Question 1

Evaluate each expression
a) $\left( \frac { 5 } { 3 } \right) ^ { 0 } 3 ^ { - 1 }$

b) $\frac { 3 ^ { - 3 } } { 5 ^ { 0 } }$

c) $\left( \frac { 1 } { 3 } \right) ^ { - 2 }$

Accepted Answer

The answer of Evaluate each expression
a) \(\left( \frac { 5...

Question 2

Express the repeating decimal as a fraction. $0 . \overline { 8 }$

Accepted Answer

The answer of Express the repeating decimal as a fraction....

Question 3

Express each set in interval notation. 
(a)
 
(b)

Accepted Answer

The answer of Express each set in interval notation. 
(a)
...

Question 4

Simplify the expression. $$\frac { x } { x ^ { 2 } + 10 x + 25 } - \frac { 6 } { x ^ { 2 } + 11 x + 30 }$$

Accepted Answer

The answer of Simplify the expression. \[\frac { x }...

Question 5

Simplify the expression. $\frac { \left( x ^ { 8 } y ^ { 4 } \right) ^ { 5 } \left( x ^ { 2 } y ^ { 8 } \right) ^ { - 5 } } { x ^ { 2 } y ^ { 10 } }$

Accepted Answer

A)  $\frac { x ^ { 29 } } { y ^ { 30 } }$ 
B)  $\frac { x ^ { 31 } } { y ^ { 32 } }$ 
C)  $\frac { x ^ { 28 } } { y ^ { 31 } }$ 
D)  $\frac { x ^ { 2 } } { y ^ { 30 } }$ 
E)  $\frac { x ^ { 30 } } { y ^ { 28 } }$ 
A)  $\frac { x ^ { 29 } } { y ^ { 30 } }$ 
B)  $\frac { x ^ { 31 } } { y ^ { 32 } }$ 
C)  $\frac { x ^ { 28 } } { y ^ { 31 } }$ 
D)  $\frac { x ^ { 2 } } { y ^ { 30 } }$ 
E)  $\frac { x ^ { 30 } } { y ^ { 28 } }$

Question 6

Simplify the expression. Assume the letters denote any real numbers. $\sqrt [ 5 ] { a ^ { 3 } b } \cdot \sqrt [ 5 ] { a ^ { 7 } b }$

Accepted Answer

A)  $b ^ { 5 } \sqrt [ 5 ] { a ^ { 2 } }$ 
B)  $a ^ { 2 } \sqrt [ 5 ] { b }$ 
C)  $a ^ { 5 } \sqrt { b ^ { 2 } }$ 
D)  $a ^ { 2 } \sqrt [ 5 ] { b ^ { 2 } }$ 
E)  $a ^ { 2 } b ^ { 2 } \sqrt { 5 }$ 
A)  $b ^ { 5 } \sqrt [ 5 ] { a ^ { 2 } }$ 
B)  $a ^ { 2 } \sqrt [ 5 ] { b }$ 
C)  $a ^ { 5 } \sqrt { b ^ { 2 } }$ 
D)  $a ^ { 2 } \sqrt [ 5 ] { b ^ { 2 } }$ 
E)  $a ^ { 2 } b ^ { 2 } \sqrt { 5 }$

Question 7

Simplify the expression and eliminate any negative exponent(s). $\frac { 16 u ^ { 3 } v ^ { - 4 } } { 2 u ^ { - 5 } v ^ { 5 } }$

Accepted Answer

The answer of Simplify the expression and eliminate any negative...

Question 8

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

Accepted Answer

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

Question 9

Evaluate the arithmetic expression. $- 3 + \left[ 4 \cdot 7 - 5 \left( 9 - \frac { 8 } { 2 } \right) \right]$

Accepted Answer

The answer of Evaluate the arithmetic expression. \(- 3 +...

Question 10

Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers. $$\frac { \left( 64 y ^ { 6 } z ^ { - 12 } \right) ^ { - 1 / 6 } } { \left( 32 y ^ { - 5 } z ^ { 10 } \right) ^ { 1 / 5 } }$$

Accepted Answer

The answer of Simplify the expression and eliminate any negative...

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

A)  37.8 mi 
B)  73.8 mi 
C) 1428.8 mi 
D) 428.8 mi 
E) none of these 
A)  37.8 mi 
B)  73.8 mi 
C) 1428.8 mi 
D) 428.8 mi 
E) none of these

Question 12

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

Accepted Answer

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

Question 13

Use properties of real numbers to write the following expression without parentheses. $- \frac { 5 } { 3 } ( 9 x - 12 y )$

Accepted Answer

The answer of Use properties of real numbers to write...

Question 14

Simplify the expression. $\sqrt { 80 } + \sqrt { 45 }$

Accepted Answer

A)  $7 \sqrt { 6 }$ 
B)  $7 \sqrt { 5 }$ 
C)  $6 \sqrt { 5 }$ 
D)  $9 \sqrt { 5 }$ 
E)  $6 \sqrt { 6 }$ 
A)  $7 \sqrt { 6 }$ 
B)  $7 \sqrt { 5 }$ 
C)  $6 \sqrt { 5 }$ 
D)  $9 \sqrt { 5 }$ 
E)  $6 \sqrt { 6 }$

Question 15

Factor the expression completely. $x ^ { 4 } + 2 x ^ { 3 } - 15 x ^ { 2 }$

Accepted Answer

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

Question 16

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 17

Factor the expression. $25 s ^ { 2 } - 4 r ^ { 2 }$

Accepted Answer

The answer of Factor the expression. \(25 s ^ {...

Question 18

Factor the expression completely. $x ^ { 4 } + 5 x ^ { 3 } - 6 x ^ { 2 }$

Accepted Answer

A)  $x ^ { 2 } ( x - 1 ) ( x + 6 )$ 
B)  $x ^ { 2 } ( x - 4 ) ( x - 5 )$ 
C)  $x ^ { 2 } ( x - 4 ) ( x + 5 )$ 
D)  $x ^ { 2 } ( x - 1 ) ( x + 5 )$ 
E)  $x ^ { 2 } ( x - 4 ) ( x + 6 )$ 
A)  $x ^ { 2 } ( x - 1 ) ( x + 6 )$ 
B)  $x ^ { 2 } ( x - 4 ) ( x - 5 )$ 
C)  $x ^ { 2 } ( x - 4 ) ( x + 5 )$ 
D)  $x ^ { 2 } ( x - 1 ) ( x + 5 )$ 
E)  $x ^ { 2 } ( x - 4 ) ( x + 6 )$

Question 19

Express the repeating decimal as a fraction. $0 . \overline { 7 }$

Accepted Answer

The answer of Express the repeating decimal as a fraction....

Question 20

Evaluate the arithmetic expression. $- 1 + \left[ 4 \cdot 7 - 5 \left( 9 - \frac { 8 } { 2 } \right) \right]$

Accepted Answer

The answer of Evaluate the arithmetic expression. \(- 1 +...

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

Express the repeating decimal as a fraction. $0 . \overline { 8 }$

Express each set in interval notation. (a) (b)

Simplify the expression. $\frac { x } { x ^ { 2 } + 10 x + 25 } - \frac { 6 } { x ^ { 2 } + 11 x + 30 }$

Simplify the expression. $\frac { \left( x ^ { 8 } y ^ { 4 } \right) ^ { 5 } \left( x ^ { 2 } y ^ { 8 } \right) ^ { - 5 } } { x ^ { 2 } y ^ { 10 } }$

Simplify the expression. Assume the letters denote any real numbers. $\sqrt [ 5 ] { a ^ { 3 } b } \cdot \sqrt [ 5 ] { a ^ { 7 } b }$

Simplify the expression and eliminate any negative exponent(s). $\frac { 16 u ^ { 3 } v ^ { - 4 } } { 2 u ^ { - 5 } v ^ { 5 } }$

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

Evaluate the arithmetic expression. $- 3 + \left[ 4 \cdot 7 - 5 \left( 9 - \frac { 8 } { 2 } \right) \right]$

Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers. $\frac { \left( 64 y ^ { 6 } z ^ { - 12 } \right) ^ { - 1 / 6 } } { \left( 32 y ^ { - 5 } z ^ { 10 } \right) ^ { 1 / 5 } }$

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

Use properties of real numbers to write the following expression without parentheses. $- \frac { 5 } { 3 } ( 9 x - 12 y )$

Simplify the expression. $\sqrt { 80 } + \sqrt { 45 }$

Factor the expression completely. $x ^ { 4 } + 2 x ^ { 3 } - 15 x ^ { 2 }$

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

Factor the expression. $25 s ^ { 2 } - 4 r ^ { 2 }$

Factor the expression completely. $x ^ { 4 } + 5 x ^ { 3 } - 6 x ^ { 2 }$

Express the repeating decimal as a fraction. $0 . \overline { 7 }$

Evaluate the arithmetic expression. $- 1 + \left[ 4 \cdot 7 - 5 \left( 9 - \frac { 8 } { 2 } \right) \right]$

Equations and Graphs

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Exam 14: Counting and Probability

Evaluate each expression a) (53)03−1\left( \frac { 5 } { 3 } \right) ^ { 0 } 3 ^ { - 1 }(35​)03−1 b) 3−350\frac { 3 ^ { - 3 } } { 5 ^ { 0 } }503−3​ c) (13)−2\left( \frac { 1 } { 3 } \right) ^ { - 2 }(31​)−2

Express the repeating decimal as a fraction. 0.8‾0 . \overline { 8 }0.8

Express each set in interval notation. (a) (b)

Simplify the expression. xx2+10x+25−6x2+11x+30\frac { x } { x ^ { 2 } + 10 x + 25 } - \frac { 6 } { x ^ { 2 } + 11 x + 30 }x2+10x+25x​−x2+11x+306​

Simplify the expression. (x8y4)5(x2y8)−5x2y10\frac { \left( x ^ { 8 } y ^ { 4 } \right) ^ { 5 } \left( x ^ { 2 } y ^ { 8 } \right) ^ { - 5 } } { x ^ { 2 } y ^ { 10 } }x2y10(x8y4)5(x2y8)−5​

Simplify the expression. Assume the letters denote any real numbers. a3b5⋅a7b5\sqrt [ 5 ] { a ^ { 3 } b } \cdot \sqrt [ 5 ] { a ^ { 7 } b }5a3b​⋅5a7b​

Simplify the expression and eliminate any negative exponent(s). 16u3v−42u−5v5\frac { 16 u ^ { 3 } v ^ { - 4 } } { 2 u ^ { - 5 } v ^ { 5 } }2u−5v516u3v−4​

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

Evaluate the arithmetic expression. −3+[4⋅7−5(9−82)]- 3 + \left[ 4 \cdot 7 - 5 \left( 9 - \frac { 8 } { 2 } \right) \right]−3+[4⋅7−5(9−28​)]

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

Use properties of real numbers to write the following expression without parentheses. −53(9x−12y)- \frac { 5 } { 3 } ( 9 x - 12 y )−35​(9x−12y)

Simplify the expression. 80+45\sqrt { 80 } + \sqrt { 45 }80​+45​

Factor the expression completely. x4+2x3−15x2x ^ { 4 } + 2 x ^ { 3 } - 15 x ^ { 2 }x4+2x3−15x2

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​

Factor the expression. 25s2−4r225 s ^ { 2 } - 4 r ^ { 2 }25s2−4r2

Factor the expression completely. x4+5x3−6x2x ^ { 4 } + 5 x ^ { 3 } - 6 x ^ { 2 }x4+5x3−6x2

Express the repeating decimal as a fraction. 0.7‾0 . \overline { 7 }0.7

Evaluate the arithmetic expression. −1+[4⋅7−5(9−82)]- 1 + \left[ 4 \cdot 7 - 5 \left( 9 - \frac { 8 } { 2 } \right) \right]−1+[4⋅7−5(9−28​)]

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

Express the repeating decimal as a fraction. $0 . \overline { 8 }$

Simplify the expression. $\frac { x } { x ^ { 2 } + 10 x + 25 } - \frac { 6 } { x ^ { 2 } + 11 x + 30 }$

Simplify the expression. $\frac { \left( x ^ { 8 } y ^ { 4 } \right) ^ { 5 } \left( x ^ { 2 } y ^ { 8 } \right) ^ { - 5 } } { x ^ { 2 } y ^ { 10 } }$

Simplify the expression. Assume the letters denote any real numbers. $\sqrt [ 5 ] { a ^ { 3 } b } \cdot \sqrt [ 5 ] { a ^ { 7 } b }$

Simplify the expression and eliminate any negative exponent(s). $\frac { 16 u ^ { 3 } v ^ { - 4 } } { 2 u ^ { - 5 } v ^ { 5 } }$

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

Evaluate the arithmetic expression. $- 3 + \left[ 4 \cdot 7 - 5 \left( 9 - \frac { 8 } { 2 } \right) \right]$

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

Use properties of real numbers to write the following expression without parentheses. $- \frac { 5 } { 3 } ( 9 x - 12 y )$

Simplify the expression. $\sqrt { 80 } + \sqrt { 45 }$

Factor the expression completely. $x ^ { 4 } + 2 x ^ { 3 } - 15 x ^ { 2 }$

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

Factor the expression. $25 s ^ { 2 } - 4 r ^ { 2 }$

Factor the expression completely. $x ^ { 4 } + 5 x ^ { 3 } - 6 x ^ { 2 }$

Express the repeating decimal as a fraction. $0 . \overline { 7 }$

Evaluate the arithmetic expression. $- 1 + \left[ 4 \cdot 7 - 5 \left( 9 - \frac { 8 } { 2 } \right) \right]$