Question 1

Solve the equation. $\frac { 1 } { y } - \frac { 1 } { 5 y } + \frac { 1 } { y + 1 } = \frac { 5 } { 2 y }$

Accepted Answer

A)  $\frac { 10 } { 7 }$ 
B)  $17$ 
C)  $7$ 
D)  $- \frac { 7 } { 17 }$ 
E)  $\frac { 7 } { 17 }$ 
A)  $\frac { 10 } { 7 }$ 
B)  $17$ 
C)  $7$ 
D)  $- \frac { 7 } { 17 }$ 
E)  $\frac { 7 } { 17 }$

Question 2

Perform the indicated operation(s) and simplify. $\frac { 1 } { 5 } \div \left[ \frac { 1 } { 4 } \left( \frac { 1 } { 2 } + \frac { 1 } { 3 } \right) \right]$

Accepted Answer

A)  $\frac { 3 } { 2 }$ 
B)  $\frac { 25 } { 24 }$ 
C)  $1$ 
D)  $\frac { 2 } { 3 }$ 
E)  $\frac { 24 } { 25 }$ 
A)  $\frac { 3 } { 2 }$ 
B)  $\frac { 25 } { 24 }$ 
C)  $1$ 
D)  $\frac { 2 } { 3 }$ 
E)  $\frac { 24 } { 25 }$

Question 3

Factor the expression completely. $x ^ { 2 } \left( x ^ { 2 } - 1 \right) - 25 \left( x ^ { 2 } - 1 \right)$

Accepted Answer

The answer of Factor the expression completely. \(x ^ {...

Question 4

Write an equation that expresses the statement.
V is inversely proportional to y.

Accepted Answer

The answer of Write an equation that expresses the statement.
V...

Question 5

Solve the equation. $10 x ^ { 2 } = 13 x - 4$

Accepted Answer

A)  $x = 1 \pm 5 \sqrt { 2 }$ 
B)  $x = \frac { 3 } { 2 }$ or
$6$ 
C)  $x = \frac { 1 } { 2 }$ or
$\frac { 4 } { 3 }$ 
D)  $x = - \frac { 11 } { 2 }$ or
$\frac { 1 } { 2 }$ 
E)  $x = \frac { 3 } { 2 }$ or
$1$ 
A)  $x = 1 \pm 5 \sqrt { 2 }$ 
B)  $x = \frac { 3 } { 2 }$ or
$6$ 
C)  $x = \frac { 1 } { 2 }$ or
$\frac { 4 } { 3 }$ 
D)  $x = - \frac { 11 } { 2 }$ or
$\frac { 1 } { 2 }$ 
E)  $x = \frac { 3 } { 2 }$ or
$1$

Question 6

Solve the equation. $2 x - 4 = 15$

Accepted Answer

A) 
 $x = \frac { 15 } { 4 }$ 
B) 
 $x = 11$ 
C) 
 $x = \frac { 35 } { 3 }$ 
D) 
 $x = \frac { 19 } { 2 }$ 
E) 
 $x = 13$ 
A) 
 $x = \frac { 15 } { 4 }$ 
B) 
 $x = 11$ 
C) 
 $x = \frac { 35 } { 3 }$ 
D) 
 $x = \frac { 19 } { 2 }$ 
E) 
 $x = 13$

Question 7

Simplify the expression $\sqrt [ 3 ] { \frac { y ^ { 3 } z ^ { 3 } } { 64 } }$ .

Accepted Answer

The answer of Simplify the expression \(\sqrt [ 3 ]...

Question 8

The loudness L of a sound (measured in decibels, dB) is inversely proportional to the square of the distance d from the source of the sound. A person who is 10 ft from a lawn mower experiences a sound level of 70 dB. How loud is the lawn mower when the person is 25 ft away?

Accepted Answer

The answer of The loudness L of a sound (measured...

Question 9

If the recommended adult dosage for a drug is D (in mg), then to determine the appropriate dosage c for a child of age a, pharmacists use the equation $c = 0.0417 D ( a + 1 )$ Suppose the dosage for an adult is 400 mg. 
(c) Find the slope. What does it represent?
(d) What is the dosage for a newborn?

Accepted Answer

(a) 12.51; the slope represent

Question 10

Factor the expression. $x \left( x - \frac { 1 } { 2 } \right) ^ { 3 } + y \left( x - \frac { 1 } { 2 } \right) ^ { 2 }$

Accepted Answer

The answer of Factor the expression. \(x \left( x -...

Question 11

The stopping distance D of a car after the brakes have been applied varies directly as the square of the speed s. A certain car traveling at 50 mi/h can stop in 240 ft. What is the maximum speed it can be traveling if it needs to stop in 150 ft? Round your answer to one decimal place.

Accepted Answer

The answer of The stopping distance D of a car...

Question 12

Simplify the expression. Assume the letters denote any real numbers. $\sqrt [ 5 ] { u ^ { 6 } v ^ { 7 } }$

Accepted Answer

The answer of Simplify the expression. Assume the letters denote...

Question 13

Simplify the compound fractional expression. $x + \frac { y } { \frac { x } { y } - \frac { y } { x } }$

Accepted Answer

The answer of Simplify the compound fractional expression. \(x +...

Question 14

The loudness L of a sound (measured in decibels, dB) is inversely proportional to the square of the distance d from the source of the sound. A person who is 10 ft from a lawn mower experiences a sound level of 70 dB. How loud is the lawn mower when the person is 50 ft away?

Accepted Answer

The answer of The loudness L of a sound (measured...

Question 15

Solve the equation. $z = \frac { 5 z } { 7 } - 7$

Accepted Answer

A)  $z = 23$ 
B)  $z = \frac { 47 } { 2 }$ 
C)  $z = - \frac { 49 } { 2 }$ 
D)  $z = - \frac { 70 } { 3 }$ 
E)  $z = - \frac { 47 } { 2 }$ 
A)  $z = 23$ 
B)  $z = \frac { 47 } { 2 }$ 
C)  $z = - \frac { 49 } { 2 }$ 
D)  $z = - \frac { 70 } { 3 }$ 
E)  $z = - \frac { 47 } { 2 }$

Question 16

Use a graphing calculator or computer to decide which one of the viewing rectangles produces the most appropriate graph of the equation $$y = x ^ { 4 } + 3$$ .

Accepted Answer

A)  $$[ - 2,2 ]$$ by
$$[ - 2,2 ]$$ 
B)  $[ - 1,2 ]$ by
$[ - 12,3 ]$ 
C)  $[ 2,6 ]$ by
$[ - 10,4 ]$ 
D)  $[ - 1,1 ]$ by
$[ 0,4 ]$ 
E)  $[ - 5,5 ]$ by
$[ - 10 , - 6 ]$ 
A)  $$[ - 2,2 ]$$ by
$$[ - 2,2 ]$$ 
B)  $[ - 1,2 ]$ by
$[ - 12,3 ]$ 
C)  $[ 2,6 ]$ by
$[ - 10,4 ]$ 
D)  $[ - 1,1 ]$ by
$[ 0,4 ]$ 
E)  $[ - 5,5 ]$ by
$[ - 10 , - 6 ]$

Question 17

Solve the equation $S = \frac { a } { 1 -r }$ for $r$ .

Accepted Answer

The answer of Solve the equation \(S = \frac {...

Question 18

A rectangular garden is surrounded by 300 ft of chain-link fence. Find the length and width of the garden if the area is 3600 $\mathrm { ft } ^ { 2 }$ .

Accepted Answer

Perimeter

Question 19

If Arnold invests $\$ 6500$ at $4 \%$ per year, how much additional money must he invest at $10 \%$ to ensure that the interest he receives each year is $8 \%$ of the total invested?

Accepted Answer

A) 
 $\$ 13,000$ 
B) 
 $\$ 12,375$ 
C) 
 $\$ 18,000$ 
D) 
 $\$ 21,000$ 
E) 
 $\$ 22,500$ 
A) 
 $\$ 13,000$ 
B) 
 $\$ 12,375$ 
C) 
 $\$ 18,000$ 
D) 
 $\$ 21,000$ 
E) 
 $\$ 22,500$

Question 20

Factor the expression. $x ^ { 2 } + 8 x + 15$

Accepted Answer

A) 
 $( x + 3 ) ( x + 5 )$ 
B) 
 $( x - 3 ) ( x + 5 )$ 
C) 
 $( x - 3 ) ( x - 5 )$ 
D) 
 $( x + 3 ) ( x - 5 )$ 
E) 
 $( - x - 3 ) ( x - 5 )$ 
A) 
 $( x + 3 ) ( x + 5 )$ 
B) 
 $( x - 3 ) ( x + 5 )$ 
C) 
 $( x - 3 ) ( x - 5 )$ 
D) 
 $( x + 3 ) ( x - 5 )$ 
E) 
 $( - x - 3 ) ( x - 5 )$

Solve the equation. $\frac { 1 } { y } - \frac { 1 } { 5 y } + \frac { 1 } { y + 1 } = \frac { 5 } { 2 y }$

Perform the indicated operation(s) and simplify. $\frac { 1 } { 5 } \div \left[ \frac { 1 } { 4 } \left( \frac { 1 } { 2 } + \frac { 1 } { 3 } \right) \right]$

Factor the expression completely. $x ^ { 2 } \left( x ^ { 2 } - 1 \right) - 25 \left( x ^ { 2 } - 1 \right)$

Write an equation that expresses the statement. V is inversely proportional to y.

Solve the equation. $10 x ^ { 2 } = 13 x - 4$

Solve the equation. $2 x - 4 = 15$

Simplify the expression $\sqrt [ 3 ] { \frac { y ^ { 3 } z ^ { 3 } } { 64 } }$ .

The loudness L of a sound (measured in decibels, dB) is inversely proportional to the square of the distance d from the source of the sound. A person who is 10 ft from a lawn mower experiences a sound level of 70 dB. How loud is the lawn mower when the person is 25 ft away?

If the recommended adult dosage for a drug is D (in mg), then to determine the appropriate dosage c for a child of age a, pharmacists use the equation $c = 0.0417 D ( a + 1 )$ Suppose the dosage for an adult is 400 mg. (c) Find the slope. What does it represent? (d) What is the dosage for a newborn?

Factor the expression. $x \left( x - \frac { 1 } { 2 } \right) ^ { 3 } + y \left( x - \frac { 1 } { 2 } \right) ^ { 2 }$

The stopping distance D of a car after the brakes have been applied varies directly as the square of the speed s. A certain car traveling at 50 mi/h can stop in 240 ft. What is the maximum speed it can be traveling if it needs to stop in 150 ft? Round your answer to one decimal place.

Simplify the expression. Assume the letters denote any real numbers. $\sqrt [ 5 ] { u ^ { 6 } v ^ { 7 } }$

Simplify the compound fractional expression. $x + \frac { y } { \frac { x } { y } - \frac { y } { x } }$

The loudness L of a sound (measured in decibels, dB) is inversely proportional to the square of the distance d from the source of the sound. A person who is 10 ft from a lawn mower experiences a sound level of 70 dB. How loud is the lawn mower when the person is 50 ft away?

Solve the equation. $z = \frac { 5 z } { 7 } - 7$

Use a graphing calculator or computer to decide which one of the viewing rectangles produces the most appropriate graph of the equation $y = x ^ { 4 } + 3$ .

Solve the equation $S = \frac { a } { 1 -r }$ for $r$ .

A rectangular garden is surrounded by 300 ft of chain-link fence. Find the length and width of the garden if the area is 3600 $\mathrm { ft } ^ { 2 }$ .

If Arnold invests $\$ 6500$ at $4 \%$ per year, how much additional money must he invest at $10 \%$ to ensure that the interest he receives each year is $8 \%$ of the total invested?

Factor the expression. $x ^ { 2 } + 8 x + 15$

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

Trigonometric Functions: Right Triangle Approach

Analytic Trigonometry

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Conic Sections

Sequences and Series

Limits: a Preview of Calculus

Filters

Exam 1: Fundamentals

Solve the equation. 1y−15y+1y+1=52y\frac { 1 } { y } - \frac { 1 } { 5 y } + \frac { 1 } { y + 1 } = \frac { 5 } { 2 y }y1​−5y1​+y+11​=2y5​

Perform the indicated operation(s) and simplify. 15÷[14(12+13)]\frac { 1 } { 5 } \div \left[ \frac { 1 } { 4 } \left( \frac { 1 } { 2 } + \frac { 1 } { 3 } \right) \right]51​÷[41​(21​+31​)]

Factor the expression completely. x2(x2−1)−25(x2−1)x ^ { 2 } \left( x ^ { 2 } - 1 \right) - 25 \left( x ^ { 2 } - 1 \right)x2(x2−1)−25(x2−1)

Write an equation that expresses the statement. V is inversely proportional to y.

Solve the equation. 10x2=13x−410 x ^ { 2 } = 13 x - 410x2=13x−4

Solve the equation. 2x−4=152 x - 4 = 152x−4=15

Simplify the expression y3z3643\sqrt [ 3 ] { \frac { y ^ { 3 } z ^ { 3 } } { 64 } }364y3z3​​ .

The loudness L of a sound (measured in decibels, dB) is inversely proportional to the square of the distance d from the source of the sound. A person who is 10 ft from a lawn mower experiences a sound level of 70 dB. How loud is the lawn mower when the person is 25 ft away?

Factor the expression. x(x−12)3+y(x−12)2x \left( x - \frac { 1 } { 2 } \right) ^ { 3 } + y \left( x - \frac { 1 } { 2 } \right) ^ { 2 }x(x−21​)3+y(x−21​)2

The stopping distance D of a car after the brakes have been applied varies directly as the square of the speed s. A certain car traveling at 50 mi/h can stop in 240 ft. What is the maximum speed it can be traveling if it needs to stop in 150 ft? Round your answer to one decimal place.

Simplify the expression. Assume the letters denote any real numbers. u6v75\sqrt [ 5 ] { u ^ { 6 } v ^ { 7 } }5u6v7​

Simplify the compound fractional expression. x+yxy−yxx + \frac { y } { \frac { x } { y } - \frac { y } { x } }x+yx​−xy​y​

The loudness L of a sound (measured in decibels, dB) is inversely proportional to the square of the distance d from the source of the sound. A person who is 10 ft from a lawn mower experiences a sound level of 70 dB. How loud is the lawn mower when the person is 50 ft away?

Solve the equation. z=5z7−7z = \frac { 5 z } { 7 } - 7z=75z​−7

Use a graphing calculator or computer to decide which one of the viewing rectangles produces the most appropriate graph of the equation y=x4+3y = x ^ { 4 } + 3y=x4+3 .

Solve the equation S=a1−rS = \frac { a } { 1 -r }S=1−ra​ for rrr .

A rectangular garden is surrounded by 300 ft of chain-link fence. Find the length and width of the garden if the area is 3600 ft2\mathrm { ft } ^ { 2 }ft2 .

If Arnold invests $6500\$ 6500$6500 at 4%4 \%4% per year, how much additional money must he invest at 10%10 \%10% to ensure that the interest he receives each year is 8%8 \%8% of the total invested?

Factor the expression. x2+8x+15x ^ { 2 } + 8 x + 15x2+8x+15

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

Trigonometric Functions: Right Triangle Approach

Analytic Trigonometry

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Conic Sections

Sequences and Series

Limits: a Preview of Calculus

Filters

Solve the equation. $\frac { 1 } { y } - \frac { 1 } { 5 y } + \frac { 1 } { y + 1 } = \frac { 5 } { 2 y }$

Perform the indicated operation(s) and simplify. $\frac { 1 } { 5 } \div \left[ \frac { 1 } { 4 } \left( \frac { 1 } { 2 } + \frac { 1 } { 3 } \right) \right]$

Factor the expression completely. $x ^ { 2 } \left( x ^ { 2 } - 1 \right) - 25 \left( x ^ { 2 } - 1 \right)$

Solve the equation. $10 x ^ { 2 } = 13 x - 4$

Solve the equation. $2 x - 4 = 15$

Simplify the expression $\sqrt [ 3 ] { \frac { y ^ { 3 } z ^ { 3 } } { 64 } }$ .

Factor the expression. $x \left( x - \frac { 1 } { 2 } \right) ^ { 3 } + y \left( x - \frac { 1 } { 2 } \right) ^ { 2 }$

Simplify the expression. Assume the letters denote any real numbers. $\sqrt [ 5 ] { u ^ { 6 } v ^ { 7 } }$

Simplify the compound fractional expression. $x + \frac { y } { \frac { x } { y } - \frac { y } { x } }$

Solve the equation. $z = \frac { 5 z } { 7 } - 7$

Use a graphing calculator or computer to decide which one of the viewing rectangles produces the most appropriate graph of the equation $y = x ^ { 4 } + 3$ .

Solve the equation $S = \frac { a } { 1 -r }$ for $r$ .

A rectangular garden is surrounded by 300 ft of chain-link fence. Find the length and width of the garden if the area is 3600 $\mathrm { ft } ^ { 2 }$ .

If Arnold invests $\$ 6500$ at $4 \%$ per year, how much additional money must he invest at $10 \%$ to ensure that the interest he receives each year is $8 \%$ of the total invested?

Factor the expression. $x ^ { 2 } + 8 x + 15$