Question 1

Evaluate the expression $| | - 9 | - | - 11 | |$

Accepted Answer

The answer of Evaluate the expression \(| | - 9...

Question 2

Perform the indicated operation and simplify. $( 3 - 2 y ) ^ { 3 }$

Accepted Answer

A)  $- 8 y ^ { 3 } + 36 y ^ { 2 } - 54 y + 27$ 
B)  $8 y ^ { 3 } - 36 y ^ { 2 } + 54 y - 27$ 
C)  $- 8 y ^ { 3 } + 31 y ^ { 2 } - 54 y + 30$ 
D)  $- 8 y ^ { 3 } + 54 y ^ { 2 } - 36 y + 27$ 
E)  $8 y ^ { 3 } - 31 y ^ { 2 } + 54 y - 30$ 
A)  $- 8 y ^ { 3 } + 36 y ^ { 2 } - 54 y + 27$ 
B)  $8 y ^ { 3 } - 36 y ^ { 2 } + 54 y - 27$ 
C)  $- 8 y ^ { 3 } + 31 y ^ { 2 } - 54 y + 30$ 
D)  $- 8 y ^ { 3 } + 54 y ^ { 2 } - 36 y + 27$ 
E)  $8 y ^ { 3 } - 31 y ^ { 2 } + 54 y - 30$

Question 3

List the elements of the given set that are rational numbers. $\left\{ 0 , - 8,100,22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 } \right\}$

Accepted Answer

A)  $0 , - 8,100,22 / 7,1 . \overline { 23 } , - \frac { 1 } { 9 }$ 
B)  $0 , - 8,100,22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 }$ 
C)  $0 , - 8,100,22 / 7,1 . \overline { 23 } , \sqrt [ 3 ] { 4 }$ 
D)  $0 , - 8,100$ 
E)  $22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 }$ 
A)  $0 , - 8,100,22 / 7,1 . \overline { 23 } , - \frac { 1 } { 9 }$ 
B)  $0 , - 8,100,22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 }$ 
C)  $0 , - 8,100,22 / 7,1 . \overline { 23 } , \sqrt [ 3 ] { 4 }$ 
D)  $0 , - 8,100$ 
E)  $22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 }$

Question 4

Evaluate the arithmetic expression. $\frac { 6 + 9 } { 5 } - 3 [ 15 - ( 17 - 2 \cdot 3 ) ]$

Accepted Answer

The answer of Evaluate the arithmetic expression. \(\frac { 6...

Question 5

Perform the division and simplify. $\frac { 4 x ^ { 2 } - 9 } { x + 3 } \div \frac { 2 x ^ { 2 } + 7 x - 15 } { x ^ { 2 } + 7 x + 12 }$

Accepted Answer

The answer of Perform the division and simplify. \(\frac {...

Question 6

Use properties of real numbers to write the following expression without parentheses. $- \frac { 3 } { 2 } ( 6 x - 4 y )$

Accepted Answer

A) 9y - 6x 
B) 9x + 6y 
C) 9x - 6y 
D) 6y - 9x 
E) 6x - 9y 
A) 9y - 6x 
B) 9x + 6y 
C) 9x - 6y 
D) 6y - 9x 
E) 6x - 9y

Question 7

Perform the indicated operations and simplify. $3 ( 3 t - 2 ) - \left( t ^ { 2 } + 1 \right) - 4 t ( t - 1 )$

Accepted Answer

The answer of Perform the indicated operations and simplify. \(3...

Question 8

Simplify the expression. $\sqrt { 98 } + \sqrt { 50 }$

Accepted Answer

The answer of Simplify the expression. \(\sqrt { 98 }...

Question 9

Rationalize the denominator
a) $\frac { 18 } { \sqrt { 3 } }$

b) $\frac { 7 } { \sqrt { 2 } }$

c) $\frac { 3 } { \sqrt { 6 } }$

Accepted Answer

The answer of Rationalize the denominator
a) \(\frac { 18 }...

Question 10

Due to the curvature of the earth, the maximum distance D that you can see from the top of a tall building of height h is estimated by the formula $D = \sqrt { 2 r h + h ^ { 2 } }$ where r = 3960 mi is the radius of the earth and D and h are also measured in miles. How far can you see from the observation deck of a tower, 1000 ft above the ground? Round the answer to one decimal place

Accepted Answer

A) 37.9 mi 
B) 428.1 mi 
C) 1428.4 mi 
D) 73.9 mi 
E) none of these 
A) 37.9 mi 
B) 428.1 mi 
C) 1428.4 mi 
D) 73.9 mi 
E) none of these

Question 11

Due to the curvature of the earth, the maximum distance D that you can see from the top of a tall building of height h is estimated by the formula $D = \sqrt { 2 r h + h ^ { 2 } }$  where r = 3960 mi is the radius of the earth and D and h are also measured in miles. How far can you see from the observation deck of a tower, 955 ft above the ground? Round the answer to one decimal place.

Accepted Answer

The answer of Due to the curvature of the earth,...

Question 12

Evaluate the expression. $\left( \frac { 2 } { 3 } \right) ^ { - 3 }$

Accepted Answer

A)  $- \frac { 8 } { 27 }$ 
B)  $- \frac { 27 } { 8 }$ 
C)  $\frac { 1 } { 8 }$ 
D)  $\frac { 27 } { 8 }$ 
E)  $\frac { 8 } { 27 }$ 
A)  $- \frac { 8 } { 27 }$ 
B)  $- \frac { 27 } { 8 }$ 
C)  $\frac { 1 } { 8 }$ 
D)  $\frac { 27 } { 8 }$ 
E)  $\frac { 8 } { 27 }$

Question 13

Rationalize the denominator. $\frac { 1 } { \sqrt [ 5 ] { x ^ { 2 } } }$

Accepted Answer

A)  $\frac { \sqrt [ 5 ] { x ^ { 3 } } } { x }$ 
B)  $x ^ { - \frac { 2 } { 5 } }$ 
C)  $\frac { \sqrt [ 3 ] { x ^ { 5 } } } { x }$ 
D)  $\frac { 1 } { \sqrt [ 5 ] { x ^ { 2 } } }$ 
E)  $\frac { 1 } { x ^ { 2 / 5 } }$ 
A)  $\frac { \sqrt [ 5 ] { x ^ { 3 } } } { x }$ 
B)  $x ^ { - \frac { 2 } { 5 } }$ 
C)  $\frac { \sqrt [ 3 ] { x ^ { 5 } } } { x }$ 
D)  $\frac { 1 } { \sqrt [ 5 ] { x ^ { 2 } } }$ 
E)  $\frac { 1 } { x ^ { 2 / 5 } }$

Question 14

Simplify the expression. $\left( 15 x ^ { 6 } y ^ { 8 } \right) \left( \frac { 1 } { 5 } x ^ { 2 } y ^ { 2 } \right)$

Accepted Answer

A)  $3 x ^ { 8 } y ^ { 10 }$ 
B)  $3 x ^ { 16 } y ^ { 12 }$ 
C)  $3 x ^ { 12 } y ^ { 16 }$ 
D)  $3 x ^ { 10 } y ^ { 8 }$ 
E)  $75 x ^ { 8 } y ^ { 10 }$ 
A)  $3 x ^ { 8 } y ^ { 10 }$ 
B)  $3 x ^ { 16 } y ^ { 12 }$ 
C)  $3 x ^ { 12 } y ^ { 16 }$ 
D)  $3 x ^ { 10 } y ^ { 8 }$ 
E)  $75 x ^ { 8 } y ^ { 10 }$

Question 15

Rationalize the denominator. $\frac { 1 } { \sqrt [ 7 ] { x ^ { 4 } } }$

Accepted Answer

The answer of Rationalize the denominator. \(\frac { 1 }...

Question 16

Evaluate each expression
a) $\left( \frac { 7 } { 3 } \right) ^ { 0 } 2 ^ { - 1 }$

b) $\frac { 3 ^ { - 3 } } { 4 ^ { 0 } }$

c) $\left( \frac { 1 } { 5 } \right) ^ { - 2 }$

Accepted Answer

The answer of Evaluate each expression
a) \(\left( \frac { 7...

Question 17

Simplify the expression. $\frac { x } { x ^ { 2 } + 10 x + 21 } - \frac { 2 } { x ^ { 2 } + 9 x + 14 }$

Accepted Answer

A)  $\frac { x ^ { 2 } - 6 } { ( x + 3 ) ( x + 7 ) ( x + 2 ) }$ 
B)  $\frac { x - 2 } { ( x + 3 ) ( x + 2 ) }$ 
C)  $\frac { x ^ { 2 } - 14 } { ( x + 3 ) ( x + 2 ) }$ 
D)  $\frac { x ^ { 2 } - 6 } { ( x + 3 ) ( x + 2 ) }$ 
E)  $\frac { x ^ { 2 } - 21 } { ( x + 3 ) ( x + 7 ) ( x + 2 ) }$ 
A)  $\frac { x ^ { 2 } - 6 } { ( x + 3 ) ( x + 7 ) ( x + 2 ) }$ 
B)  $\frac { x - 2 } { ( x + 3 ) ( x + 2 ) }$ 
C)  $\frac { x ^ { 2 } - 14 } { ( x + 3 ) ( x + 2 ) }$ 
D)  $\frac { x ^ { 2 } - 6 } { ( x + 3 ) ( x + 2 ) }$ 
E)  $\frac { x ^ { 2 } - 21 } { ( x + 3 ) ( x + 7 ) ( x + 2 ) }$

Question 18

Factor the expression completely. $30 x ^ { 2 } - 11 x - 30$

Accepted Answer

A)  (9x + 7)(5x - 6) 
B)  (9x - 7)(7x + 9) 
C)  (9x + 7)(7x - 9) 
D)  (6x + 5)(5x - 6) 
E)  (6x + 5)(7x - 9) 
A)  (9x + 7)(5x - 6) 
B)  (9x - 7)(7x + 9) 
C)  (9x + 7)(7x - 9) 
D)  (6x + 5)(5x - 6) 
E)  (6x + 5)(7x - 9)

Question 19

Simplify the expression. $\frac { t - 4 } { t ^ { 2 } - 16 } \cdot \frac { t + 4 } { t ^ { 2 } + 16 }$

Accepted Answer

A)  $\frac { 1 } { t - 16 }$ 
B)  $\frac { 1 } { t ^ { 2 } + 16 }$ 
C)  $t ^ { 2 } + 16$ 
D)  $\frac { t ^ { 2 } - 4 } { t + 16 }$ 
E)  $\frac { t ^ { 2 } + 4 } { t + 16 }$ 
A)  $\frac { 1 } { t - 16 }$ 
B)  $\frac { 1 } { t ^ { 2 } + 16 }$ 
C)  $t ^ { 2 } + 16$ 
D)  $\frac { t ^ { 2 } - 4 } { t + 16 }$ 
E)  $\frac { t ^ { 2 } + 4 } { t + 16 }$

Question 20

Simplify the expression. $\frac { 4 y ^ { 2 } - 3 y - 7 } { 16 y ^ { 2 } - 49 } \div \frac { y ^ { 2 } - 2 y - 3 } { 4 y ^ { 2 } - 5 y - 21 }$

Accepted Answer

The answer of Simplify the expression. \(\frac { 4 y...

Evaluate the expression $| | - 9 | - | - 11 | |$

Perform the indicated operation and simplify. $( 3 - 2 y ) ^ { 3 }$

List the elements of the given set that are rational numbers. $\left\{ 0 , - 8,100,22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 } \right\}$

Evaluate the arithmetic expression. $\frac { 6 + 9 } { 5 } - 3 [ 15 - ( 17 - 2 \cdot 3 ) ]$

Perform the division and simplify. $\frac { 4 x ^ { 2 } - 9 } { x + 3 } \div \frac { 2 x ^ { 2 } + 7 x - 15 } { x ^ { 2 } + 7 x + 12 }$

Use properties of real numbers to write the following expression without parentheses. $- \frac { 3 } { 2 } ( 6 x - 4 y )$

Perform the indicated operations and simplify. $3 ( 3 t - 2 ) - \left( t ^ { 2 } + 1 \right) - 4 t ( t - 1 )$

Simplify the expression. $\sqrt { 98 } + \sqrt { 50 }$

Rationalize the denominator a) $\frac { 18 } { \sqrt { 3 } }$ b) $\frac { 7 } { \sqrt { 2 } }$ c) $\frac { 3 } { \sqrt { 6 } }$

Evaluate the expression. $\left( \frac { 2 } { 3 } \right) ^ { - 3 }$

Rationalize the denominator. $\frac { 1 } { \sqrt [ 5 ] { x ^ { 2 } } }$

Simplify the expression. $\left( 15 x ^ { 6 } y ^ { 8 } \right) \left( \frac { 1 } { 5 } x ^ { 2 } y ^ { 2 } \right)$

Rationalize the denominator. $\frac { 1 } { \sqrt [ 7 ] { x ^ { 4 } } }$

Evaluate each expression a) $\left( \frac { 7 } { 3 } \right) ^ { 0 } 2 ^ { - 1 }$ b) $\frac { 3 ^ { - 3 } } { 4 ^ { 0 } }$ c) $\left( \frac { 1 } { 5 } \right) ^ { - 2 }$

Simplify the expression. $\frac { x } { x ^ { 2 } + 10 x + 21 } - \frac { 2 } { x ^ { 2 } + 9 x + 14 }$

Factor the expression completely. $30 x ^ { 2 } - 11 x - 30$

Simplify the expression. $\frac { t - 4 } { t ^ { 2 } - 16 } \cdot \frac { t + 4 } { t ^ { 2 } + 16 }$

Simplify the expression. $\frac { 4 y ^ { 2 } - 3 y - 7 } { 16 y ^ { 2 } - 49 } \div \frac { y ^ { 2 } - 2 y - 3 } { 4 y ^ { 2 } - 5 y - 21 }$

Equations and Graphs

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

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Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

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Filters

Exam 14: Counting and Probability

Evaluate the expression ∣∣−9∣−∣−11∣∣| | - 9 | - | - 11 | |∣∣−9∣−∣−11∣∣

Perform the indicated operation and simplify. (3−2y)3( 3 - 2 y ) ^ { 3 }(3−2y)3

List the elements of the given set that are rational numbers. {0,−8,100,22/7,5,1.23‾,−19,43}\left\{ 0 , - 8,100,22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 } \right\}{0,−8,100,22/7,5​,1.23,−91​,34​}

Evaluate the arithmetic expression. 6+95−3[15−(17−2⋅3)]\frac { 6 + 9 } { 5 } - 3 [ 15 - ( 17 - 2 \cdot 3 ) ]56+9​−3[15−(17−2⋅3)]

Perform the division and simplify. 4x2−9x+3÷2x2+7x−15x2+7x+12\frac { 4 x ^ { 2 } - 9 } { x + 3 } \div \frac { 2 x ^ { 2 } + 7 x - 15 } { x ^ { 2 } + 7 x + 12 }x+34x2−9​÷x2+7x+122x2+7x−15​

Use properties of real numbers to write the following expression without parentheses. −32(6x−4y)- \frac { 3 } { 2 } ( 6 x - 4 y )−23​(6x−4y)

Perform the indicated operations and simplify. 3(3t−2)−(t2+1)−4t(t−1)3 ( 3 t - 2 ) - \left( t ^ { 2 } + 1 \right) - 4 t ( t - 1 )3(3t−2)−(t2+1)−4t(t−1)

Simplify the expression. 98+50\sqrt { 98 } + \sqrt { 50 }98​+50​

Rationalize the denominator a) 183\frac { 18 } { \sqrt { 3 } }3​18​ b) 72\frac { 7 } { \sqrt { 2 } }2​7​ c) 36\frac { 3 } { \sqrt { 6 } }6​3​

Evaluate the expression. (23)−3\left( \frac { 2 } { 3 } \right) ^ { - 3 }(32​)−3

Rationalize the denominator. 1x25\frac { 1 } { \sqrt [ 5 ] { x ^ { 2 } } }5x2​1​

Simplify the expression. (15x6y8)(15x2y2)\left( 15 x ^ { 6 } y ^ { 8 } \right) \left( \frac { 1 } { 5 } x ^ { 2 } y ^ { 2 } \right)(15x6y8)(51​x2y2)

Rationalize the denominator. 1x47\frac { 1 } { \sqrt [ 7 ] { x ^ { 4 } } }7x4​1​

Evaluate each expression a) (73)02−1\left( \frac { 7 } { 3 } \right) ^ { 0 } 2 ^ { - 1 }(37​)02−1 b) 3−340\frac { 3 ^ { - 3 } } { 4 ^ { 0 } }403−3​ c) (15)−2\left( \frac { 1 } { 5 } \right) ^ { - 2 }(51​)−2

Simplify the expression. xx2+10x+21−2x2+9x+14\frac { x } { x ^ { 2 } + 10 x + 21 } - \frac { 2 } { x ^ { 2 } + 9 x + 14 }x2+10x+21x​−x2+9x+142​

Factor the expression completely. 30x2−11x−3030 x ^ { 2 } - 11 x - 3030x2−11x−30

Simplify the expression. t−4t2−16⋅t+4t2+16\frac { t - 4 } { t ^ { 2 } - 16 } \cdot \frac { t + 4 } { t ^ { 2 } + 16 }t2−16t−4​⋅t2+16t+4​

Simplify the expression. 4y2−3y−716y2−49÷y2−2y−34y2−5y−21\frac { 4 y ^ { 2 } - 3 y - 7 } { 16 y ^ { 2 } - 49 } \div \frac { y ^ { 2 } - 2 y - 3 } { 4 y ^ { 2 } - 5 y - 21 }16y2−494y2−3y−7​÷4y2−5y−21y2−2y−3​

Equations and Graphs

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Filters

Evaluate the expression $| | - 9 | - | - 11 | |$

Perform the indicated operation and simplify. $( 3 - 2 y ) ^ { 3 }$

List the elements of the given set that are rational numbers. $\left\{ 0 , - 8,100,22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 } \right\}$

Evaluate the arithmetic expression. $\frac { 6 + 9 } { 5 } - 3 [ 15 - ( 17 - 2 \cdot 3 ) ]$

Perform the division and simplify. $\frac { 4 x ^ { 2 } - 9 } { x + 3 } \div \frac { 2 x ^ { 2 } + 7 x - 15 } { x ^ { 2 } + 7 x + 12 }$

Use properties of real numbers to write the following expression without parentheses. $- \frac { 3 } { 2 } ( 6 x - 4 y )$

Perform the indicated operations and simplify. $3 ( 3 t - 2 ) - \left( t ^ { 2 } + 1 \right) - 4 t ( t - 1 )$

Simplify the expression. $\sqrt { 98 } + \sqrt { 50 }$

Rationalize the denominator a) $\frac { 18 } { \sqrt { 3 } }$ b) $\frac { 7 } { \sqrt { 2 } }$ c) $\frac { 3 } { \sqrt { 6 } }$

Evaluate the expression. $\left( \frac { 2 } { 3 } \right) ^ { - 3 }$

Rationalize the denominator. $\frac { 1 } { \sqrt [ 5 ] { x ^ { 2 } } }$

Simplify the expression. $\left( 15 x ^ { 6 } y ^ { 8 } \right) \left( \frac { 1 } { 5 } x ^ { 2 } y ^ { 2 } \right)$

Rationalize the denominator. $\frac { 1 } { \sqrt [ 7 ] { x ^ { 4 } } }$

Evaluate each expression a) $\left( \frac { 7 } { 3 } \right) ^ { 0 } 2 ^ { - 1 }$ b) $\frac { 3 ^ { - 3 } } { 4 ^ { 0 } }$ c) $\left( \frac { 1 } { 5 } \right) ^ { - 2 }$

Simplify the expression. $\frac { x } { x ^ { 2 } + 10 x + 21 } - \frac { 2 } { x ^ { 2 } + 9 x + 14 }$

Factor the expression completely. $30 x ^ { 2 } - 11 x - 30$

Simplify the expression. $\frac { t - 4 } { t ^ { 2 } - 16 } \cdot \frac { t + 4 } { t ^ { 2 } + 16 }$

Simplify the expression. $\frac { 4 y ^ { 2 } - 3 y - 7 } { 16 y ^ { 2 } - 49 } \div \frac { y ^ { 2 } - 2 y - 3 } { 4 y ^ { 2 } - 5 y - 21 }$