Question 1

Solve for the indicated variable.
-$A=\frac{h(B+b)}{2}$ for $b$

Accepted Answer

A)  $b=\frac{2 A+B h}{h}$ 
B)  $b=\frac{A-B h}{h}$ 
C)  $b=2 A-B h$ 
D)  $b=\frac{2 A-B h}{h}$ 
A)  $b=\frac{2 A+B h}{h}$ 
B)  $b=\frac{A-B h}{h}$ 
C)  $b=2 A-B h$ 
D)  $b=\frac{2 A-B h}{h}$ D

Question 2

Add or subtract as indicated. Write the answer in lowest terms.
-$\frac{2}{r}+\frac{3}{r-8}$

Accepted Answer

A)  $\frac{16 r-5}{r(8-r)}$ 
B)  $\frac{5 r-16}{r(8-r)}$ 
C)  $\frac{5 r-16}{r(r-8)}$ 
D)  $\frac{16 r-5}{r(r-8)}$ 
A)  $\frac{16 r-5}{r(8-r)}$ 
B)  $\frac{5 r-16}{r(8-r)}$ 
C)  $\frac{5 r-16}{r(r-8)}$ 
D)  $\frac{16 r-5}{r(r-8)}$ C

Question 3

Perform the indicated operation and express in lowest terms.
-$\frac{(x-2)(x+3)}{(x+8)(x-2)} \cdot \frac{(x-9)(x+8)}{(x+3)(x+5)}$

Accepted Answer

A)  $\frac{x+9}{x-5}$ 
B)  $\frac{x-9}{x+5}$ 
C)  $\frac{x+3}{x-2}$ 
D)  $-\frac{x-9}{x+5}$ 
A)  $\frac{x+9}{x-5}$ 
B)  $\frac{x-9}{x+5}$ 
C)  $\frac{x+3}{x-2}$ 
D)  $-\frac{x-9}{x+5}$ B

Question 4

Choose the one alternative that best completes the statement or answers the question.
Solve the problem. Round your answer, as needed.
-A gas law in chemistry says that $\frac{P V}{T}=\frac{p v}{t}$. If $T=300, t=390, V=8, P=80$, and $v=5$, find the value of $\mathrm{p}$.

Accepted Answer

A)  1152 
B)  0.427 
C)  16.64 
D)  166.4 
A)  1152 
B)  0.427 
C)  16.64 
D)  166.4

Question 5

Perform the indicated operation and express in lowest terms.
-$\frac{2 x+7}{x^{2}+4 x+3}-\frac{x+4}{x^{2}+4 x+3}$

Accepted Answer

A)  $\frac{1}{x+1}$ 
B)  $\frac{x+11}{x^{2}+4 x+3}$ 
C)  $x+3$ 
D)  $\frac{8}{x^{2}+4 x+3}$ 
A)  $\frac{1}{x+1}$ 
B)  $\frac{x+11}{x^{2}+4 x+3}$ 
C)  $x+3$ 
D)  $\frac{8}{x^{2}+4 x+3}$

Question 6

Find all numbers not in the domain of the function
-$f(x)=\frac{2}{x+9}$

Accepted Answer

A)  0 
B)  None 
C)  -9 
D)  9 
A)  0 
B)  None 
C)  -9 
D)  9

Question 7

Mary drives to work at 63 miles per hour before the morning rush hour, but returns home during the evening rush hour at only 33 miles per hour. Explain why 48 is not a valid solution to the problem "What was her average speed for the day's driving?"

Accepted Answer

Answers may vary. One possibility: This

Question 8

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 $a=17$ and $b=19$, find $c$.

Accepted Answer

A)  2.235 
B)  1.789 
C)  161.5 
D)  0.006 
A)  2.235 
B)  1.789 
C)  161.5 
D)  0.006

Question 9

Solve the formula for the specified variable.
-$\frac{1}{a}+\frac{1}{b}=\frac{1}{c}$ for $c$

Accepted Answer

A)  $c=a+b$ 
B)  $c=\frac{a+b}{a b}$ 
C)  $c=\frac{a b}{a+b}$ 
D)  $c=a b(a+b)$ 
A)  $c=a+b$ 
B)  $c=\frac{a+b}{a b}$ 
C)  $c=\frac{a b}{a+b}$ 
D)  $c=a b(a+b)$

Question 10

$\frac{10}{x-2}=1+\frac{12}{x+2}$

Accepted Answer

A)  $\{6,-8\}$ 
B)  $\{-12,8\}$ 
C)  $\{-6,8\}$ 
D)  $\varnothing$ 
A)  $\{6,-8\}$ 
B)  $\{-12,8\}$ 
C)  $\{-6,8\}$ 
D)  $\varnothing$

Question 11

Solve the formula for the specified variable.
-$V=\frac{1}{3} B h$ for $h$

Accepted Answer

A)  $h=\frac{B}{3 V}$ 
B)  $h=\frac{V}{3 B}$ 
C)  $h=\frac{3 B}{V}$ 
D)  $h=\frac{3 V}{B}$ 
A)  $h=\frac{B}{3 V}$ 
B)  $h=\frac{V}{3 B}$ 
C)  $h=\frac{3 B}{V}$ 
D)  $h=\frac{3 V}{B}$

Question 12

Graph the rational function. Give the equations of the vertical and horizontal asymptotes.
-$f(x)=-\frac{7}{x}$

Accepted Answer

A)  $x=0 ; y=-3$
  
B)  $x=0 ; y=0$
  
C)  $x=0 ; y=0$
  
D)  $x=-2 ; y=0$
  
A)  $x=0 ; y=-3$
  
B)  $x=0 ; y=0$
  
C)  $x=0 ; y=0$
  
D)  $x=-2 ; y=0$

Question 13

For the equation $\frac{t+3}{3}-\frac{t-5}{3}=\frac{1}{21}$, would any numbers have to be rejected if they appeared as potential solutions? Explain.

Accepted Answer

No. There are no var

Question 14

Choose the one alternative that best completes the statement or answers the question.
Solve the problem. Round your answer, as needed.
-A formula for the focal length of a lens is
$\mathrm{f}=\frac{\mathrm{ab}}{\mathrm{b}+\mathrm{a}}$
Calculate $\mathrm{f}$ (the focal length) for $\mathrm{a}=8 \mathrm{~cm}$ and $\mathrm{b}=15 \mathrm{~cm}$.

Accepted Answer

A)  $5.2 \mathrm{~cm}$ 
B)  $2.8 \mathrm{~cm}$ 
C)  $7.5 \mathrm{~cm}$ 
D)  $4.0 \mathrm{~cm}$ 
A)  $5.2 \mathrm{~cm}$ 
B)  $2.8 \mathrm{~cm}$ 
C)  $7.5 \mathrm{~cm}$ 
D)  $4.0 \mathrm{~cm}$

Question 15

Choose the one alternative that best completes the statement or answers the question.
Simplify the complex fraction
-$\frac{\frac{16 s^{2}-64 t^{2}}{s t}}{\frac{4}{t}-\frac{8}{s}}$

Accepted Answer

A)  $\frac{s t}{4 s+8 t}$ 
B)  $8 s+4 t$ 
C)  $4 s+8 t$ 
D)  $\frac{8 s+4 t}{s t}$ 
A)  $\frac{s t}{4 s+8 t}$ 
B)  $8 s+4 t$ 
C)  $4 s+8 t$ 
D)  $\frac{8 s+4 t}{s t}$

Question 16

Multiply or divide.
-$\frac{x^{2}-64}{x^{2}-14 x+49} \div \frac{7 x-56}{x^{2}-3 x-28}$

Accepted Answer

A)  $\frac{(x+8)(x+4)}{7(x-7)}$ 
B)  $\frac{(x+8)(x+4)}{x-7}$ 
C)  $\frac{(x-8)(x-4)}{7(x+7)}$ 
D)  $\frac{x-7}{(x+8)(x+4)}$ 
A)  $\frac{(x+8)(x+4)}{7(x-7)}$ 
B)  $\frac{(x+8)(x+4)}{x-7}$ 
C)  $\frac{(x-8)(x-4)}{7(x+7)}$ 
D)  $\frac{x-7}{(x+8)(x+4)}$

Question 17

Choose the one alternative that best completes the statement or answers the question.
Simplify the complex fraction
-$\frac{\frac{9}{y}}{\frac{6}{y-8}}$

Accepted Answer

A)  $\frac{y-8}{54 y}$ 
B)  $54 y(y-8)$ 
C)  $\frac{3(y-8)}{2 y}$ 
D)  $\frac{2 y}{3(y-8)}$ 
A)  $\frac{y-8}{54 y}$ 
B)  $54 y(y-8)$ 
C)  $\frac{3(y-8)}{2 y}$ 
D)  $\frac{2 y}{3(y-8)}$

Question 18

Solve the problem. Round your answer, as needed.
-Sven can type 33 words per minute. How many words would he type in $\frac{2}{3}$ hour (40 minutes)?

Accepted Answer

A)  880 words 
B)  1320 words 
C)  22 words 
D)  50 words 
A)  880 words 
B)  1320 words 
C)  22 words 
D)  50 words

Question 19

Give the first step in solving the given equation for $x$.
$x y-z=x z+y$

Accepted Answer

The first step is to subtract

Question 20

Choose the one alternative that best completes the statement or answers the question.
-The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 58 miles per hour?

Accepted Answer

A)  $247.78 \mathrm{ft}$ 
B)  $235.48 \mathrm{ft}$ 
C)  $201.84 \mathrm{ft}$ 
D)  $235.82 \mathrm{ft}$ 
A)  $247.78 \mathrm{ft}$ 
B)  $235.48 \mathrm{ft}$ 
C)  $201.84 \mathrm{ft}$ 
D)  $235.82 \mathrm{ft}$

Solve for the indicated variable. - $A=\frac{h(B+b)}{2}$ for $b$

Add or subtract as indicated. Write the answer in lowest terms. - $\frac{2}{r}+\frac{3}{r-8}$

Perform the indicated operation and express in lowest terms. - $\frac{(x-2)(x+3)}{(x+8)(x-2)} \cdot \frac{(x-9)(x+8)}{(x+3)(x+5)}$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. Round your answer, as needed. -A gas law in chemistry says that $\frac{P V}{T}=\frac{p v}{t}$ . If $T=300, t=390, V=8, P=80$ , and $v=5$ , find the value of $\mathrm{p}$ .

Perform the indicated operation and express in lowest terms. - $\frac{2 x+7}{x^{2}+4 x+3}-\frac{x+4}{x^{2}+4 x+3}$

Find all numbers not in the domain of the function - $f(x)=\frac{2}{x+9}$

Mary drives to work at 63 miles per hour before the morning rush hour, but returns home during the evening rush hour at only 33 miles per hour. Explain why 48 is not a valid solution to the problem "What was her average speed for the day's driving?"

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 $a=17$ and $b=19$ , find $c$ .

Solve the formula for the specified variable. - $\frac{1}{a}+\frac{1}{b}=\frac{1}{c}$ for $c$

$\frac{10}{x-2}=1+\frac{12}{x+2}$

Solve the formula for the specified variable. - $V=\frac{1}{3} B h$ for $h$

Graph the rational function. Give the equations of the vertical and horizontal asymptotes. - $f(x)=-\frac{7}{x}$ $Graph the rational function. Give the equations of the vertical and horizontal asymptotes. - f(x)=-\frac{7}{x}$

For the equation $\frac{t+3}{3}-\frac{t-5}{3}=\frac{1}{21}$ , would any numbers have to be rejected if they appeared as potential solutions? Explain.

Choose the one alternative that best completes the statement or answers the question. Simplify the complex fraction - $\frac{\frac{16 s^{2}-64 t^{2}}{s t}}{\frac{4}{t}-\frac{8}{s}}$

Multiply or divide. - $\frac{x^{2}-64}{x^{2}-14 x+49} \div \frac{7 x-56}{x^{2}-3 x-28}$

Choose the one alternative that best completes the statement or answers the question. Simplify the complex fraction - $\frac{\frac{9}{y}}{\frac{6}{y-8}}$

Solve the problem. Round your answer, as needed. -Sven can type 33 words per minute. How many words would he type in $\frac{2}{3}$ hour (40 minutes)?

Give the first step in solving the given equation for $x$ . $x y-z=x z+y$

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

Solve for the indicated variable. - A=h(B+b)2A=\frac{h(B+b)}{2}A=2h(B+b)​ for bbb

Add or subtract as indicated. Write the answer in lowest terms. - 2r+3r−8\frac{2}{r}+\frac{3}{r-8}r2​+r−83​

Perform the indicated operation and express in lowest terms. - (x−2)(x+3)(x+8)(x−2)⋅(x−9)(x+8)(x+3)(x+5)\frac{(x-2)(x+3)}{(x+8)(x-2)} \cdot \frac{(x-9)(x+8)}{(x+3)(x+5)}(x+8)(x−2)(x−2)(x+3)​⋅(x+3)(x+5)(x−9)(x+8)​

Perform the indicated operation and express in lowest terms. - 2x+7x2+4x+3−x+4x2+4x+3\frac{2 x+7}{x^{2}+4 x+3}-\frac{x+4}{x^{2}+4 x+3}x2+4x+32x+7​−x2+4x+3x+4​

Find all numbers not in the domain of the function - f(x)=2x+9f(x)=\frac{2}{x+9}f(x)=x+92​

Mary drives to work at 63 miles per hour before the morning rush hour, but returns home during the evening rush hour at only 33 miles per hour. Explain why 48 is not a valid solution to the problem "What was her average speed for the day's driving?"

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 a=17a=17a=17 and b=19b=19b=19 , find ccc .

Solve the formula for the specified variable. - 1a+1b=1c\frac{1}{a}+\frac{1}{b}=\frac{1}{c}a1​+b1​=c1​ for ccc

10x−2=1+12x+2\frac{10}{x-2}=1+\frac{12}{x+2}x−210​=1+x+212​

Solve the formula for the specified variable. - V=13BhV=\frac{1}{3} B hV=31​Bh for hhh

Graph the rational function. Give the equations of the vertical and horizontal asymptotes. - f(x)=−7xf(x)=-\frac{7}{x}f(x)=−x7​

For the equation t+33−t−53=121\frac{t+3}{3}-\frac{t-5}{3}=\frac{1}{21}3t+3​−3t−5​=211​ , would any numbers have to be rejected if they appeared as potential solutions? Explain.

Choose the one alternative that best completes the statement or answers the question. Simplify the complex fraction - 16s2−64t2st4t−8s\frac{\frac{16 s^{2}-64 t^{2}}{s t}}{\frac{4}{t}-\frac{8}{s}}t4​−s8​st16s2−64t2​​

Multiply or divide. - x2−64x2−14x+49÷7x−56x2−3x−28\frac{x^{2}-64}{x^{2}-14 x+49} \div \frac{7 x-56}{x^{2}-3 x-28}x2−14x+49x2−64​÷x2−3x−287x−56​

Choose the one alternative that best completes the statement or answers the question. Simplify the complex fraction - 9y6y−8\frac{\frac{9}{y}}{\frac{6}{y-8}}y−86​y9​​

Solve the problem. Round your answer, as needed. -Sven can type 33 words per minute. How many words would he type in 23\frac{2}{3}32​ hour (40 minutes)?

Give the first step in solving the given equation for xxx . xy−z=xz+yx y-z=x z+yxy−z=xz+y

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

Solve for the indicated variable. - $A=\frac{h(B+b)}{2}$ for $b$

Add or subtract as indicated. Write the answer in lowest terms. - $\frac{2}{r}+\frac{3}{r-8}$

Perform the indicated operation and express in lowest terms. - $\frac{(x-2)(x+3)}{(x+8)(x-2)} \cdot \frac{(x-9)(x+8)}{(x+3)(x+5)}$

Perform the indicated operation and express in lowest terms. - $\frac{2 x+7}{x^{2}+4 x+3}-\frac{x+4}{x^{2}+4 x+3}$

Find all numbers not in the domain of the function - $f(x)=\frac{2}{x+9}$

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 $a=17$ and $b=19$ , find $c$ .

Solve the formula for the specified variable. - $\frac{1}{a}+\frac{1}{b}=\frac{1}{c}$ for $c$

$\frac{10}{x-2}=1+\frac{12}{x+2}$

Solve the formula for the specified variable. - $V=\frac{1}{3} B h$ for $h$

Graph the rational function. Give the equations of the vertical and horizontal asymptotes. - $f(x)=-\frac{7}{x}$ $Graph the rational function. Give the equations of the vertical and horizontal asymptotes. - f(x)=-\frac{7}{x}$

For the equation $\frac{t+3}{3}-\frac{t-5}{3}=\frac{1}{21}$ , would any numbers have to be rejected if they appeared as potential solutions? Explain.

Choose the one alternative that best completes the statement or answers the question. Simplify the complex fraction - $\frac{\frac{16 s^{2}-64 t^{2}}{s t}}{\frac{4}{t}-\frac{8}{s}}$

Multiply or divide. - $\frac{x^{2}-64}{x^{2}-14 x+49} \div \frac{7 x-56}{x^{2}-3 x-28}$

Choose the one alternative that best completes the statement or answers the question. Simplify the complex fraction - $\frac{\frac{9}{y}}{\frac{6}{y-8}}$

Solve the problem. Round your answer, as needed. -Sven can type 33 words per minute. How many words would he type in $\frac{2}{3}$ hour (40 minutes)?

Give the first step in solving the given equation for $x$ . $x y-z=x z+y$