Question 1

Assume that the expressions given are denominators of fractions. Find the least common denominator.
-$t, t+7$

Accepted Answer

A)  $\mathrm{t}(\mathrm{t}+7)$ 
B)  -7 
C)  $t+7$ 
D)  7 
A)  $\mathrm{t}(\mathrm{t}+7)$ 
B)  -7 
C)  $t+7$ 
D)  7

Question 2

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 balance on your credit card and the amount of available credit

Accepted Answer

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

Question 3

Perform the indicated operation and express in lowest terms.
-$\frac{2 k^{2}+15 k p+18 p^{2}}{9 k^{2}-18 k p+8 p^{2}} \div \frac{6 k^{2}+17 k p+12 p^{2}}{9 k^{2}-16 p^{2}}$

Accepted Answer

A)  $\frac{k+p}{3 k+2 p}$ 
B)  $\frac{k+6 p}{3 k-2 p}$ 
C)  $\frac{k+7 p}{2 k-3 p}$ 
D)  -1 
A)  $\frac{k+p}{3 k+2 p}$ 
B)  $\frac{k+6 p}{3 k-2 p}$ 
C)  $\frac{k+7 p}{2 k-3 p}$ 
D)  -1

Question 4

Find all numbers that are not in the domain of the function. Then give the domain using set notation.
-$f(x)=\frac{x-9}{x^{2}+9}$

Accepted Answer

A)  none; $(-\infty, \infty)$ 
B)  $-9,9 ;\{x \mid x \neq-9,9\}$ 
C)  $9 ;\{x \mid x \neq 9\}$ 
D)  $-9 ;\{x \mid x \neq-9\}$ 
A)  none; $(-\infty, \infty)$ 
B)  $-9,9 ;\{x \mid x \neq-9,9\}$ 
C)  $9 ;\{x \mid x \neq 9\}$ 
D)  $-9 ;\{x \mid x \neq-9\}$

Question 5

$\frac{2 y+3}{y}=\frac{3}{2}$

Accepted Answer

A)  $\{0\}$ 
B)  $\{3\}$ 
C)  $\{-6\}$ 
D)  $\{6\}$ 
A)  $\{0\}$ 
B)  $\{3\}$ 
C)  $\{-6\}$ 
D)  $\{6\}$

Question 6

Perform the indicated operation and express in lowest terms.
-$\frac{8 p-8}{p} \cdot \frac{7 p^{2}}{9 p-9}$

Accepted Answer

A)  $\frac{9}{56 p}$ 
B)  $\frac{56 p^{3}-56 p^{2}}{9 p^{2}-9 p}$ 
C)  $\frac{56 p}{9}$ 
D)  $\frac{72 p^{2}+144 p+72}{7 p^{3}}$ 
A)  $\frac{9}{56 p}$ 
B)  $\frac{56 p^{3}-56 p^{2}}{9 p^{2}-9 p}$ 
C)  $\frac{56 p}{9}$ 
D)  $\frac{72 p^{2}+144 p+72}{7 p^{3}}$

Question 7

Choose the one alternative that best completes the statement or answers the question.
-If $\mathrm{f}$ varies jointly as $\mathrm{q}^{2}$ and $\mathrm{h}$, and $\mathrm{f}=64$ when $\mathrm{q}=4$ and $\mathrm{h}=2$, find $\mathrm{q}$ when $\mathrm{f}=90$ and $\mathrm{h}=5$.

Accepted Answer

A)  4 
B)  3 
C)  2 
D)  5 
A)  4 
B)  3 
C)  2 
D)  5

Question 8

To determine the number of fish in a lake, a park ranger catches 240 fish, tags them, and returns them to the lake. Later, 144 fish are caught, and it is found that 24 of them are tagged. Estimate the number of fish in the lake.

Accepted Answer

A)  1440 
B)  14 
C)  40 
D)  829,440 
A)  1440 
B)  14 
C)  40 
D)  829,440

Question 9

Choose the one alternative that best completes the statement or answers the question.
-If $\mathrm{f}$ varies jointly as $\mathrm{q}^{2}$ and $\mathrm{h}$, and $\mathrm{f}=-54$ when $\mathrm{q}=3$ and $\mathrm{h}=3$, find $\mathrm{f}$ when $\mathrm{q}=4$ and $\mathrm{h}=2$.

Accepted Answer

A)  -32 
B)  -4 
C)  -64 
D)  -16 
A)  -32 
B)  -4 
C)  -64 
D)  -16

Question 10

Graph the rational function. Give the equations of the vertical and horizontal asymptotes.
-$f(x)=\frac{3}{x}$

Accepted Answer

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

Question 11

Choose the one alternative that best completes the statement or answers the question.
Without actually solving the equation, list all possible numbers that would have to be rejected if they appeared as
potential solutions.
-$\frac{4 x+1}{x+7}=\frac{18 x+11}{16 x+7}$

Accepted Answer

A)  $-7, \frac{7}{16}$ 
B)  $0,-7,-\frac{7}{16}$ 
C)  $-7,-\frac{7}{16}$ 
D)  There are no numbers that would have to be rejected. 
A)  $-7, \frac{7}{16}$ 
B)  $0,-7,-\frac{7}{16}$ 
C)  $-7,-\frac{7}{16}$ 
D)  There are no numbers that would have to be rejected.

Question 12

Find all numbers that are not in the domain of the function. Then give the domain using set notation.
-$f(x)=\frac{2 x+18}{3 x^{2}-6 x-9}$

Accepted Answer

A)  $-3,1 ;\{x \mid x \neq-3,1\}$ 
B)  $\frac{1}{3},-1 ;\left\{x \mid x \neq \frac{1}{3},-1\right\}$ 
C)  $-9,-1,3 ;\{x \mid x \neq-9,-1,3\}$ 
D)  $3,-1 ;\{x \mid x \neq 3,-1\}$ 
A)  $-3,1 ;\{x \mid x \neq-3,1\}$ 
B)  $\frac{1}{3},-1 ;\left\{x \mid x \neq \frac{1}{3},-1\right\}$ 
C)  $-9,-1,3 ;\{x \mid x \neq-9,-1,3\}$ 
D)  $3,-1 ;\{x \mid x \neq 3,-1\}$

Question 13

Two machines are turned on at 8:00 A.M. If one can produce 51 items each hour and the other can produce 43 items each hour, at what time will they produce a total of 188 items?

Accepted Answer

A)  9:00 A.M. 
B)  11:30 A.M. 
C)  10:00 A.M. 
D)  11:00 A.M. 
A)  9:00 A.M. 
B)  11:30 A.M. 
C)  10:00 A.M. 
D)  11:00 A.M.

Question 14

Perform the indicated operation and express in lowest terms.
-$\frac{12}{q-9}-\frac{3}{q-9}$

Accepted Answer

A)  $\frac{12(q-9)}{3(q-9)}$ 
B)  $\frac{15}{q-9}$ 
C)  $\frac{9}{\mathrm{q}}$ 
D)  $\frac{9}{q-9}$ 
A)  $\frac{12(q-9)}{3(q-9)}$ 
B)  $\frac{15}{q-9}$ 
C)  $\frac{9}{\mathrm{q}}$ 
D)  $\frac{9}{q-9}$

Question 15

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)  21 
B)  9 
C)  11 
D)  10 
A)  21 
B)  9 
C)  11 
D)  10

Question 16

Consider an equation of inverse variation $y=\frac{k}{x}$. When $x$ increases, does $y$ increase or decrease?

Accepted Answer

The answer of Consider an equation of inverse variation $y=\frac{k}{x}$....

Question 17

$\frac{4 x-6}{2 x+1}=\frac{2 x-1}{x+6}$

Accepted Answer

A)  $\varnothing$ 
B)  $\left\{\frac{13}{6}\right\}$ 
C)  $\left\{\frac{35}{18}\right\}$ 
D)  $\left\{-\frac{37}{18}\right\}$ 
A)  $\varnothing$ 
B)  $\left\{\frac{13}{6}\right\}$ 
C)  $\left\{\frac{35}{18}\right\}$ 
D)  $\left\{-\frac{37}{18}\right\}$

Question 18

Choose the one alternative that best completes the statement or answers the question.
-If $m$ varies directly as $p$, and $m=35$ when $p=7$, find $m$ when $p$ is 4 .

Accepted Answer

A)  49 
B)  20 
C)  25 
D)  16 
A)  49 
B)  20 
C)  25 
D)  16

Question 19

Add or subtract as indicated.
-$\frac{1}{6 x^{3} y^{2}}-\frac{11}{2 x y}$

Accepted Answer

A)  $\frac{1-33 x^{2} y}{6 x^{3} y^{2}}$ 
B)  $\frac{6-33 x^{3} y}{6 x^{4} y^{3}}$ 
C)  $\frac{4-33 x^{4}}{6 x^{3} y}$ 
D)  $\frac{1-33 x}{6 x^{3} y^{2}}$ 
A)  $\frac{1-33 x^{2} y}{6 x^{3} y^{2}}$ 
B)  $\frac{6-33 x^{3} y}{6 x^{4} y^{3}}$ 
C)  $\frac{4-33 x^{4}}{6 x^{3} y}$ 
D)  $\frac{1-33 x}{6 x^{3} y^{2}}$

Question 20

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

Accepted Answer

The first step is th

Assume that the expressions given are denominators of fractions. Find the least common denominator. - $t, t+7$

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 balance on your credit card and the amount of available credit

Perform the indicated operation and express in lowest terms. - $\frac{2 k^{2}+15 k p+18 p^{2}}{9 k^{2}-18 k p+8 p^{2}} \div \frac{6 k^{2}+17 k p+12 p^{2}}{9 k^{2}-16 p^{2}}$

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - $f(x)=\frac{x-9}{x^{2}+9}$

$\frac{2 y+3}{y}=\frac{3}{2}$

Perform the indicated operation and express in lowest terms. - $\frac{8 p-8}{p} \cdot \frac{7 p^{2}}{9 p-9}$

Choose the one alternative that best completes the statement or answers the question. -If $\mathrm{f}$ varies jointly as $\mathrm{q}^{2}$ and $\mathrm{h}$ , and $\mathrm{f}=64$ when $\mathrm{q}=4$ and $\mathrm{h}=2$ , find $\mathrm{q}$ when $\mathrm{f}=90$ and $\mathrm{h}=5$ .

To determine the number of fish in a lake, a park ranger catches 240 fish, tags them, and returns them to the lake. Later, 144 fish are caught, and it is found that 24 of them are tagged. Estimate the number of fish in the lake.

Choose the one alternative that best completes the statement or answers the question. -If $\mathrm{f}$ varies jointly as $\mathrm{q}^{2}$ and $\mathrm{h}$ , and $\mathrm{f}=-54$ when $\mathrm{q}=3$ and $\mathrm{h}=3$ , find $\mathrm{f}$ when $\mathrm{q}=4$ and $\mathrm{h}=2$ .

Graph the rational function. Give the equations of the vertical and horizontal asymptotes. - $f(x)=\frac{3}{x}$

Choose the one alternative that best completes the statement or answers the question. Without actually solving the equation, list all possible numbers that would have to be rejected if they appeared as potential solutions. - $\frac{4 x+1}{x+7}=\frac{18 x+11}{16 x+7}$

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - $f(x)=\frac{2 x+18}{3 x^{2}-6 x-9}$

Two machines are turned on at 8:00 A.M. If one can produce 51 items each hour and the other can produce 43 items each hour, at what time will they produce a total of 188 items?

Perform the indicated operation and express in lowest terms. - $\frac{12}{q-9}-\frac{3}{q-9}$

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 $x$ ?

Consider an equation of inverse variation $y=\frac{k}{x}$ . When $x$ increases, does $y$ increase or decrease?

$\frac{4 x-6}{2 x+1}=\frac{2 x-1}{x+6}$

Choose the one alternative that best completes the statement or answers the question. -If $m$ varies directly as $p$ , and $m=35$ when $p=7$ , find $m$ when $p$ is 4 .

Add or subtract as indicated. - $\frac{1}{6 x^{3} y^{2}}-\frac{11}{2 x y}$

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

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

Assume that the expressions given are denominators of fractions. Find the least common denominator. - t,t+7t, t+7t,t+7

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 balance on your credit card and the amount of available credit

Perform the indicated operation and express in lowest terms. - 2k2+15kp+18p29k2−18kp+8p2÷6k2+17kp+12p29k2−16p2\frac{2 k^{2}+15 k p+18 p^{2}}{9 k^{2}-18 k p+8 p^{2}} \div \frac{6 k^{2}+17 k p+12 p^{2}}{9 k^{2}-16 p^{2}}9k2−18kp+8p22k2+15kp+18p2​÷9k2−16p26k2+17kp+12p2​

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - f(x)=x−9x2+9f(x)=\frac{x-9}{x^{2}+9}f(x)=x2+9x−9​

2y+3y=32\frac{2 y+3}{y}=\frac{3}{2}y2y+3​=23​

Perform the indicated operation and express in lowest terms. - 8p−8p⋅7p29p−9\frac{8 p-8}{p} \cdot \frac{7 p^{2}}{9 p-9}p8p−8​⋅9p−97p2​

To determine the number of fish in a lake, a park ranger catches 240 fish, tags them, and returns them to the lake. Later, 144 fish are caught, and it is found that 24 of them are tagged. Estimate the number of fish in the lake.

Graph the rational function. Give the equations of the vertical and horizontal asymptotes. - f(x)=3xf(x)=\frac{3}{x}f(x)=x3​

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - f(x)=2x+183x2−6x−9f(x)=\frac{2 x+18}{3 x^{2}-6 x-9}f(x)=3x2−6x−92x+18​

Two machines are turned on at 8:00 A.M. If one can produce 51 items each hour and the other can produce 43 items each hour, at what time will they produce a total of 188 items?

Perform the indicated operation and express in lowest terms. - 12q−9−3q−9\frac{12}{q-9}-\frac{3}{q-9}q−912​−q−93​

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 ?

Consider an equation of inverse variation y=kxy=\frac{k}{x}y=xk​ . When xxx increases, does yyy increase or decrease?

4x−62x+1=2x−1x+6\frac{4 x-6}{2 x+1}=\frac{2 x-1}{x+6}2x+14x−6​=x+62x−1​

Choose the one alternative that best completes the statement or answers the question. -If mmm varies directly as ppp , and m=35m=35m=35 when p=7p=7p=7 , find mmm when ppp is 4 .

Add or subtract as indicated. - 16x3y2−112xy\frac{1}{6 x^{3} y^{2}}-\frac{11}{2 x y}6x3y21​−2xy11​

Give the first step in solving the given equation for xxx . xy=x(y+z)x y=x(y+z)xy=x(y+z)

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

Assume that the expressions given are denominators of fractions. Find the least common denominator. - $t, t+7$

Perform the indicated operation and express in lowest terms. - $\frac{2 k^{2}+15 k p+18 p^{2}}{9 k^{2}-18 k p+8 p^{2}} \div \frac{6 k^{2}+17 k p+12 p^{2}}{9 k^{2}-16 p^{2}}$

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - $f(x)=\frac{x-9}{x^{2}+9}$

$\frac{2 y+3}{y}=\frac{3}{2}$

Perform the indicated operation and express in lowest terms. - $\frac{8 p-8}{p} \cdot \frac{7 p^{2}}{9 p-9}$

Graph the rational function. Give the equations of the vertical and horizontal asymptotes. - $f(x)=\frac{3}{x}$

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - $f(x)=\frac{2 x+18}{3 x^{2}-6 x-9}$

Perform the indicated operation and express in lowest terms. - $\frac{12}{q-9}-\frac{3}{q-9}$

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 $x$ ?

Consider an equation of inverse variation $y=\frac{k}{x}$ . When $x$ increases, does $y$ increase or decrease?

$\frac{4 x-6}{2 x+1}=\frac{2 x-1}{x+6}$

Choose the one alternative that best completes the statement or answers the question. -If $m$ varies directly as $p$ , and $m=35$ when $p=7$ , find $m$ when $p$ is 4 .

Add or subtract as indicated. - $\frac{1}{6 x^{3} y^{2}}-\frac{11}{2 x y}$

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