Question 1

How many liters (L) of a $10 \%$ silver iodide solution must be mixed with $6 \mathrm{~L}$ of a $4 \%$ silver iodide solution to get a $6 \%$ solution?

Accepted Answer

A)  $6.0 \mathrm{~L}$ 
B)  $3.0 \mathrm{~L}$ 
C)  $4.0 \mathrm{~L}$ 
D)  $2.0 \mathrm{~L}$ 
A)  $6.0 \mathrm{~L}$ 
B)  $3.0 \mathrm{~L}$ 
C)  $4.0 \mathrm{~L}$ 
D)  $2.0 \mathrm{~L}$

Question 2

Is the ordered triple a solution to the given system of equations?
-$(-2,6,-1)$
$-x+3 y+4 z=16$
$3 \mathrm{x}+2 \mathrm{y}-\mathrm{z}=7$
$4 x-y+3 z=-17$.

Accepted Answer

A) True 
 B)False

Question 3

Evaluate the determinant
-$\left|\begin{array}{rrr}4 & 4 & -4 \ 3 & 4 & 5 \ -5 & 1 & -3\end{array}\right|$

Accepted Answer

A)  224 
B)  -224 
C)  -96 
D)  -24 
A)  224 
B)  -224 
C)  -96 
D)  -24

Question 4

Solve the system of equations using Cramer's rule.
-$x+3 y=3$
$4 x-5 y=-5$

Accepted Answer

A)  $(1,0)$ 
B)  $(0,0)$ 
C)  $(0,1)$ 
D)  $(1,1)$ 
A)  $(1,0)$ 
B)  $(0,0)$ 
C)  $(0,1)$ 
D)  $(1,1)$

Question 5

Sketch the feasible region, and use linear programming to find the maximum value of $\mathrm{z}$ on the feasible region.
-A yoga studio will offer a workshop provided that at least 20 people sign up. Beginning students require more attention than experienced students and the number of assistants in the class will be limited to three. For this reason, the teacher would like the number of experienced students to be at least twice the number of beginners. Set up and graph a system of inequalities for the situation, letting $\mathrm{x}$ represent the number of beginning students and $\mathrm{y}$ the number of experienced students.

Accepted Answer

The answer of Sketch the feasible region, and use linear...

Question 6

Solve the system of equations using Cramer's rule.
-$\begin{aligned} 7 x+9 y-z & =63 \ x-5 y-4 z & =-33 \ -8 x+y+z & =-39\end{aligned}$

Accepted Answer

A)  $(6,3,-6)$ 
B)  $(6,3,6)$ 
C)  $(-6,3,12)$ 
D)  $(6,6,3)$ 
A)  $(6,3,-6)$ 
B)  $(6,3,6)$ 
C)  $(-6,3,12)$ 
D)  $(6,6,3)$

Question 7

Solve by addition or substitution.
-$9 x+7 y=-36$
$4 \mathrm{x}-2 \mathrm{y}=-16$

Accepted Answer

A)  $(-5,1)$ 
B)  $(-4,1)$ 
C)  $(-4,0)$ 
D)  $\varnothing$ 
A)  $(-5,1)$ 
B)  $(-4,1)$ 
C)  $(-4,0)$ 
D)  $\varnothing$

Question 8

Evaluate the determinant
-$$\text {   } \begin{array}{r}
X+y+z=-2 \
X-y+4 z=-1 \
2 x+y+z=-1 \
\end{array}$$

Accepted Answer

A) (-1,-2,1) 
B)  $(-1,1,-2)$ 
C)  $(1,-2,-1)$ 
D)  $(6,-2,-1)$ 
A) (-1,-2,1) 
B)  $(-1,1,-2)$ 
C)  $(1,-2,-1)$ 
D)  $(6,-2,-1)$

Question 9

Solve the system of equations using Cramer's rule.
-$3 x+y=7$
$6 x+4 y=4$

Accepted Answer

A)  $(-5,-4)$ 
B)  $(4,-4)$ 
C)  $(4,-5)$ 
D)  $(-5,4)$ 
A)  $(-5,-4)$ 
B)  $(4,-4)$ 
C)  $(4,-5)$ 
D)  $(-5,4)$

Question 10

Is the ordered pair a solution of the given system of equations?
-$(-3,-2), \begin{aligned} & 3 x-y=7 \ & 2 x-3 y=0\end{aligned}$

Accepted Answer

A) True 
 B)False

Question 11

A $\$ 122,000$ trust is to be invested in bonds paying $6 \%$, CDs paying $5 \%$, and mortgages paying $8 \%$. The sum of the investments in bonds and CDs must equal the mortgage investment. To earn $\$ 8400$ annual income from the investments, how much should the bank invest in bonds?

Accepted Answer

A)  $\$ 47,000$ 
B)  $\$ 14,000$ 
C)  $\$ 45,000$ 
D)  $\$ 61,000$ 
A)  $\$ 47,000$ 
B)  $\$ 14,000$ 
C)  $\$ 45,000$ 
D)  $\$ 61,000$

Question 12

Paul invested four times as much money in an account paying $7 \%$ interest than he did in an account paying $1 \%$ interest. If the total interest paid was $\$ 870$, how much did he invest in each?

Accepted Answer

A)  $\$ 120$ at $7 \%$, $\$ 30$ at $1 \%$ 
B)  $\$ 12,000$ at $7 \%, \$ 3000$ at $1 \%$ 
C)  $\$ 12,000$ at $7 \%, \$ 3500$ at $1 \%$ 
D)  $\$ 3000$ at $7 \%, \$ 12,000$ at $1 \%$ 
A)  $\$ 120$ at $7 \%$, $\$ 30$ at $1 \%$ 
B)  $\$ 12,000$ at $7 \%, \$ 3000$ at $1 \%$ 
C)  $\$ 12,000$ at $7 \%, \$ 3500$ at $1 \%$ 
D)  $\$ 3000$ at $7 \%, \$ 12,000$ at $1 \%$

Question 13

Solve the system of equations using Cramer's rule.
-$4 \mathrm{x}-15 \mathrm{y}=1$
$-16 x+3 y=-23$

Accepted Answer

A)  $\left(\frac{3}{2}, \frac{1}{3}\right)$ 
B)  $\left(\frac{5}{2},-\frac{1}{3}\right)$ 
C)  $\left(\frac{5}{2}, \frac{1}{3}\right)$ 
D)  $\left(\frac{3}{2},-\frac{1}{3}\right)$ 
A)  $\left(\frac{3}{2}, \frac{1}{3}\right)$ 
B)  $\left(\frac{5}{2},-\frac{1}{3}\right)$ 
C)  $\left(\frac{5}{2}, \frac{1}{3}\right)$ 
D)  $\left(\frac{3}{2},-\frac{1}{3}\right)$

Question 14

How many liters of a $30 \%$ - alcohol solution must be mixed with 40 liters of a solution that is $60 \%$ alcohol to get a solution that is $50 \%$ alcohol?

Accepted Answer

A)  $6 \mathrm{~L}$ 
B)  $2 \mathrm{~L}$ 
C)  $60 \mathrm{~L}$ 
D)  $20 \mathrm{~L}$ 
A)  $6 \mathrm{~L}$ 
B)  $2 \mathrm{~L}$ 
C)  $60 \mathrm{~L}$ 
D)  $20 \mathrm{~L}$

Question 15

Evaluate the determinant
-$\left|\begin{array}{rr}6 & 2 \ 0 & -6\end{array}\right|$

Accepted Answer

A)  12 
B)  36 
C)  -36 
D)  -38 
A)  12 
B)  36 
C)  -36 
D)  -38

Question 16

Solve the system of equations using matrices.
-$\frac{2}{3} x+2 y-2 z=-10$
$$\begin{aligned}
& 3 x+\frac{1}{3} y+z=21 \
& x-3 y+3 z=27
\end{aligned}$$

Accepted Answer

A)  $(9,-6,4)$ 
B)  $(9,-3,5)$ 
C)  $(6,-6,5)$ 
D)  $(6,-3,4)$ 
A)  $(9,-6,4)$ 
B)  $(9,-3,5)$ 
C)  $(6,-6,5)$ 
D)  $(6,-3,4)$

Question 17

In triangle $A B C$, the measure of angle $B$ is $5^{\circ}$ more than three times the measure of angle $A$. The measure of angle $\mathrm{C}$ is $15^{\circ}$ more than that of angle $\mathrm{A}$. Find the angle measures.

Accepted Answer

A)  $33^{\circ}, 99^{\circ}, 48^{\circ}$ 
B)  $35^{\circ}, 95^{\circ}, 50^{\circ}$ 
C)  $31^{\circ}, 103^{\circ}, 46^{\circ}$ 
D)  $32^{\circ}, 101^{\circ}, 47^{\circ}$ 
A)  $33^{\circ}, 99^{\circ}, 48^{\circ}$ 
B)  $35^{\circ}, 95^{\circ}, 50^{\circ}$ 
C)  $31^{\circ}, 103^{\circ}, 46^{\circ}$ 
D)  $32^{\circ}, 101^{\circ}, 47^{\circ}$

Question 18

Set up a system of equations, and use it to balance the chemical equation for the given reaction.
-$\mathrm{Fe}_{3} \mathrm{O}_{4}$ and $\mathrm{H}_{2}$ react to produce $\mathrm{Fe}$ and $\mathrm{H}_{2} \mathrm{O}$.

Accepted Answer

A)  $\mathrm{Fe}_{3} \mathrm{O}_{4}+4 \mathrm{H}_{2} \rightarrow 2 \mathrm{Fe}+3 \mathrm{H}_{2} \mathrm{O}$ 
B)  $\mathrm{Fe}_{3} \mathrm{O}_{4}+2 \mathrm{H}_{2} \rightarrow 3 \mathrm{Fe}+2 \mathrm{H}_{2} \mathrm{O}$ 
C)  $\mathrm{Fe}_{3} \mathrm{O}_{4}+4 \mathrm{H}_{2} \rightarrow 3 \mathrm{Fe}+4 \mathrm{H}_{2} \mathrm{O}$ 
D)  $\mathrm{Fe}_{3} \mathrm{O}_{4}+2 \mathrm{H}_{2} \rightarrow 3 \mathrm{Fe}+4 \mathrm{H}_{2} \mathrm{O}$ 
A)  $\mathrm{Fe}_{3} \mathrm{O}_{4}+4 \mathrm{H}_{2} \rightarrow 2 \mathrm{Fe}+3 \mathrm{H}_{2} \mathrm{O}$ 
B)  $\mathrm{Fe}_{3} \mathrm{O}_{4}+2 \mathrm{H}_{2} \rightarrow 3 \mathrm{Fe}+2 \mathrm{H}_{2} \mathrm{O}$ 
C)  $\mathrm{Fe}_{3} \mathrm{O}_{4}+4 \mathrm{H}_{2} \rightarrow 3 \mathrm{Fe}+4 \mathrm{H}_{2} \mathrm{O}$ 
D)  $\mathrm{Fe}_{3} \mathrm{O}_{4}+2 \mathrm{H}_{2} \rightarrow 3 \mathrm{Fe}+4 \mathrm{H}_{2} \mathrm{O}$

Question 19

For the given system of equations, which method would be the most efficient method to use when solving the system of equations: substitution, addition, or either?
-$x+y=12$
$4 \mathrm{x}+9 \mathrm{y}=41$

Accepted Answer

A)  addition 
B)  substitution 
C)  either 
A)  addition 
B)  substitution 
C)  either

Question 20

Graph the system of inequalities.
-$3 x-2 y \leq 6$
$x \geq 1$

Accepted Answer

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

How many liters (L) of a $10 \%$ silver iodide solution must be mixed with $6 \mathrm{~L}$ of a $4 \%$ silver iodide solution to get a $6 \%$ solution?

Is the ordered triple a solution to the given system of equations? - $(-2,6,-1)$ $-x+3 y+4 z=16$ $3 \mathrm{x}+2 \mathrm{y}-\mathrm{z}=7$ $4 x-y+3 z=-17$ .

Evaluate the determinant - $\left|\begin{array}{rrr}4 & 4 & -4 \\ 3 & 4 & 5 \\ -5 & 1 & -3\end{array}\right|$

Solve the system of equations using Cramer's rule. - $x+3 y=3$ $4 x-5 y=-5$

Solve the system of equations using Cramer's rule. - 7x+9y-z =63 x-5y-4z =-33 -8x+y+z =-39

Solve by addition or substitution. - $9 x+7 y=-36$ $4 \mathrm{x}-2 \mathrm{y}=-16$

Evaluate the determinant - start text end text X+y+z=-2 X-y+4z=-1 2x+y+z=-1

Solve the system of equations using Cramer's rule. - $3 x+y=7$ $6 x+4 y=4$

Is the ordered pair a solution of the given system of equations? - left parenthesisminus3commaminus2right parenthesiscomma 3x-y=7 2x-3y=0

A $\$ 122,000$ trust is to be invested in bonds paying $6 \%$ , CDs paying $5 \%$ , and mortgages paying $8 \%$ . The sum of the investments in bonds and CDs must equal the mortgage investment. To earn $\$ 8400$ annual income from the investments, how much should the bank invest in bonds?

Paul invested four times as much money in an account paying $7 \%$ interest than he did in an account paying $1 \%$ interest. If the total interest paid was $\$ 870$ , how much did he invest in each?

Solve the system of equations using Cramer's rule. - $4 \mathrm{x}-15 \mathrm{y}=1$ $-16 x+3 y=-23$

How many liters of a $30 \%$ - alcohol solution must be mixed with 40 liters of a solution that is $60 \%$ alcohol to get a solution that is $50 \%$ alcohol?

Evaluate the determinant - $\left|\begin{array}{rr}6 & 2 \\ 0 & -6\end{array}\right|$

Solve the system of equations using matrices. - $\frac{2}{3} x+2 y-2 z=-10$ 3x+y+z=21 x-3y+3z=27

In triangle $A B C$ , the measure of angle $B$ is $5^{\circ}$ more than three times the measure of angle $A$ . The measure of angle $\mathrm{C}$ is $15^{\circ}$ more than that of angle $\mathrm{A}$ . Find the angle measures.

Set up a system of equations, and use it to balance the chemical equation for the given reaction. - $\mathrm{Fe}_{3} \mathrm{O}_{4}$ and $\mathrm{H}_{2}$ react to produce $\mathrm{Fe}$ and $\mathrm{H}_{2} \mathrm{O}$ .

For the given system of equations, which method would be the most efficient method to use when solving the system of equations: substitution, addition, or either? - $x+y=12$ $4 \mathrm{x}+9 \mathrm{y}=41$

Graph the system of inequalities. - $3 x-2 y \leq 6$ $x \geq 1$ $Graph the system of inequalities. - 3 x-2 y \leq 6 x \geq 1$

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 4: Systems of Equations

How many liters (L) of a 10%10 \%10% silver iodide solution must be mixed with 6 L6 \mathrm{~L}6 L of a 4%4 \%4% silver iodide solution to get a 6%6 \%6% solution?

Is the ordered triple a solution to the given system of equations? - (−2,6,−1)(-2,6,-1)(−2,6,−1) −x+3y+4z=16-x+3 y+4 z=16−x+3y+4z=16 3x+2y−z=73 \mathrm{x}+2 \mathrm{y}-\mathrm{z}=73x+2y−z=7 4x−y+3z=−174 x-y+3 z=-174x−y+3z=−17 .

Evaluate the determinant - ∣44−4345−51−3∣\left|\begin{array}{rrr}4 & 4 & -4 \\ 3 & 4 & 5 \\ -5 & 1 & -3\end{array}\right|​43−5​441​−45−3​​

Solve the system of equations using Cramer's rule. - x+3y=3x+3 y=3x+3y=3 4x−5y=−54 x-5 y=-54x−5y=−5

Solve the system of equations using Cramer's rule. - 7x+9y-z =63 x-5y-4z =-33 -8x+y+z =-39

Solve by addition or substitution. - 9x+7y=−369 x+7 y=-369x+7y=−36 4x−2y=−164 \mathrm{x}-2 \mathrm{y}=-164x−2y=−16

Evaluate the determinant - start text end text X+y+z=-2 X-y+4z=-1 2x+y+z=-1

Solve the system of equations using Cramer's rule. - 3x+y=73 x+y=73x+y=7 6x+4y=46 x+4 y=46x+4y=4

Is the ordered pair a solution of the given system of equations? - left parenthesisminus3commaminus2right parenthesiscomma 3x-y=7 2x-3y=0

Paul invested four times as much money in an account paying 7%7 \%7% interest than he did in an account paying 1%1 \%1% interest. If the total interest paid was $870\$ 870$870 , how much did he invest in each?

Solve the system of equations using Cramer's rule. - 4x−15y=14 \mathrm{x}-15 \mathrm{y}=14x−15y=1 −16x+3y=−23-16 x+3 y=-23−16x+3y=−23

How many liters of a 30%30 \%30% - alcohol solution must be mixed with 40 liters of a solution that is 60%60 \%60% alcohol to get a solution that is 50%50 \%50% alcohol?

Evaluate the determinant - ∣620−6∣\left|\begin{array}{rr}6 & 2 \\ 0 & -6\end{array}\right|​60​2−6​​

Solve the system of equations using matrices. - 23x+2y−2z=−10\frac{2}{3} x+2 y-2 z=-1032​x+2y−2z=−10 3x+y+z=21 x-3y+3z=27

In triangle ABCA B CABC , the measure of angle BBB is 5∘5^{\circ}5∘ more than three times the measure of angle AAA . The measure of angle C\mathrm{C}C is 15∘15^{\circ}15∘ more than that of angle A\mathrm{A}A . Find the angle measures.

Set up a system of equations, and use it to balance the chemical equation for the given reaction. - Fe3O4\mathrm{Fe}_{3} \mathrm{O}_{4}Fe3​O4​ and H2\mathrm{H}_{2}H2​ react to produce Fe\mathrm{Fe}Fe and H2O\mathrm{H}_{2} \mathrm{O}H2​O .

For the given system of equations, which method would be the most efficient method to use when solving the system of equations: substitution, addition, or either? - x+y=12x+y=12x+y=12 4x+9y=414 \mathrm{x}+9 \mathrm{y}=414x+9y=41

Graph the system of inequalities. - 3x−2y≤63 x-2 y \leq 63x−2y≤6 x≥1x \geq 1x≥1

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

How many liters (L) of a $10 \%$ silver iodide solution must be mixed with $6 \mathrm{~L}$ of a $4 \%$ silver iodide solution to get a $6 \%$ solution?

Is the ordered triple a solution to the given system of equations? - $(-2,6,-1)$ $-x+3 y+4 z=16$ $3 \mathrm{x}+2 \mathrm{y}-\mathrm{z}=7$ $4 x-y+3 z=-17$ .

Evaluate the determinant - $\left|\begin{array}{rrr}4 & 4 & -4 \\ 3 & 4 & 5 \\ -5 & 1 & -3\end{array}\right|$

Solve the system of equations using Cramer's rule. - $x+3 y=3$ $4 x-5 y=-5$

Solve by addition or substitution. - $9 x+7 y=-36$ $4 \mathrm{x}-2 \mathrm{y}=-16$

Solve the system of equations using Cramer's rule. - $3 x+y=7$ $6 x+4 y=4$

Paul invested four times as much money in an account paying $7 \%$ interest than he did in an account paying $1 \%$ interest. If the total interest paid was $\$ 870$ , how much did he invest in each?

Solve the system of equations using Cramer's rule. - $4 \mathrm{x}-15 \mathrm{y}=1$ $-16 x+3 y=-23$

How many liters of a $30 \%$ - alcohol solution must be mixed with 40 liters of a solution that is $60 \%$ alcohol to get a solution that is $50 \%$ alcohol?

Evaluate the determinant - $\left|\begin{array}{rr}6 & 2 \\ 0 & -6\end{array}\right|$

Solve the system of equations using matrices. - $\frac{2}{3} x+2 y-2 z=-10$ 3x+y+z=21 x-3y+3z=27

In triangle $A B C$ , the measure of angle $B$ is $5^{\circ}$ more than three times the measure of angle $A$ . The measure of angle $\mathrm{C}$ is $15^{\circ}$ more than that of angle $\mathrm{A}$ . Find the angle measures.

Set up a system of equations, and use it to balance the chemical equation for the given reaction. - $\mathrm{Fe}_{3} \mathrm{O}_{4}$ and $\mathrm{H}_{2}$ react to produce $\mathrm{Fe}$ and $\mathrm{H}_{2} \mathrm{O}$ .

For the given system of equations, which method would be the most efficient method to use when solving the system of equations: substitution, addition, or either? - $x+y=12$ $4 \mathrm{x}+9 \mathrm{y}=41$

Graph the system of inequalities. - $3 x-2 y \leq 6$ $x \geq 1$ $Graph the system of inequalities. - 3 x-2 y \leq 6 x \geq 1$