Question 1

Find the value of y so that the slope of the line between the points ( $$( - 1 , - 2 ) \text { and } ( 5 , y ) \text { is } \frac { 1 } { 2 }$$

Accepted Answer

A)  y = -12 
B)  y = 12 
C)  y = 1 
D)  y = -1 
A)  y = -12 
B)  y = 12 
C)  y = 1 
D)  y = -1

Question 2

Write a variation model. Use k as the constant of variation. P varies jointly as x and the square root of y.

Accepted Answer

A)  $P = \frac { k } { x \sqrt { y } }$ 
B)  $P = \frac { k x } { \sqrt { y } }$ 
C)  $P = k x \sqrt { y }$ 
D)  $P = k x y ^ { 2 }$ 
A)  $P = \frac { k } { x \sqrt { y } }$ 
B)  $P = \frac { k x } { \sqrt { y } }$ 
C)  $P = k x \sqrt { y }$ 
D)  $P = k x y ^ { 2 }$

Question 3

Solve the proportion. $$\frac { 8 } { 7 } = \frac { 168 } { x }$$

Accepted Answer

A)  $\{ 1176 \}$ 
B)  $\{ 147 \}$ 
C)  $\left\{ \frac { 1 } { 21 } \right\}$ 
D)  $\{ 49 \}$ 
A)  $\{ 1176 \}$ 
B)  $\{ 147 \}$ 
C)  $\left\{ \frac { 1 } { 21 } \right\}$ 
D)  $\{ 49 \}$

Question 4

Simplify the rational expression. $$\frac { y + 1 } { y ^ { 2 } + 1 }$$

Accepted Answer

A)  1 
B)  $\frac { 1 } { y }$ 
C)  $\frac { 1 } { y - 1 }$ 
D)  $\frac { y + 1 } { y ^ { 2 } + 1 }$; cannot be simplified 
A)  1 
B)  $\frac { 1 } { y }$ 
C)  $\frac { 1 } { y - 1 }$ 
D)  $\frac { y + 1 } { y ^ { 2 } + 1 }$; cannot be simplified

Question 5

Find the least common denominator (LCD). $$\frac { 2 } { 3 x } , \frac { 5 } { 14 x ^ { 3 } } , \frac { - 2 } { 7 x ^ { 2 } }$$

Accepted Answer

A)  $3 x$ 
B)  $42 x ^ { 3 }$ 
C)  $42 x$ 
D)  $294 x ^ { 6 }$ 
A)  $3 x$ 
B)  $42 x ^ { 3 }$ 
C)  $42 x$ 
D)  $294 x ^ { 6 }$

Question 6

Simplify the rational expression. $$\frac { 4 - 3 x } { 3 x ^ { 2 } + 11 x - 20 }$$

Accepted Answer

The answer of Simplify the rational expression. \[\frac { 4...

Question 7

Find the least common denominator (LCD). $$\frac { 8 y + 2 } { y ^ { 2 } } , \frac { 2 } { y ^ { 2 } - 8 y } , \frac { - 2 y ^ { 3 } } { y ^ { 2 } - 16 y + 64 }$$

Accepted Answer

A)  $y ^ { 3 } ( y - 8 ) ^ { 3 }$ 
B)  $y ^ { 2 } ( y - 8 ) ^ { 2 }$ 
C)  $y ^ { 2 }$ 
D)  $y ^ { 2 } - 16 y + 64$ 
A)  $y ^ { 3 } ( y - 8 ) ^ { 3 }$ 
B)  $y ^ { 2 } ( y - 8 ) ^ { 2 }$ 
C)  $y ^ { 2 }$ 
D)  $y ^ { 2 } - 16 y + 64$

Question 8

Simplify the complex fraction by using Method II. $$\frac { \frac { y ^ { 2 } + 10 y } { y - 10 } } { \frac { 6 y ^ { 3 } + 60 y ^ { 2 } } { y ^ { 2 } - 9 y - 10 } }$$

Accepted Answer

The answer of Simplify the complex fraction by using Method...

Question 9

Add. $$\frac { 7 } { 2 x ( x + 2 ) } + \frac { x + 3 } { x + 2 }$$

Accepted Answer

The answer of Add. \[\frac { 7 } { 2...

Question 10

Add or subtract as indicated and simplify if possible. $$\frac { 12 x } { 5 y } - \frac { x + 5 } { 5 y } + \frac { x ^ { 2 } + 2 } { 5 y }$$

Accepted Answer

A)  $\frac { 11 x + x ^ { 2 } + 7 x } { 15 y }$ 
B)  $\frac { x ^ { 2 } + 11 x - 3 } { 5 y }$ 
C)  $\frac { x ^ { 2 } + 11 x - 7 } { 125 y ^ { 3 } }$ 
D)  $\frac { 11 x + 7 + x ^ { 2 } } { 5 y }$ 
A)  $\frac { 11 x + x ^ { 2 } + 7 x } { 15 y }$ 
B)  $\frac { x ^ { 2 } + 11 x - 3 } { 5 y }$ 
C)  $\frac { x ^ { 2 } + 11 x - 7 } { 125 y ^ { 3 } }$ 
D)  $\frac { 11 x + 7 + x ^ { 2 } } { 5 y }$

Question 11

Simplify. $$\frac { t + 1 } { t + 4 } - \frac { t - 2 } { t - 4 } + \frac { 16 } { x ^ { 2 } - 16 }$$

Accepted Answer

A)  $\frac { 5 } { ( t + 4 ) }$ 
B)  $- \frac { 5 } { ( t - 4 ) }$ 
C)  $- \frac { 5 } { ( t + 4 ) }$ 
D)  $\frac { 5 } { ( t - 4 ) }$ 
A)  $\frac { 5 } { ( t + 4 ) }$ 
B)  $- \frac { 5 } { ( t - 4 ) }$ 
C)  $- \frac { 5 } { ( t + 4 ) }$ 
D)  $\frac { 5 } { ( t - 4 ) }$

Question 12

Write an expression that represents the perimeter of the figure and simplify.

Accepted Answer

A)  $\frac { x ^ { 2 } + 2 x + 7 } { x ^ { 2 } }$ 
B)  $\frac { 3 x ^ { 2 } + 7 x + 21 } { 3 x ^ { 2 } }$ 
C)  $\frac { 3 x ^ { 2 } + 7 x + 7 } { 3 x ^ { 2 } }$ 
D)  $\frac { 7 x ^ { 2 } + 7 x + 7 } { 3 x ^ { 2 } }$ 
A)  $\frac { x ^ { 2 } + 2 x + 7 } { x ^ { 2 } }$ 
B)  $\frac { 3 x ^ { 2 } + 7 x + 21 } { 3 x ^ { 2 } }$ 
C)  $\frac { 3 x ^ { 2 } + 7 x + 7 } { 3 x ^ { 2 } }$ 
D)  $\frac { 7 x ^ { 2 } + 7 x + 7 } { 3 x ^ { 2 } }$

Question 13

Solve for a. $$K = \frac { m a } { F }$$

Accepted Answer

A)  $a = \frac { F K } { m }$ 
B)  $a = \frac { K } { F m }$ 
C)  $a = \frac { m } { F K }$ 
D)  $a = \frac { F m } { K }$ 
A)  $a = \frac { F K } { m }$ 
B)  $a = \frac { K } { F m }$ 
C)  $a = \frac { m } { F K }$ 
D)  $a = \frac { F m } { K }$

Question 14

On a certain map, Detroit and Cleveland are 3" apart. The actual distance from Detroit to Cleveland is 170 miles. How far apart are two cities that are 10" apart on this map? Round to the nearest tenth Of a mile.

Accepted Answer

A)  566.7 miles 
B)  425.7 miles 
C)  660.7 miles 
D)  0.2 miles 
A)  566.7 miles 
B)  425.7 miles 
C)  660.7 miles 
D)  0.2 miles

Question 15

The amount of interest earned by an account based on simple interest varies jointly as the principal amount and the number of years the investment has been held. If a principal of $6000 invested for 3 Years earns $540.00 in interest, how much would be drawn by $4000 invested for 8 years?

Accepted Answer

A)  $480.00 
B)  $545.00 
C)  $960.00 
D)  $360.00 
A)  $480.00 
B)  $545.00 
C)  $960.00 
D)  $360.00

Question 16

Write the domain of the rational function in set-builder notation. $$f ( y ) = \frac { y - 16 } { y ^ { 2 } - 7 y - 18 }$$

Accepted Answer

A)  $\{ y \mid y \neq 16 , y \neq 9 , y \neq - 2 \}$ 
B)  $\{ y \mid y \neq 16 \}$ 
C)  $\{ y \mid y \neq 9 , y \neq - 2 \}$ 
D)  $\{ y \mid y$ is a real number $\}$ 
A)  $\{ y \mid y \neq 16 , y \neq 9 , y \neq - 2 \}$ 
B)  $\{ y \mid y \neq 16 \}$ 
C)  $\{ y \mid y \neq 9 , y \neq - 2 \}$ 
D)  $\{ y \mid y$ is a real number $\}$

Question 17

Simplify the rational expression. $\frac { 2 x ^ { 4 } + 12 x ^ { 3 } + 10 x ^ { 2 } } { x ^ { 3 } + 1 }$

Accepted Answer

A)  $\frac { 2 x ^ { 4 } + 12 x ^ { 3 } + 10 } { x + 1 }$ (Provided $\left. x \neq - 1 \right)$ 
B)  $2 x ^ { 4 } + 12 + 10 x ^ { 2 } \quad$ (Provided $x \neq - 1$ ) 
C)  $\frac { 2 x ^ { 2 } ( x + 5 ) } { x ^ { 2 } - x + 1 }$
(Provided $x \neq - 1$ ) 
D)  $\frac { 2 x ^ { 4 } + 12 x ^ { 3 } + 10 x ^ { 2 } } { x ^ { 3 } + 1 }$; cannot be simplified 
A)  $\frac { 2 x ^ { 4 } + 12 x ^ { 3 } + 10 } { x + 1 }$ (Provided $\left. x \neq - 1 \right)$ 
B)  $2 x ^ { 4 } + 12 + 10 x ^ { 2 } \quad$ (Provided $x \neq - 1$ ) 
C)  $\frac { 2 x ^ { 2 } ( x + 5 ) } { x ^ { 2 } - x + 1 }$
(Provided $x \neq - 1$ ) 
D)  $\frac { 2 x ^ { 4 } + 12 x ^ { 3 } + 10 x ^ { 2 } } { x ^ { 3 } + 1 }$; cannot be simplified

Question 18

If 6 is added to the reciprocal of a number, the result is $\frac { 49 } { 8 }$. Find the number.

Accepted Answer

A)  $\frac { 1 } { 8 }$ 
B)  $\frac { 97 } { 8 }$ 
C)  $\frac { 8 } { 97 }$ 
D)  8 
A)  $\frac { 1 } { 8 }$ 
B)  $\frac { 97 } { 8 }$ 
C)  $\frac { 8 } { 97 }$ 
D)  8

Question 19

Solve the proportion. $$\frac { 2 x } { x + 3 } = \frac { 25 } { x }$$

Accepted Answer

A)  $\left\{ - \frac { 8 } { 11 } , \frac { 17 } { 4 } \right\}$ 
B)  $\left\{ - \frac { 5 } { 2 } , \frac { 31 } { 16 } \right\}$ 
C)  $\left\{ - \frac { 5 } { 2 } , 15 \right\}$ 
D)  $\{ 15 \}$ 
A)  $\left\{ - \frac { 8 } { 11 } , \frac { 17 } { 4 } \right\}$ 
B)  $\left\{ - \frac { 5 } { 2 } , \frac { 31 } { 16 } \right\}$ 
C)  $\left\{ - \frac { 5 } { 2 } , 15 \right\}$ 
D)  $\{ 15 \}$

Question 20

Competing in a mini-triathlon, Catherine ran 3 miles in the same amount of time she biked 12 miles. Her average speed on the bike was 18 mph more than her average running speed. What was her Running speed?

Accepted Answer

A)  4 mph 
B)  6 mph 
C)  8 mph 
D)  5 mph 
A)  4 mph 
B)  6 mph 
C)  8 mph 
D)  5 mph

Find the value of y so that the slope of the line between the points ( $( - 1 , - 2 ) \text { and } ( 5 , y ) \text { is } \frac { 1 } { 2 }$

Write a variation model. Use k as the constant of variation. P varies jointly as x and the square root of y.

Solve the proportion. $\frac { 8 } { 7 } = \frac { 168 } { x }$

Simplify the rational expression. $\frac { y + 1 } { y ^ { 2 } + 1 }$

Find the least common denominator (LCD). $\frac { 2 } { 3 x } , \frac { 5 } { 14 x ^ { 3 } } , \frac { - 2 } { 7 x ^ { 2 } }$

Simplify the rational expression. $\frac { 4 - 3 x } { 3 x ^ { 2 } + 11 x - 20 }$

Find the least common denominator (LCD). $\frac { 8 y + 2 } { y ^ { 2 } } , \frac { 2 } { y ^ { 2 } - 8 y } , \frac { - 2 y ^ { 3 } } { y ^ { 2 } - 16 y + 64 }$

Simplify the complex fraction by using Method II. $\frac { \frac { y ^ { 2 } + 10 y } { y - 10 } } { \frac { 6 y ^ { 3 } + 60 y ^ { 2 } } { y ^ { 2 } - 9 y - 10 } }$

Add. $\frac { 7 } { 2 x ( x + 2 ) } + \frac { x + 3 } { x + 2 }$

Add or subtract as indicated and simplify if possible. $\frac { 12 x } { 5 y } - \frac { x + 5 } { 5 y } + \frac { x ^ { 2 } + 2 } { 5 y }$

Simplify. $\frac { t + 1 } { t + 4 } - \frac { t - 2 } { t - 4 } + \frac { 16 } { x ^ { 2 } - 16 }$

Write an expression that represents the perimeter of the figure and simplify.

Solve for a. $K = \frac { m a } { F }$

On a certain map, Detroit and Cleveland are 3" apart. The actual distance from Detroit to Cleveland is 170 miles. How far apart are two cities that are 10" apart on this map? Round to the nearest tenth Of a mile.

The amount of interest earned by an account based on simple interest varies jointly as the principal amount and the number of years the investment has been held. If a principal of $6000 invested for 3 Years earns $540.00 in interest, how much would be drawn by $4000 invested for 8 years?

Write the domain of the rational function in set-builder notation. $f ( y ) = \frac { y - 16 } { y ^ { 2 } - 7 y - 18 }$

Simplify the rational expression. $\frac { 2 x ^ { 4 } + 12 x ^ { 3 } + 10 x ^ { 2 } } { x ^ { 3 } + 1 }$

If 6 is added to the reciprocal of a number, the result is $\frac { 49 } { 8 }$ . Find the number.

Solve the proportion. $\frac { 2 x } { x + 3 } = \frac { 25 } { x }$

Competing in a mini-triathlon, Catherine ran 3 miles in the same amount of time she biked 12 miles. Her average speed on the bike was 18 mph more than her average running speed. What was her Running speed?

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

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Exam 5: Rational Expressions and Rational Equations

Find the value of y so that the slope of the line between the points ( (−1,−2) and (5,y) is 12( - 1 , - 2 ) \text { and } ( 5 , y ) \text { is } \frac { 1 } { 2 }(−1,−2) and (5,y) is 21​

Write a variation model. Use k as the constant of variation. P varies jointly as x and the square root of y.

Solve the proportion. 87=168x\frac { 8 } { 7 } = \frac { 168 } { x }78​=x168​

Simplify the rational expression. y+1y2+1\frac { y + 1 } { y ^ { 2 } + 1 }y2+1y+1​

Find the least common denominator (LCD). 23x,514x3,−27x2\frac { 2 } { 3 x } , \frac { 5 } { 14 x ^ { 3 } } , \frac { - 2 } { 7 x ^ { 2 } }3x2​,14x35​,7x2−2​

Simplify the rational expression. 4−3x3x2+11x−20\frac { 4 - 3 x } { 3 x ^ { 2 } + 11 x - 20 }3x2+11x−204−3x​

Find the least common denominator (LCD). 8y+2y2,2y2−8y,−2y3y2−16y+64\frac { 8 y + 2 } { y ^ { 2 } } , \frac { 2 } { y ^ { 2 } - 8 y } , \frac { - 2 y ^ { 3 } } { y ^ { 2 } - 16 y + 64 }y28y+2​,y2−8y2​,y2−16y+64−2y3​

Simplify the complex fraction by using Method II. y2+10yy−106y3+60y2y2−9y−10\frac { \frac { y ^ { 2 } + 10 y } { y - 10 } } { \frac { 6 y ^ { 3 } + 60 y ^ { 2 } } { y ^ { 2 } - 9 y - 10 } }y2−9y−106y3+60y2​y−10y2+10y​​

Add. 72x(x+2)+x+3x+2\frac { 7 } { 2 x ( x + 2 ) } + \frac { x + 3 } { x + 2 }2x(x+2)7​+x+2x+3​

Add or subtract as indicated and simplify if possible. 12x5y−x+55y+x2+25y\frac { 12 x } { 5 y } - \frac { x + 5 } { 5 y } + \frac { x ^ { 2 } + 2 } { 5 y }5y12x​−5yx+5​+5yx2+2​

Simplify. t+1t+4−t−2t−4+16x2−16\frac { t + 1 } { t + 4 } - \frac { t - 2 } { t - 4 } + \frac { 16 } { x ^ { 2 } - 16 }t+4t+1​−t−4t−2​+x2−1616​

Write an expression that represents the perimeter of the figure and simplify.

Solve for a. K=maFK = \frac { m a } { F }K=Fma​

On a certain map, Detroit and Cleveland are 3" apart. The actual distance from Detroit to Cleveland is 170 miles. How far apart are two cities that are 10" apart on this map? Round to the nearest tenth Of a mile.

The amount of interest earned by an account based on simple interest varies jointly as the principal amount and the number of years the investment has been held. If a principal of $6000 invested for 3 Years earns $540.00 in interest, how much would be drawn by $4000 invested for 8 years?

Write the domain of the rational function in set-builder notation. f(y)=y−16y2−7y−18f ( y ) = \frac { y - 16 } { y ^ { 2 } - 7 y - 18 }f(y)=y2−7y−18y−16​

Simplify the rational expression. 2x4+12x3+10x2x3+1\frac { 2 x ^ { 4 } + 12 x ^ { 3 } + 10 x ^ { 2 } } { x ^ { 3 } + 1 }x3+12x4+12x3+10x2​

If 6 is added to the reciprocal of a number, the result is 498\frac { 49 } { 8 }849​ . Find the number.

Solve the proportion. 2xx+3=25x\frac { 2 x } { x + 3 } = \frac { 25 } { x }x+32x​=x25​

Competing in a mini-triathlon, Catherine ran 3 miles in the same amount of time she biked 12 miles. Her average speed on the bike was 18 mph more than her average running speed. What was her Running speed?

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

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Find the value of y so that the slope of the line between the points ( $( - 1 , - 2 ) \text { and } ( 5 , y ) \text { is } \frac { 1 } { 2 }$

Solve the proportion. $\frac { 8 } { 7 } = \frac { 168 } { x }$

Simplify the rational expression. $\frac { y + 1 } { y ^ { 2 } + 1 }$

Find the least common denominator (LCD). $\frac { 2 } { 3 x } , \frac { 5 } { 14 x ^ { 3 } } , \frac { - 2 } { 7 x ^ { 2 } }$

Simplify the rational expression. $\frac { 4 - 3 x } { 3 x ^ { 2 } + 11 x - 20 }$

Find the least common denominator (LCD). $\frac { 8 y + 2 } { y ^ { 2 } } , \frac { 2 } { y ^ { 2 } - 8 y } , \frac { - 2 y ^ { 3 } } { y ^ { 2 } - 16 y + 64 }$

Simplify the complex fraction by using Method II. $\frac { \frac { y ^ { 2 } + 10 y } { y - 10 } } { \frac { 6 y ^ { 3 } + 60 y ^ { 2 } } { y ^ { 2 } - 9 y - 10 } }$

Add. $\frac { 7 } { 2 x ( x + 2 ) } + \frac { x + 3 } { x + 2 }$

Add or subtract as indicated and simplify if possible. $\frac { 12 x } { 5 y } - \frac { x + 5 } { 5 y } + \frac { x ^ { 2 } + 2 } { 5 y }$

Simplify. $\frac { t + 1 } { t + 4 } - \frac { t - 2 } { t - 4 } + \frac { 16 } { x ^ { 2 } - 16 }$

Solve for a. $K = \frac { m a } { F }$

Write the domain of the rational function in set-builder notation. $f ( y ) = \frac { y - 16 } { y ^ { 2 } - 7 y - 18 }$

Simplify the rational expression. $\frac { 2 x ^ { 4 } + 12 x ^ { 3 } + 10 x ^ { 2 } } { x ^ { 3 } + 1 }$

If 6 is added to the reciprocal of a number, the result is $\frac { 49 } { 8 }$ . Find the number.

Solve the proportion. $\frac { 2 x } { x + 3 } = \frac { 25 } { x }$