

Question 19

Solve the system by substitution.
-$$\begin{aligned}
x + 2 y & = 10 \
2 x - 7 y & = - 2
\end{aligned}$$

Accepted Answer

A)  $\{ ( 6,2 ) \}$ 
B)  $\left\{ ( x , y ) \mid y = - \frac { 1 } { 2 } x + 5 \right\}$; The equations are dependent 
C)  $\{ ( 14 , - 2 ) \}$ 
D)  $\{ ( 13,4 ) \}$ 
A)  $\{ ( 6,2 ) \}$ 
B)  $\left\{ ( x , y ) \mid y = - \frac { 1 } { 2 } x + 5 \right\}$; The equations are dependent 
C)  $\{ ( 14 , - 2 ) \}$ 
D)  $\{ ( 13,4 ) \}$

Question 20

Solve the system by the substitution method.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 37 \
y = \sqrt { x - 5 }
\end{array}$$

Accepted Answer

A)  $\{ ( - 7 , - 12 ) \}$ 
B)  $\{ ( - 7 , - 12 ) , ( 6,1 ) \}$ 
C)  \{ \} 
D)  $\{ ( 6,1 ) \}$ 
A)  $\{ ( - 7 , - 12 ) \}$ 
B)  $\{ ( - 7 , - 12 ) , ( 6,1 ) \}$ 
C)  \{ \} 
D)  $\{ ( 6,1 ) \}$

Solve the system by using any method. - (x+2+(y+3=25 (x-3+(y-3=8

Solve the system. - +=10 3-=14

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution of the system. - ,-5 36x+5y =-9 -27x-4y =12

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - +\leq64 y\geqx y\geq1

Find the measure of angles x and y. -(The figure is not necessarily drawn to scale.)

Solve the system of equations by using the substitution method. - y=-2 x=

Solve the system of equations by using the substitution method. - y= y=25x

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - 3(4x-3)=-15y-1 x+y=-

Choose the one alternative that best completes the statement or answers the question. Find three ordered triples that are solutions to the linear equation in three variables. - $4 x - 4 y - 2 z = 32$

Determine the values of x and y that produce the maximum value of the objective function on the given feasible region. -Maximize $z = 40 x + 50 y$

Find the partial fraction decomposition. - $\frac { - 4 x - 2 } { x ^ { 2 } + 2 x }$

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution of the system. - 5x-7y=-21;(7,8) 4x+9y=97

Find the partial fraction decomposition. - $\frac { - 13 x - 8 } { ( x + 4 ) ( 5 x - 2 ) }$

Solve the problem. -The measure of the largest angle in a triangle is 6° more than the sum of the measures of the other two angles. The measure of the smallest angle is one-half the measure of the middle angle. Find the Measure of each angle.

Find the partial fraction decomposition. - $\frac { - 4 x ^ { 2 } - 33 x - 54 } { x ^ { 3 } + 6 x ^ { 2 } + 9 x }$

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution of the system. - $\left( \begin{array} { r l } \left( \frac { 3 } { 4 } , - \frac { 6 } { 5 } \right) \\12 x + 5 y & = 3 \\4 x + 15 y & = - 15\end{array} \right.$

Solve the system by substitution. - x+2y =10 2x-7y =-2

Solve the system by the substitution method. - +=37 y=

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Exam 5: Systems of Equations and Inequalities