Question 1

Solve the formula for the specified variable.
-$P=\frac{A}{1+r t}$ for $r$

Accepted Answer

A)  $r=\frac{P-A}{1+t}$ 
B)  $r=\frac{P-1}{A t}$ 
C)  $r=\frac{A-P}{P t}$ 
D)  $\mathrm{r}=\mathrm{P}-\mathrm{tA}$ 
A)  $r=\frac{P-A}{1+t}$ 
B)  $r=\frac{P-1}{A t}$ 
C)  $r=\frac{A-P}{P t}$ 
D)  $\mathrm{r}=\mathrm{P}-\mathrm{tA}$

Question 2

Solve the formula for the specified variable.
-$S=2 \pi r h+2 \pi r^{2}$ for $h$

Accepted Answer

A)  $h=\frac{S-2 \pi r^{2}}{2 \pi r}$ 
B)  $h=2 \pi(S-r)$ 
C)  $h=h S-r$ 
D)  $h=\frac{S}{2 \pi r}-1$ 
A)  $h=\frac{S-2 \pi r^{2}}{2 \pi r}$ 
B)  $h=2 \pi(S-r)$ 
C)  $h=h S-r$ 
D)  $h=\frac{S}{2 \pi r}-1$

Question 3

Suppose the velocity of an automobile starting from rest is given by
$$\mathrm{v}=\frac{200 \mathrm{t}}{2 \mathrm{t}+10}$$
Where $v$ is the velocity in miles per hour and $t$ is the time in seconds. Find the number of seconds when the velocity is 50 miles per hour.

Accepted Answer

A)  $6 \mathrm{sec}$ 
B)  $5 \mathrm{sec}$ 
C)  $7 \mathrm{sec}$ 
D)  $2.5 \mathrm{sec}$ 
A)  $6 \mathrm{sec}$ 
B)  $5 \mathrm{sec}$ 
C)  $7 \mathrm{sec}$ 
D)  $2.5 \mathrm{sec}$

Question 4

Express the rational expression in lowest terms.
-$\frac{y^{2}-2 y-15}{y^{2}+12 y+27}$

Accepted Answer

A)  $\frac{-2 y+15}{12 y-12}$ 
B)  $-\frac{y^{2}-2 y-15}{y^{2}+12 y+27}$ 
C)  $\frac{-2 y-15}{12 y+27}$ 
D)  $\frac{y-5}{y+9}$ 
A)  $\frac{-2 y+15}{12 y-12}$ 
B)  $-\frac{y^{2}-2 y-15}{y^{2}+12 y+27}$ 
C)  $\frac{-2 y-15}{12 y+27}$ 
D)  $\frac{y-5}{y+9}$

Question 5

Choose the one alternative that best completes the statement or answers the question.
Simplify the complex fraction
-$\frac{\frac{1}{a}+1}{\frac{1}{a}-1}$

Accepted Answer

A)  $\frac{1+a}{1-a}$ 
B)  $\frac{a}{1-a^{2}}$ 
C)  $1-\mathrm{a}^{2}$ 
D)  1 
A)  $\frac{1+a}{1-a}$ 
B)  $\frac{a}{1-a^{2}}$ 
C)  $1-\mathrm{a}^{2}$ 
D)  1

Question 6

Consider an equation of direct variation $y=k x$. When $x$ increases, does $y$ increase or decrease?

Accepted Answer

The answer of Consider an equation of direct variation \(y=k...

Question 7

Tell whether or not the rational expressions are equivalent.
-$\frac{a c+a d-b c-b d}{a b+a c-b^{2}-b c}, \frac{c+d}{b+c}$

Accepted Answer

A) True 
 B)False

Question 8

Find the requested expression for the function.
-A cost-benefit model expresses the cost of an undertaking in terms of the benefits received. One cost-benefit model gives the cost in thousands of dollars to clean up $x$ percent of an oil spill as $c(x)=\frac{7.5 x}{50-x}$. Another model produces the relationship $c(x)=\frac{7.2 x}{52-x}$. Find the cost function found by averaging the two models. Simplify the expression for this function by performing the indicated operations.

Accepted Answer

A)  $c(x)=\frac{750 x-14.7 x^{2}}{2(50-x)(52-x)}$ 
B)  $c(x)=\frac{750 x-14.7 x^{2}}{(50-x)(52-x)}$ 
C)  $c(x)=\frac{735.6 x-15.7 x^{2}}{(50-x)(52-x)}$ 
D)  $c(x)=\frac{1500 x-29.4 x^{2}}{(50-x)(52-x)}$ 
A)  $c(x)=\frac{750 x-14.7 x^{2}}{2(50-x)(52-x)}$ 
B)  $c(x)=\frac{750 x-14.7 x^{2}}{(50-x)(52-x)}$ 
C)  $c(x)=\frac{735.6 x-15.7 x^{2}}{(50-x)(52-x)}$ 
D)  $c(x)=\frac{1500 x-29.4 x^{2}}{(50-x)(52-x)}$

Question 9

Use the example to give a step-by-step explanation of the method to add or subtract two fractions with different denominators.
$$\frac{1}{y^{2}-12 y+32}+\frac{1}{y^{2}-4 y}$$

Accepted Answer

Answers will vary. One possibility: Find

Question 10

Choose the one alternative that best completes the statement or answers the question.
Simplify the complex fraction
-$\frac{\frac{x}{5}}{\frac{9}{x+7}}$

Accepted Answer

A)  $\frac{x+7}{45 x}$ 
B)  $\frac{9 x}{5(x+7)}$ 
C)  $45 x(x+7)$ 
D)  $\frac{x(x+7)}{45}$ 
A)  $\frac{x+7}{45 x}$ 
B)  $\frac{9 x}{5(x+7)}$ 
C)  $45 x(x+7)$ 
D)  $\frac{x(x+7)}{45}$

Question 11

Add or subtract as indicated. Write the answer in lowest terms.
-$\frac{5}{x+2}+\frac{2}{x^{2}-2 x+4}-\frac{60}{x^{3}+8}$

Accepted Answer

A)  $\frac{5 x-18}{x^{2}-2 x+4}$ 
B)  $-\frac{1}{x^{2}-4}$ 
C)  $\frac{7 x-20}{x+2}$ 
D)  $\frac{5 x-18}{x^{3}-8}$ 
A)  $\frac{5 x-18}{x^{2}-2 x+4}$ 
B)  $-\frac{1}{x^{2}-4}$ 
C)  $\frac{7 x-20}{x+2}$ 
D)  $\frac{5 x-18}{x^{3}-8}$

Question 12

Choose the one alternative that best completes the statement or answers the question.
-If $s$ varies directly as $t^{2}$, and $s=45$ when $t=3$, find $s$ when $t$ is 7 .

Accepted Answer

A)  245 
B)  105 
C)  15 
D)  21 
A)  245 
B)  105 
C)  15 
D)  21

Question 13

Choose the one alternative that best completes the statement or answers the question.
-The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container $5 \mathrm{~cm}$ on a side is $250 \mathrm{~g}$, find the weight of the liquid in a cubical container $3 \mathrm{~cm}$ on a side.

Accepted Answer

A)  $6 \mathrm{~g}$ 
B)  $27 \mathrm{~g}$ 
C)  $12 \mathrm{~g}$ 
D)  $54 \mathrm{~g}$ 
A)  $6 \mathrm{~g}$ 
B)  $27 \mathrm{~g}$ 
C)  $12 \mathrm{~g}$ 
D)  $54 \mathrm{~g}$

Question 14

Determine whether the equation represents direct, inverse, joint, or combined variation.
-$y=\frac{2 x}{s t}$

Accepted Answer

A)  Inverse 
B)  Joint 
C)  Combined 
D)  Direct 
A)  Inverse 
B)  Joint 
C)  Combined 
D)  Direct

Question 15

Choose the equivalent form of the given formula for area of a regular polygon.
$$\mathrm{A}=\frac{1}{2} \mathrm{nsa}$$

Accepted Answer

A)  $\mathrm{s}=\frac{2 \mathrm{n}}{\mathrm{aA}}$ 
B)  $\mathrm{s}=\frac{\mathrm{nA}}{2 \mathrm{a}}$ 
C)  $a=\frac{2 \mathrm{~A}}{\mathrm{~ns}}$ 
D)  $\mathrm{a}=\frac{\mathrm{ns}}{2 \mathrm{~A}}$ 
A)  $\mathrm{s}=\frac{2 \mathrm{n}}{\mathrm{aA}}$ 
B)  $\mathrm{s}=\frac{\mathrm{nA}}{2 \mathrm{a}}$ 
C)  $a=\frac{2 \mathrm{~A}}{\mathrm{~ns}}$ 
D)  $\mathrm{a}=\frac{\mathrm{ns}}{2 \mathrm{~A}}$

Question 16

Find the least common denominator for the group of denominators.
-$2 a+14, a^{2}+7 a$

Accepted Answer

A)  $2 a^{2}+7$ 
B)  $2 \mathrm{a}+7$ 
C)  $2 a(a+7)$ 
D)  $2 a^{2}+14$ 
A)  $2 a^{2}+7$ 
B)  $2 \mathrm{a}+7$ 
C)  $2 a(a+7)$ 
D)  $2 a^{2}+14$

Question 17

Find all numbers that are not in the domain of the function. Then give the domain using set notation.
-$f(x)=\frac{4}{x-2}$

Accepted Answer

A)  $2 ;\{x \mid x \neq 2\}$ 
B)  $-2,2 ;\{x \mid x \neq-2,2\}$ 
C)  $-4 ;\{x \mid x \neq-4\}$ 
D)  none; $(\infty, \infty)$ 
A)  $2 ;\{x \mid x \neq 2\}$ 
B)  $-2,2 ;\{x \mid x \neq-2,2\}$ 
C)  $-4 ;\{x \mid x \neq-4\}$ 
D)  none; $(\infty, \infty)$

Question 18

Wind resistance or atmospheric drag tends to slow down moving objects. Atmospheric drag varies jointly as an object's surface area A and velocity $\mathrm{v}$. If a car traveling at a speed of $60 \mathrm{mph}$ with a surface area of $31 \mathrm{ft}^{2}$ experiences a drag of $316.2 \mathrm{~N}$ (Newtons), how fast must a car with $36 \mathrm{ft}^{2}$ of surface area travel in order to experience a drag force of $330.48 \mathrm{~N}$ ?

Accepted Answer

A)  $51 \mathrm{mph}$ 
B)  $54 \mathrm{mph}$ 
C)  $56 \mathrm{mph}$ 
D)  $59 \mathrm{mph}$ 
A)  $51 \mathrm{mph}$ 
B)  $54 \mathrm{mph}$ 
C)  $56 \mathrm{mph}$ 
D)  $59 \mathrm{mph}$

Question 19

A plane flies 420 miles with the wind and 340 miles against the wind in the same length of time. If the speed of the wind is $22 \mathrm{mph}$, what is the speed of the plane in still air?

Accepted Answer

A)  $199 \mathrm{mph}$ 
B)  $209 \mathrm{mph}$ 
C)  $214 \mathrm{mph}$ 
D)  $234 \mathrm{mph}$ 
A)  $199 \mathrm{mph}$ 
B)  $209 \mathrm{mph}$ 
C)  $214 \mathrm{mph}$ 
D)  $234 \mathrm{mph}$

Question 20

Determine whether the equation represents direct, inverse, joint, or combined variation.
-$y=3 x^{3} z^{4}$

Accepted Answer

A)  Combined 
B)  Joint 
C)  Inverse 
D)  Direct 
A)  Combined 
B)  Joint 
C)  Inverse 
D)  Direct

Solve the formula for the specified variable. - $P=\frac{A}{1+r t}$ for $r$

Solve the formula for the specified variable. - $S=2 \pi r h+2 \pi r^{2}$ for $h$

Suppose the velocity of an automobile starting from rest is given by $\mathrm{v}=\frac{200 \mathrm{t}}{2 \mathrm{t}+10}$ Where $v$ is the velocity in miles per hour and $t$ is the time in seconds. Find the number of seconds when the velocity is 50 miles per hour.

Express the rational expression in lowest terms. - $\frac{y^{2}-2 y-15}{y^{2}+12 y+27}$

Choose the one alternative that best completes the statement or answers the question. Simplify the complex fraction - $\frac{\frac{1}{a}+1}{\frac{1}{a}-1}$

Consider an equation of direct variation $y=k x$ . When $x$ increases, does $y$ increase or decrease?

Tell whether or not the rational expressions are equivalent. - $\frac{a c+a d-b c-b d}{a b+a c-b^{2}-b c}, \frac{c+d}{b+c}$

Use the example to give a step-by-step explanation of the method to add or subtract two fractions with different denominators. $\frac{1}{y^{2}-12 y+32}+\frac{1}{y^{2}-4 y}$

Choose the one alternative that best completes the statement or answers the question. Simplify the complex fraction - $\frac{\frac{x}{5}}{\frac{9}{x+7}}$

Add or subtract as indicated. Write the answer in lowest terms. - $\frac{5}{x+2}+\frac{2}{x^{2}-2 x+4}-\frac{60}{x^{3}+8}$

Choose the one alternative that best completes the statement or answers the question. -If $s$ varies directly as $t^{2}$ , and $s=45$ when $t=3$ , find $s$ when $t$ is 7 .

Determine whether the equation represents direct, inverse, joint, or combined variation. - $y=\frac{2 x}{s t}$

Choose the equivalent form of the given formula for area of a regular polygon. $\mathrm{A}=\frac{1}{2} \mathrm{nsa}$

Find the least common denominator for the group of denominators. - $2 a+14, a^{2}+7 a$

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - $f(x)=\frac{4}{x-2}$

A plane flies 420 miles with the wind and 340 miles against the wind in the same length of time. If the speed of the wind is $22 \mathrm{mph}$ , what is the speed of the plane in still air?

Determine whether the equation represents direct, inverse, joint, or combined variation. - $y=3 x^{3} z^{4}$

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 the formula for the specified variable. - P=A1+rtP=\frac{A}{1+r t}P=1+rtA​ for rrr

Solve the formula for the specified variable. - S=2πrh+2πr2S=2 \pi r h+2 \pi r^{2}S=2πrh+2πr2 for hhh

Suppose the velocity of an automobile starting from rest is given by v=200t2t+10\mathrm{v}=\frac{200 \mathrm{t}}{2 \mathrm{t}+10}v=2t+10200t​ Where vvv is the velocity in miles per hour and ttt is the time in seconds. Find the number of seconds when the velocity is 50 miles per hour.

Express the rational expression in lowest terms. - y2−2y−15y2+12y+27\frac{y^{2}-2 y-15}{y^{2}+12 y+27}y2+12y+27y2−2y−15​

Choose the one alternative that best completes the statement or answers the question. Simplify the complex fraction - 1a+11a−1\frac{\frac{1}{a}+1}{\frac{1}{a}-1}a1​−1a1​+1​

Consider an equation of direct variation y=kxy=k xy=kx . When xxx increases, does yyy increase or decrease?

Tell whether or not the rational expressions are equivalent. - ac+ad−bc−bdab+ac−b2−bc,c+db+c\frac{a c+a d-b c-b d}{a b+a c-b^{2}-b c}, \frac{c+d}{b+c}ab+ac−b2−bcac+ad−bc−bd​,b+cc+d​

Use the example to give a step-by-step explanation of the method to add or subtract two fractions with different denominators. 1y2−12y+32+1y2−4y\frac{1}{y^{2}-12 y+32}+\frac{1}{y^{2}-4 y}y2−12y+321​+y2−4y1​

Choose the one alternative that best completes the statement or answers the question. Simplify the complex fraction - x59x+7\frac{\frac{x}{5}}{\frac{9}{x+7}}x+79​5x​​

Add or subtract as indicated. Write the answer in lowest terms. - 5x+2+2x2−2x+4−60x3+8\frac{5}{x+2}+\frac{2}{x^{2}-2 x+4}-\frac{60}{x^{3}+8}x+25​+x2−2x+42​−x3+860​

Choose the one alternative that best completes the statement or answers the question. -If sss varies directly as t2t^{2}t2 , and s=45s=45s=45 when t=3t=3t=3 , find sss when ttt is 7 .

Determine whether the equation represents direct, inverse, joint, or combined variation. - y=2xsty=\frac{2 x}{s t}y=st2x​

Choose the equivalent form of the given formula for area of a regular polygon. A=12nsa\mathrm{A}=\frac{1}{2} \mathrm{nsa}A=21​nsa

Find the least common denominator for the group of denominators. - 2a+14,a2+7a2 a+14, a^{2}+7 a2a+14,a2+7a

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - f(x)=4x−2f(x)=\frac{4}{x-2}f(x)=x−24​

A plane flies 420 miles with the wind and 340 miles against the wind in the same length of time. If the speed of the wind is 22mph22 \mathrm{mph}22mph , what is the speed of the plane in still air?

Determine whether the equation represents direct, inverse, joint, or combined variation. - y=3x3z4y=3 x^{3} z^{4}y=3x3z4