Question 1

Solve the system by the substitution method.
-$$x ^ { 2 } + y ^ { 2 } = 49$$
$y - x = 7$

Accepted Answer

A)  $\{ ( 0,7 ) , ( 7,0 ) \}$ 
B)  $\{ ( 0 , - 7 ) , ( - 7,0 ) \}$ 
C)  $\{ ( 0,7 ) , ( - 7,0 ) \}$ 
D)  $\{ ( 0 , - 7 ) , ( 7,0 ) \}$ 
A)  $\{ ( 0,7 ) , ( 7,0 ) \}$ 
B)  $\{ ( 0 , - 7 ) , ( - 7,0 ) \}$ 
C)  $\{ ( 0,7 ) , ( - 7,0 ) \}$ 
D)  $\{ ( 0 , - 7 ) , ( 7,0 ) \}$

Question 2

Choose the one alternative that best completes the statement or answers the question.
Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on.
-$$\frac { 7 x ^ { 5 } + 5 x ^ { 3 } + 7 x ^ { 2 } + 6 } { x ( x - 5 ) ^ { 3 } \left( x ^ { 2 } + 2 x + 5 \right) ^ { 2 } }$$

Accepted Answer

A)  $\frac { A } { x } + \frac { B } { x - 5 } + \frac { C } { ( x - 5 ) ^ { 2 } } + \frac { D } { ( x - 5 ) ^ { 3 } } + \frac { E x } { x ^ { 2 } + 2 x + 5 } + \frac { F x } { \left( x ^ { 2 } + 2 x + 5 \right) ^ { 2 } }$ 
B)  $\frac { A } { x } + \frac { B } { x - 5 } + \frac { C } { ( x - 5 ) ^ { 2 } } + \frac { D } { ( x - 5 ) ^ { 3 } } + \frac { E } { x ^ { 2 } + 2 x + 5 } + \frac { F } { \left( x ^ { 2 } + 2 x + 5 \right) ^ { 2 } }$ 
C)  $\frac { A } { x } + \frac { B } { x - 5 } + \frac { C } { ( x - 5 ) ^ { 2 } } + \frac { D } { ( x - 5 ) ^ { 3 } } + \frac { E x + F } { x ^ { 2 } + 2 x + 5 } + \frac { G x + H } { \left( x ^ { 2 } + 2 x + 5 \right) ^ { 2 } }$ 
D)  $\frac { A } { x } + \frac { B } { ( x - 5 ) ^ { 3 } } + \frac { C x + D } { \left( x ^ { 2 } + 2 x + 5 \right) ^ { 2 } }$ 
A)  $\frac { A } { x } + \frac { B } { x - 5 } + \frac { C } { ( x - 5 ) ^ { 2 } } + \frac { D } { ( x - 5 ) ^ { 3 } } + \frac { E x } { x ^ { 2 } + 2 x + 5 } + \frac { F x } { \left( x ^ { 2 } + 2 x + 5 \right) ^ { 2 } }$ 
B)  $\frac { A } { x } + \frac { B } { x - 5 } + \frac { C } { ( x - 5 ) ^ { 2 } } + \frac { D } { ( x - 5 ) ^ { 3 } } + \frac { E } { x ^ { 2 } + 2 x + 5 } + \frac { F } { \left( x ^ { 2 } + 2 x + 5 \right) ^ { 2 } }$ 
C)  $\frac { A } { x } + \frac { B } { x - 5 } + \frac { C } { ( x - 5 ) ^ { 2 } } + \frac { D } { ( x - 5 ) ^ { 3 } } + \frac { E x + F } { x ^ { 2 } + 2 x + 5 } + \frac { G x + H } { \left( x ^ { 2 } + 2 x + 5 \right) ^ { 2 } }$ 
D)  $\frac { A } { x } + \frac { B } { ( x - 5 ) ^ { 3 } } + \frac { C x + D } { \left( x ^ { 2 } + 2 x + 5 \right) ^ { 2 } }$

Question 3

Solve the problem.
-An investment grows exponentially under continuous compounding. After 2 yr, the amount in the account is $6,962.58. After 5 yr, the amount in the account is $8,089.36. Use the model $A ( t ) = P e ^ { r t }$ to
a. Find the interest rate r. Round to the nearest percent.
b. Find the original principal P. Round to the nearest dollar.
c. Determine the amount of time required for the account to reach a value of $17,000. Round to the
Nearest year.

Accepted Answer

A)  $r = 6 \%$;
$P = \$ 6,000$;
$\mathrm { t } = 17 \mathrm { yr }$ 
B)  $r = 5 \%$;
$P = \$ 6,000$;
$\mathrm { t } = 21 \mathrm { yr }$ 
C)  $r = 5 \%$;
$P = \$ 6,300$;
$\mathrm { t } = 20 \mathrm { yr }$ 
D)  $r = 5 \%$;
$P = \$ 6,300$;
$\mathrm { t } = 19 \mathrm { yr }$ 
A)  $r = 6 \%$;
$P = \$ 6,000$;
$\mathrm { t } = 17 \mathrm { yr }$ 
B)  $r = 5 \%$;
$P = \$ 6,000$;
$\mathrm { t } = 21 \mathrm { yr }$ 
C)  $r = 5 \%$;
$P = \$ 6,300$;
$\mathrm { t } = 20 \mathrm { yr }$ 
D)  $r = 5 \%$;
$P = \$ 6,300$;
$\mathrm { t } = 19 \mathrm { yr }$

Question 4

Solve the problem.
-A weak earthquake occurred roughly 4 km south and 5 km west of the center of Shelbyville. The quake could be felt 7 km away. Suppose the origin of the map is placed at the center of Shelbyville With the positive x-axis pointing east and the positive y-axis pointing north. Write an inequality that Describes the points on the map for which the earthquake could be felt, and determine whether the Quake could be felt at the center of Shelbyville.

Accepted Answer

A)  $| x + 4 | + | y + 5 | \leq 7$; No, the quake was $9 \mathrm {~km}$ from the center of Shelbyville. 
B)  $( x + 4 ) ^ { 2 } + ( y + 5 ) ^ { 2 } \leq 49 ;$ No, the quake was $9 \mathrm {~km}$ from the center of Shelbyville. 
C)  $( x + 4 ) ^ { 2 } + ( y + 5 ) ^ { 2 } \leq 49$; Yes, the quake was $6.4 \mathrm {~km}$ from the center of Shelbyville. 
D)  $| x + 4 | + | y + 5 | \leq 7 ; \mathrm { Yes }$, the quake was $6.4 \mathrm {~km}$ from the center of Shelbyville. 
A)  $| x + 4 | + | y + 5 | \leq 7$; No, the quake was $9 \mathrm {~km}$ from the center of Shelbyville. 
B)  $( x + 4 ) ^ { 2 } + ( y + 5 ) ^ { 2 } \leq 49 ;$ No, the quake was $9 \mathrm {~km}$ from the center of Shelbyville. 
C)  $( x + 4 ) ^ { 2 } + ( y + 5 ) ^ { 2 } \leq 49$; Yes, the quake was $6.4 \mathrm {~km}$ from the center of Shelbyville. 
D)  $| x + 4 | + | y + 5 | \leq 7 ; \mathrm { Yes }$, the quake was $6.4 \mathrm {~km}$ from the center of Shelbyville.

Question 5

Solve the problem.
-One angle measures 27° more than 2 times another. If the two angles are complementary, find the measures of the angles.

Accepted Answer

A)  26°; 64° 
B)  23°; 67° 
C)  21°; 69° 
D)  31°; 59° 
A)  26°; 64° 
B)  23°; 67° 
C)  21°; 69° 
D)  31°; 59°

Question 6

Solve the problem.
-A plant nursery sells two sizes of oak trees to landscapers. Large trees cost the nursery $120 from the grower and small trees cost $70. The profit for each large tree sold is $40, and the profit for each
Small tree sold is $25. The monthly demand is at most 475 oak trees. Furthermore, the nursery does
Not want to allocate more than $43,000 each month on inventory for oak trees. Determine the
Number of large oak trees and the number of small oak trees that the nursery should have in its
Inventory each month to maximize profit, and determine the maximum profit. (Assume that all trees
In inventory are sold.)

Accepted Answer

A)  275 large oaks and 200 small oaks for a maximum profit of $16,000. 
B)  280 large oaks and 195 small oaks for a maximum profit of $16,075. 
C)  200 large oaks and 275 small oaks for a maximum profit of $14,875. 
D)  195 large oaks and 280 small oaks for a maximum profit of $14,800. 
A)  275 large oaks and 200 small oaks for a maximum profit of $16,000. 
B)  280 large oaks and 195 small oaks for a maximum profit of $16,075. 
C)  200 large oaks and 275 small oaks for a maximum profit of $14,875. 
D)  195 large oaks and 280 small oaks for a maximum profit of $14,800.

Question 7

A system of equations that has no solution is called an ________system.

Accepted Answer

The answer of A system of equations that has no...

Question 8

Choose the one alternative that best completes the statement or answers the question.
Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on.
-$$\frac { x ^ { 2 } + 4 x + 8 } { ( x - 2 ) ( x - 5 ) ^ { 2 } \left( x ^ { 2 } + 49 \right) ^ { 2 } }$$

Accepted Answer

A)  $\frac { A } { x - 2 } + \frac { B } { ( x - 5 ) ^ { 2 } } + \frac { C } { \left( x ^ { 2 } + 49 \right) ^ { 2 } }$ 
B)  $\frac { A } { x - 2 } + \frac { B } { ( x - 5 ) ^ { 2 } } + \frac { C x + D } { \left( x ^ { 2 } + 49 \right) ^ { 2 } }$ 
C)  $\frac { A } { x - 2 } + \frac { B } { x - 5 } + \frac { C } { ( x - 5 ) ^ { 2 } } + \frac { D } { x ^ { 2 } + 49 } + \frac { F } { \left( x ^ { 2 } + 49 \right) ^ { 2 } }$ 
D)  $\frac { A } { x - 2 } + \frac { B } { x - 5 } + \frac { C } { ( x - 5 ) ^ { 2 } } + \frac { D x + E } { x ^ { 2 } + 49 } + \frac { F x + G } { \left( x ^ { 2 } + 49 \right) ^ { 2 } }$ 
A)  $\frac { A } { x - 2 } + \frac { B } { ( x - 5 ) ^ { 2 } } + \frac { C } { \left( x ^ { 2 } + 49 \right) ^ { 2 } }$ 
B)  $\frac { A } { x - 2 } + \frac { B } { ( x - 5 ) ^ { 2 } } + \frac { C x + D } { \left( x ^ { 2 } + 49 \right) ^ { 2 } }$ 
C)  $\frac { A } { x - 2 } + \frac { B } { x - 5 } + \frac { C } { ( x - 5 ) ^ { 2 } } + \frac { D } { x ^ { 2 } + 49 } + \frac { F } { \left( x ^ { 2 } + 49 \right) ^ { 2 } }$ 
D)  $\frac { A } { x - 2 } + \frac { B } { x - 5 } + \frac { C } { ( x - 5 ) ^ { 2 } } + \frac { D x + E } { x ^ { 2 } + 49 } + \frac { F x + G } { \left( x ^ { 2 } + 49 \right) ^ { 2 } }$

Question 9

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-For a constant real number k, the inequality x < k represents the half-plane to the (left/right) of the
(horizontal/vertical) line x = k.

Accepted Answer

The answer of Write the word or phrase that best...

Question 10

Solve the problem.
-The number of adults in a certain county with a college degree has been rising since the year 2005. Let x represent the number of years since the year 2000, and let y represent the number of 1000s of Adults in the county with a college degree for year x. 
$$\begin{array}{l}
\text { Number of Years Number of Adults with a College }\
\begin{array} { c | c } 
\text { Since } 2005 ( x ) & \text { Degree } ( y \text { in } 1000 \mathrm {~s} ) \
\hline 0 & 10 \
\hline 4 & 18 \
\hline 6 & 52
\end{array}
\end{array}$$ 
(a) Use the data to create a model of the form $y = a x ^ { 2 } + b x + c$ 
(b) Use the model to approximate the number of adults in the county who will have a college degree for the Year 2015.

Accepted Answer

A)  $y = 10 x ^ { 2 } + 18 x + 52 ; 452,500$ adults 
B)  $y = 6 x ^ { 2 } + 4 x + 10 ; 180,000$ adults 
C)  $y = - 8 x ^ { 2 } + 2.5 x + 10 ; 452,500$ adults 
D)  $y = 2.5 x ^ { 2 } - 8 x + 10 ; 180,000$ adults 
A)  $y = 10 x ^ { 2 } + 18 x + 52 ; 452,500$ adults 
B)  $y = 6 x ^ { 2 } + 4 x + 10 ; 180,000$ adults 
C)  $y = - 8 x ^ { 2 } + 2.5 x + 10 ; 452,500$ adults 
D)  $y = 2.5 x ^ { 2 } - 8 x + 10 ; 180,000$ adults

Question 11

Solve the system of equations by using the addition method.
-$$\begin{array} { l } 
5 x ^ { 2 } - 2 y ^ { 2 } = 17 \
x ^ { 2 } = 1 - 3 y ^ { 2 }
\end{array}$$

Accepted Answer

A)  $\{ ( 1,0 ) , ( - 1,0 ) \}$ 
B)  $\{ ( 1,0 ) \}$ 
C) {   } 
D)  $\{ ( 1,17 ) \}$ 
A)  $\{ ( 1,0 ) , ( - 1,0 ) \}$ 
B)  $\{ ( 1,0 ) \}$ 
C) {   } 
D)  $\{ ( 1,17 ) \}$

Question 12

Solve the problem.
-The points shown in the graph represent the per capita consumption of chicken and beef in a country x years after the year 2000. Yearly Per Capita Consumption of Chicken and Beef
 
 a. Use the given data points to write a linear function that approximates per capita consumption of Chicken C(x) (in lb) at a time x years since the year 2000.
b. Use the given data points to write a linear function that approximates per capita consumption of Beef B(x) (in lb) at a time x years since the year 2000.
c. Approximate the solution to the system of linear equations defined by the functions from parts (a)
And (b). Round to 1 decimal place. Interpret the meaning of the solution to the system.

Accepted Answer

A)  a. $C ( x ) = 1.25 x + 55.5$
b. $B ( x ) = - 0.33 x + 65.6$
c. $\{ ( 6.5,63.4 ) \}$ Midyear in 2,006 , the per capita consumption of beef and chicken was approximately equal at $63.4 \mathrm { lb }$ each 
B)  a. $C ( x ) = 1.2 x + 55.6$;
b. $B ( x ) = - 0.34 x + 65.6$
c. $\{ ( 6.5,63.4 ) \}$ Midyear in 2,006 , the per capita consumption of beef and chicken was approximately equal at $63.4 \mathrm { lb }$ each 
C)  a. $C ( x ) = 1.25 x + 55.5$
b. $B ( x ) = - 0.33 x + 65.6$
c. $\{ ( 6.6,63.5 ) \}$ Midyear in 2,007 , the per capita consumption of beef and chicken was approximately equal at $63.5 \mathrm { lb }$ each 
D)  a. $C ( x ) = 1.2 x + 55.6$;
b. $B ( x ) = - 0.34 x + 65.6$
c. $\{ ( 6.6,63.5 ) \}$ Midyear in 2,007 , the per capita consumption of beef and chicken was approximately equal at $63.5 \mathrm { lb }$ each 
A)  a. $C ( x ) = 1.25 x + 55.5$
b. $B ( x ) = - 0.33 x + 65.6$
c. $\{ ( 6.5,63.4 ) \}$ Midyear in 2,006 , the per capita consumption of beef and chicken was approximately equal at $63.4 \mathrm { lb }$ each 
B)  a. $C ( x ) = 1.2 x + 55.6$;
b. $B ( x ) = - 0.34 x + 65.6$
c. $\{ ( 6.5,63.4 ) \}$ Midyear in 2,006 , the per capita consumption of beef and chicken was approximately equal at $63.4 \mathrm { lb }$ each 
C)  a. $C ( x ) = 1.25 x + 55.5$
b. $B ( x ) = - 0.33 x + 65.6$
c. $\{ ( 6.6,63.5 ) \}$ Midyear in 2,007 , the per capita consumption of beef and chicken was approximately equal at $63.5 \mathrm { lb }$ each 
D)  a. $C ( x ) = 1.2 x + 55.6$;
b. $B ( x ) = - 0.34 x + 65.6$
c. $\{ ( 6.6,63.5 ) \}$ Midyear in 2,007 , the per capita consumption of beef and chicken was approximately equal at $63.5 \mathrm { lb }$ each

Question 13

Solve the problem.
-Nail polish remover is essentially a mixture of water and a chemical called acetone. How much pure acetone must be combined with a solution that is 28% acetone to make 24 oz of a 58% solution?

Accepted Answer

A)  14 oz 
B)  12 oz 
C)  10 oz 
D)  17 oz 
A)  14 oz 
B)  12 oz 
C)  10 oz 
D)  17 oz

Question 14

Solve the system by using any method.
-$$\begin{array} { l } 
y = x ^ { 2 } + 7 x - 4 \
y = 5 x - 5
\end{array}$$

Accepted Answer

A)  $\{ ( - 1 , - 10 ) , ( 1,0 ) \}$ 
B)  $\{ ( 1,0 ) \}$ 
C)  $\{ ( - 1 , - 10 ) \}$ 
D)  {   } 
A)  $\{ ( - 1 , - 10 ) , ( 1,0 ) \}$ 
B)  $\{ ( 1,0 ) \}$ 
C)  $\{ ( - 1 , - 10 ) \}$ 
D)  {   }

Question 15

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent.
-$$\begin{array} { l } 
0.8 x = 0.4 y - 0.3 z \
0.004 x + 0.007 y - 0.002 z = 0 \
30 x - 50 y = 60 z
\end{array}$$

Accepted Answer

A)  No solution; inconsistent 
B)  $\{ ( 0,0,0 ) \}$ 
C)  $\{ ( - 3 , - 2 , - 3 ) \}$ 
D)  Infinitely many solutions; dependent 
A)  No solution; inconsistent 
B)  $\{ ( 0,0,0 ) \}$ 
C)  $\{ ( - 3 , - 2 , - 3 ) \}$ 
D)  Infinitely many solutions; dependent

Question 16

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.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 25 \
4 x + 3 y = 0
\end{array}$$

Accepted Answer

A)  $\{ ( - 3,4 ) , ( 3 , - 4 ) \}$
  
B)  $\{ ( - 4 , - 3 ) , ( 4,3 ) \}$
  
C)  $\{ ( - 4,3 ) , ( 4 , - 3 ) \}$
  
D)  $\{ ( - 3 , - 4 ) , ( 3,4 ) \}$
  
A)  $\{ ( - 3,4 ) , ( 3 , - 4 ) \}$
  
B)  $\{ ( - 4 , - 3 ) , ( 4,3 ) \}$
  
C)  $\{ ( - 4,3 ) , ( 4 , - 3 ) \}$
  
D)  $\{ ( - 3 , - 4 ) , ( 3,4 ) \}$

Question 17

Solve the problem.
-A closed box is in the shape of a rectangular solid with height 2 m. Its surface area is $56 \mathrm {~m} ^ { 2 }$ . If the volume is $24 \mathrm {~m} ^ { 3 }$ , find the dimensions of the box.

Accepted Answer

A)  The box is 1 m by 12 m by 2 m. 
B)  The box is 1 m by 3 m by 2 m. 
C)  The box is 2 m by 6 m by 2 m. 
D)  The box is 4 m by 3 m by 2 m. 
A)  The box is 1 m by 12 m by 2 m. 
B)  The box is 1 m by 3 m by 2 m. 
C)  The box is 2 m by 6 m by 2 m. 
D)  The box is 4 m by 3 m by 2 m.

Question 18

A system of linear equations in two variables may have infinitely many solutions. In such a case, the equations are said to be________

Accepted Answer

The answer of A system of linear equations in two...

Question 19

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent.
-$$\begin{array} { l } 
- 4 x - 6 y - 5 z = 9 \
4 ( x + y ) + 3 z = x - 5 y + 9 \
6 ( x + y ) - 7 z = 2 x + 3 y + 18
\end{array}$$

Accepted Answer

A)  $\{ ( 9,9,18 \} )$ 
B)  $\{ ( - 3,3 , - 3 ) \}$ 
C)  Infinitely many solutions; dependent 
D)  No solution; inconsistent 
A)  $\{ ( 9,9,18 \} )$ 
B)  $\{ ( - 3,3 , - 3 ) \}$ 
C)  Infinitely many solutions; dependent 
D)  No solution; inconsistent

Question 20

Solve the system of equations by using the addition method.
-$$\begin{array} { l } 
6 x + 2 y = 0 \
7 x + 5 y = 8
\end{array}$$

Accepted Answer

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

Solve the system by the substitution method. - $x ^ { 2 } + y ^ { 2 } = 49$ $y - x = 7$

Solve the problem. -One angle measures 27° more than 2 times another. If the two angles are complementary, find the measures of the angles.

A system of equations that has no solution is called an ________system.

Choose the one alternative that best completes the statement or answers the question. Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on. - $\frac { x ^ { 2 } + 4 x + 8 } { ( x - 2 ) ( x - 5 ) ^ { 2 } \left( x ^ { 2 } + 49 \right) ^ { 2 } }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -For a constant real number k, the inequality x < k represents the half-plane to the (left/right) of the (horizontal/vertical) line x = k.

Solve the system of equations by using the addition method. - 5-2=17 =1-3

Solve the problem. -Nail polish remover is essentially a mixture of water and a chemical called acetone. How much pure acetone must be combined with a solution that is 28% acetone to make 24 oz of a 58% solution?

Solve the system by using any method. - y=+7x-4 y=5x-5

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. - 0.8x=0.4y-0.3z 0.004x+0.007y-0.002z=0 30x-50y=60z

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. - +=25 4x+3y=0

Solve the problem. -A closed box is in the shape of a rectangular solid with height 2 m. Its surface area is $56 \mathrm {~m} ^ { 2 }$ . If the volume is $24 \mathrm {~m} ^ { 3 }$ , find the dimensions of the box.

A system of linear equations in two variables may have infinitely many solutions. In such a case, the equations are said to be________

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. - -4x-6y-5z=9 4(x+y)+3z=x-5y+9 6(x+y)-7z=2x+3y+18

Solve the system of equations by using the addition method. - 6x+2y=0 7x+5y=8

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

Solve the system by the substitution method. - x2+y2=49x ^ { 2 } + y ^ { 2 } = 49x2+y2=49 y−x=7y - x = 7y−x=7

Solve the problem. -One angle measures 27° more than 2 times another. If the two angles are complementary, find the measures of the angles.

A system of equations that has no solution is called an ________system.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -For a constant real number k, the inequality x < k represents the half-plane to the (left/right) of the (horizontal/vertical) line x = k.

Solve the system of equations by using the addition method. - 5-2=17 =1-3

Solve the problem. -Nail polish remover is essentially a mixture of water and a chemical called acetone. How much pure acetone must be combined with a solution that is 28% acetone to make 24 oz of a 58% solution?

Solve the system by using any method. - y=+7x-4 y=5x-5

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. - 0.8x=0.4y-0.3z 0.004x+0.007y-0.002z=0 30x-50y=60z

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. - +=25 4x+3y=0

Solve the problem. -A closed box is in the shape of a rectangular solid with height 2 m. Its surface area is 56 m256 \mathrm {~m} ^ { 2 }56 m2 . If the volume is 24 m324 \mathrm {~m} ^ { 3 }24 m3 , find the dimensions of the box.

A system of linear equations in two variables may have infinitely many solutions. In such a case, the equations are said to be________

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. - -4x-6y-5z=9 4(x+y)+3z=x-5y+9 6(x+y)-7z=2x+3y+18

Solve the system of equations by using the addition method. - 6x+2y=0 7x+5y=8

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

Solve the system by the substitution method. - $x ^ { 2 } + y ^ { 2 } = 49$ $y - x = 7$

Solve the problem. -A closed box is in the shape of a rectangular solid with height 2 m. Its surface area is $56 \mathrm {~m} ^ { 2 }$ . If the volume is $24 \mathrm {~m} ^ { 3 }$ , find the dimensions of the box.