Question 1

Suppose the triangles shown are similar, with angle $A=$ angle $D$, angle $B=$ angle $E$, and angle $C=$ angle $F$. Answer the question.
- 
What is the value of $x$ ?

Accepted Answer

A)  $\frac{31}{2}$ 
B)  $\frac{23}{4}$ 
C)  4 
D)  8 
A)  $\frac{31}{2}$ 
B)  $\frac{23}{4}$ 
C)  4 
D)  8

Question 2

Suppose the triangles shown are similar, with angle $A=$ angle $D$, angle $B=$ angle $E$, and angle $C=$ angle $F$. Answer the question.
-  
What is the value of $x$ ?

Accepted Answer

A)  11 
B)  37 
C)  $\frac{9}{8}$ 
D)  32 
A)  11 
B)  37 
C)  $\frac{9}{8}$ 
D)  32

Question 3

Perform the indicated operation and express in lowest terms.
-$\frac{z^{2}+9 z+18}{z^{2}+14 z+48} \div \frac{z^{2}+3 z}{z^{2}+2 z-48}$

Accepted Answer

A)  $\frac{z-6}{z^{2}+8 z}$ 
B)  $\frac{z}{z^{2}+14 z+48}$ 
C)  $\frac{z-6}{z}$ 
D)  z - 6 
A)  $\frac{z-6}{z^{2}+8 z}$ 
B)  $\frac{z}{z^{2}+14 z+48}$ 
C)  $\frac{z-6}{z}$ 
D)  z - 6

Question 4

Find all numbers that are not in the domain of the function. Then give the domain using set notation.
-$f(x)=\frac{15 x^{2}-2 x+1}{225 x^{2}-169}$

Accepted Answer

A)  $\frac{15}{13}, \frac{15}{13} ;\left\{\left\{x \mid x \neq \frac{15}{13},-\frac{15}{13}\right\}\right.$ 
B)  $\frac{13}{15} ;\left\{x \mid x \neq \frac{13}{15}\right\}$ 
C)  $\frac{169}{225}, \frac{169}{225} ;\left\{x \mid x \neq \frac{169}{225},-\frac{169}{225}\right\}$ 
D)  $\frac{13}{15}, \frac{13}{15} ;\left\{x \mid x \neq \frac{13}{15},-\frac{13}{15}\right\}$ 
A)  $\frac{15}{13}, \frac{15}{13} ;\left\{\left\{x \mid x \neq \frac{15}{13},-\frac{15}{13}\right\}\right.$ 
B)  $\frac{13}{15} ;\left\{x \mid x \neq \frac{13}{15}\right\}$ 
C)  $\frac{169}{225}, \frac{169}{225} ;\left\{x \mid x \neq \frac{169}{225},-\frac{169}{225}\right\}$ 
D)  $\frac{13}{15}, \frac{13}{15} ;\left\{x \mid x \neq \frac{13}{15},-\frac{13}{15}\right\}$

Question 5

Find all numbers not in the domain of the function
-$f(x)=\frac{8}{x-3}$

Accepted Answer

A)  None 
B)  0 
C)  3 
D)  -3 
A)  None 
B)  0 
C)  3 
D)  -3

Question 6

Write the expression in lowest terms.
-$\frac{\mathrm{a}^{2}-25}{\mathrm{a}^{2}+7 \mathrm{a}+10}$

Accepted Answer

A)  $\frac{a+5}{a+2}$ 
B)  $\frac{a+5}{a-2}$ 
C)  $\frac{a-5}{a-2}$ 
D)  $\frac{a-5}{a+2}$ 
A)  $\frac{a+5}{a+2}$ 
B)  $\frac{a+5}{a-2}$ 
C)  $\frac{a-5}{a-2}$ 
D)  $\frac{a-5}{a+2}$

Question 7

The speed of a vehicle varies inversely as the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at 40 miles per hour in 45 minutes, how fast must it travel to cover the same distance in 20 minutes?

Accepted Answer

A)  $\frac{45}{2} \mathrm{mph}$ 
B)  $90 \mathrm{mph}$ 
C)  $\frac{160}{9} \mathrm{mph}$ 
D)  $\frac{9}{160} \mathrm{mph}$ 
A)  $\frac{45}{2} \mathrm{mph}$ 
B)  $90 \mathrm{mph}$ 
C)  $\frac{160}{9} \mathrm{mph}$ 
D)  $\frac{9}{160} \mathrm{mph}$

Question 8

Perform the indicated operation and express in lowest terms.
-$\frac{\mathrm{k}^{2}+12 \mathrm{k}+27}{\mathrm{k}^{2}+18 \mathrm{k}+81} \cdot \frac{\mathrm{k}^{2}+9 \mathrm{k}}{\mathrm{k}^{2}+8 \mathrm{k}+15}$

Accepted Answer

A)  $\frac{1}{\mathrm{k}+5}$ 
B)  $\frac{\mathrm{k}}{\mathrm{k}^{2}+18 \mathrm{k}+81}$ 
C)  $\frac{\mathrm{k}}{\mathrm{k}+5}$ 
D)  $\frac{k^{2}+9 k}{k+5}$ 
A)  $\frac{1}{\mathrm{k}+5}$ 
B)  $\frac{\mathrm{k}}{\mathrm{k}^{2}+18 \mathrm{k}+81}$ 
C)  $\frac{\mathrm{k}}{\mathrm{k}+5}$ 
D)  $\frac{k^{2}+9 k}{k+5}$

Question 9

State whether the following situation represents direct variation, inverse variation, or neither, and explain why: A runner's speed in a race and the time that it takes to run the race.

Accepted Answer

Inverse variation; t

Question 10

A boat goes 270 miles downstream in the same time it can go 240 miles upstream. The speed of the current is 8 miles per hour. Find the speed of the boat in still water.

Accepted Answer

A)  $144 \mathrm{mph}$ 
B)  $51 \mathrm{mph}$ 
C)  $136 \mathrm{mph}$ 
D)  $128 \mathrm{mph}$ 
A)  $144 \mathrm{mph}$ 
B)  $51 \mathrm{mph}$ 
C)  $136 \mathrm{mph}$ 
D)  $128 \mathrm{mph}$

Question 11

Perform the indicated operation and express in lowest terms.
-$\frac{3}{15 x}+\frac{5}{15 x}$

Accepted Answer

A)  $\frac{15 x}{8}$ 
B)  $\frac{8}{30 x}$ 
C)  $\frac{8}{15 x}$ 
D)  1 
A)  $\frac{15 x}{8}$ 
B)  $\frac{8}{30 x}$ 
C)  $\frac{8}{15 x}$ 
D)  1

Question 12

Choose the one alternative that best completes the statement or answers the question.
Solve the problem. Round your answer, as needed.
-A formula for electric circuits is $\frac{1}{a}=\frac{1}{b}+\frac{1}{c}$. If $c=19$ and $b=8$, find $a$.

Accepted Answer

A)  64.125 
B)  5.63 
C)  11.368 
D)  0.178 
A)  64.125 
B)  5.63 
C)  11.368 
D)  0.178

Question 13

Choose the one alternative that best completes the statement or answers the question.
Determine whether the variation between the indicated quantities is direct or inverse.
-The distance traveled by you in a car and the time taken to drive this distance

Accepted Answer

A)  Inverse 
B)  Direct 
A)  Inverse 
B)  Direct

Suppose the triangles shown are similar, with angle $A=$ angle $D$ , angle $B=$ angle $E$ , and angle $C=$ angle $F$ . Answer the question. - What is the value of $x$ ?

Suppose the triangles shown are similar, with angle $A=$ angle $D$ , angle $B=$ angle $E$ , and angle $C=$ angle $F$ . Answer the question. - What is the value of $x$ ?

Perform the indicated operation and express in lowest terms. - $\frac{z^{2}+9 z+18}{z^{2}+14 z+48} \div \frac{z^{2}+3 z}{z^{2}+2 z-48}$

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - $f(x)=\frac{15 x^{2}-2 x+1}{225 x^{2}-169}$

Find all numbers not in the domain of the function - $f(x)=\frac{8}{x-3}$

Write the expression in lowest terms. - $\frac{\mathrm{a}^{2}-25}{\mathrm{a}^{2}+7 \mathrm{a}+10}$

The speed of a vehicle varies inversely as the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at 40 miles per hour in 45 minutes, how fast must it travel to cover the same distance in 20 minutes?

Perform the indicated operation and express in lowest terms. - $\frac{\mathrm{k}^{2}+12 \mathrm{k}+27}{\mathrm{k}^{2}+18 \mathrm{k}+81} \cdot \frac{\mathrm{k}^{2}+9 \mathrm{k}}{\mathrm{k}^{2}+8 \mathrm{k}+15}$

State whether the following situation represents direct variation, inverse variation, or neither, and explain why: A runner's speed in a race and the time that it takes to run the race.

A boat goes 270 miles downstream in the same time it can go 240 miles upstream. The speed of the current is 8 miles per hour. Find the speed of the boat in still water.

Perform the indicated operation and express in lowest terms. - $\frac{3}{15 x}+\frac{5}{15 x}$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. Round your answer, as needed. -A formula for electric circuits is $\frac{1}{a}=\frac{1}{b}+\frac{1}{c}$ . If $c=19$ and $b=8$ , find $a$ .

Choose the one alternative that best completes the statement or answers the question. Determine whether the variation between the indicated quantities is direct or inverse. -The distance traveled by you in a car and the time taken to drive this distance

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 7: Rational Expressions and Functions

Suppose the triangles shown are similar, with angle A=A=A= angle DDD , angle B=B=B= angle EEE , and angle C=C=C= angle FFF . Answer the question. - What is the value of xxx ?

Suppose the triangles shown are similar, with angle A=A=A= angle DDD , angle B=B=B= angle EEE , and angle C=C=C= angle FFF . Answer the question. - What is the value of xxx ?

Perform the indicated operation and express in lowest terms. - z2+9z+18z2+14z+48÷z2+3zz2+2z−48\frac{z^{2}+9 z+18}{z^{2}+14 z+48} \div \frac{z^{2}+3 z}{z^{2}+2 z-48}z2+14z+48z2+9z+18​÷z2+2z−48z2+3z​

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - f(x)=15x2−2x+1225x2−169f(x)=\frac{15 x^{2}-2 x+1}{225 x^{2}-169}f(x)=225x2−16915x2−2x+1​

Find all numbers not in the domain of the function - f(x)=8x−3f(x)=\frac{8}{x-3}f(x)=x−38​

Write the expression in lowest terms. - a2−25a2+7a+10\frac{\mathrm{a}^{2}-25}{\mathrm{a}^{2}+7 \mathrm{a}+10}a2+7a+10a2−25​

The speed of a vehicle varies inversely as the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at 40 miles per hour in 45 minutes, how fast must it travel to cover the same distance in 20 minutes?

Perform the indicated operation and express in lowest terms. - k2+12k+27k2+18k+81⋅k2+9kk2+8k+15\frac{\mathrm{k}^{2}+12 \mathrm{k}+27}{\mathrm{k}^{2}+18 \mathrm{k}+81} \cdot \frac{\mathrm{k}^{2}+9 \mathrm{k}}{\mathrm{k}^{2}+8 \mathrm{k}+15}k2+18k+81k2+12k+27​⋅k2+8k+15k2+9k​

State whether the following situation represents direct variation, inverse variation, or neither, and explain why: A runner's speed in a race and the time that it takes to run the race.

A boat goes 270 miles downstream in the same time it can go 240 miles upstream. The speed of the current is 8 miles per hour. Find the speed of the boat in still water.

Perform the indicated operation and express in lowest terms. - 315x+515x\frac{3}{15 x}+\frac{5}{15 x}15x3​+15x5​

Choose the one alternative that best completes the statement or answers the question. Solve the problem. Round your answer, as needed. -A formula for electric circuits is 1a=1b+1c\frac{1}{a}=\frac{1}{b}+\frac{1}{c}a1​=b1​+c1​ . If c=19c=19c=19 and b=8b=8b=8 , find aaa .

Choose the one alternative that best completes the statement or answers the question. Determine whether the variation between the indicated quantities is direct or inverse. -The distance traveled by you in a car and the time taken to drive this distance

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Suppose the triangles shown are similar, with angle $A=$ angle $D$ , angle $B=$ angle $E$ , and angle $C=$ angle $F$ . Answer the question. - What is the value of $x$ ?

Suppose the triangles shown are similar, with angle $A=$ angle $D$ , angle $B=$ angle $E$ , and angle $C=$ angle $F$ . Answer the question. - What is the value of $x$ ?

Perform the indicated operation and express in lowest terms. - $\frac{z^{2}+9 z+18}{z^{2}+14 z+48} \div \frac{z^{2}+3 z}{z^{2}+2 z-48}$

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - $f(x)=\frac{15 x^{2}-2 x+1}{225 x^{2}-169}$

Find all numbers not in the domain of the function - $f(x)=\frac{8}{x-3}$

Write the expression in lowest terms. - $\frac{\mathrm{a}^{2}-25}{\mathrm{a}^{2}+7 \mathrm{a}+10}$

Perform the indicated operation and express in lowest terms. - $\frac{\mathrm{k}^{2}+12 \mathrm{k}+27}{\mathrm{k}^{2}+18 \mathrm{k}+81} \cdot \frac{\mathrm{k}^{2}+9 \mathrm{k}}{\mathrm{k}^{2}+8 \mathrm{k}+15}$

Perform the indicated operation and express in lowest terms. - $\frac{3}{15 x}+\frac{5}{15 x}$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. Round your answer, as needed. -A formula for electric circuits is $\frac{1}{a}=\frac{1}{b}+\frac{1}{c}$ . If $c=19$ and $b=8$ , find $a$ .