Question 1

Simplify the expression. $\frac { 2 y ^ { 2 } - 3 y - 5 } { 4 y ^ { 2 } - 25 } \div \frac { y ^ { 2 } - 6 y - 7 } { 2 y ^ { 2 } - 9 y - 35 }$

Accepted Answer

A)  $\frac { 1 } { 2 y - 5 }$ 
B)  1 
C)  $2 y - 5$ 
D)  $\frac { 1 } { y - 7 }$ 
E)  $\frac { 1 } { y - 1 }$ 
A)  $\frac { 1 } { 2 y - 5 }$ 
B)  1 
C)  $2 y - 5$ 
D)  $\frac { 1 } { y - 7 }$ 
E)  $\frac { 1 } { y - 1 }$

Question 2

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 3

Simplify the expression. $\frac { 1 + \frac { 1 } { x - 3 } } { 1 - \frac { 1 } { x - 3 } }$

Accepted Answer

The answer of Simplify the expression. \(\frac { 1 +...

Question 4

Evaluate the expression using $x = 4 , y = 5 , \text { and } z = - 2$ 
. $\sqrt [ 4 ] { x ^ { 3 } + 40 y + 4 z }$

Accepted Answer

The answer of Evaluate the expression using \(x = 4...

Question 5

List the elements of the given set that are
a) natural numbers
b) integers
c) rational numbers
d) irrational numbers

$\left\{ 0 , - 8,100,22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 } \right\}$

Accepted Answer

The answer of List the elements of the given set...

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

Question 7

Simplify the expression. Eliminate any negative exponents. $\frac { \left( x ^ { 7 } y ^ { 8 } \right) ^ { 5 } \left( x ^ { 2 } y ^ { 6 } \right) ^ { - 5 } } { x ^ { 2 } y ^ { 18 } }$

Accepted Answer

The answer of Simplify the expression. Eliminate any negative exponents....

Question 8

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 9

Perform the indicated operations and simplify. $2 ( 4 t - 1 ) - \left( t ^ { 2 } + 1 \right) - 4 t ( t - 5 )$

Accepted Answer

The answer of Perform the indicated operations and simplify. \(2...

Question 10

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

Question 11

Simplify the expression. $\frac { 1 + \frac { 1 } { x - 5 } } { 1 - \frac { 1 } { x - 5 } }$

Accepted Answer

A)  $\frac { x - 6 } { x - 4 }$ 
B)  $\frac { x - 5 } { x - 4 }$ 
C)  $\frac { 4 - x } { 6 + x }$ 
D)  $\frac { x - 5 } { x - 6 }$ 
E)  $\frac { x - 4 } { x - 6 }$ 
A)  $\frac { x - 6 } { x - 4 }$ 
B)  $\frac { x - 5 } { x - 4 }$ 
C)  $\frac { 4 - x } { 6 + x }$ 
D)  $\frac { x - 5 } { x - 6 }$ 
E)  $\frac { x - 4 } { x - 6 }$

Question 12

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

Accepted Answer

The answer of List the elements of the given set...

Question 13

Evaluate the expression using $x = 4 , y = 5 , \text { and } z = - 2$ . $\sqrt [ 4 ] { x ^ { 3 } + 40 y + 4 z }$

Accepted Answer

A) 256 
B) 2 
C) 8 
D) 4 
E) 16 
A) 256 
B) 2 
C) 8 
D) 4 
E) 16

Question 14

Perform the indicated operations and simplify. $3 ( 3 t - 5 ) - \left( t ^ { 2 } + 3 \right) - 5 t ( t - 2 )$

Accepted Answer

A)  $- 6 t ^ { 2 } - 19 t + 26$ 
B)  $- 6 t ^ { 2 } + 19 t - 18$ 
C)  $- 6 t ^ { 2 } + 14 t - 18$ 
D)  $- 9 t ^ { 2 } + 14 t - 26$ 
E)  $- 6 t ^ { 2 } + 19 t + 18$ 
A)  $- 6 t ^ { 2 } - 19 t + 26$ 
B)  $- 6 t ^ { 2 } + 19 t - 18$ 
C)  $- 6 t ^ { 2 } + 14 t - 18$ 
D)  $- 9 t ^ { 2 } + 14 t - 26$ 
E)  $- 6 t ^ { 2 } + 19 t + 18$

Question 15

Factor the trinomial. $5 x ^ { 2 } - 29 x + 20$

Accepted Answer

The answer of Factor the trinomial. \(5 x ^ {...

Question 16

Perform the indicated operation and simplify. $\left( x ^ { 2 } + x - 10 \right) \left( x ^ { 3 } - x + 5 \right)$

Accepted Answer

The answer of Perform the indicated operation and simplify. \(\left(...

Question 17

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, 1,000 ft above the ground?

Accepted Answer

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

Question 18

Multiply the algebraic expressions using a Special Product Formula and simplify. $( \sqrt { a } - b ) ( \sqrt { a } + b )$

Accepted Answer

A)  $a ^ { 2 } + b ^ { 2 }$ 
B)  $a - b ^ { 2 }$ 
C)  $a + b ^ { 2 }$ 
D)  $a - 2 a \sqrt { b } + b ^ { 2 }$ 
E)  $a - 2 \sqrt { a b } - b ^ { 2 }$ 
A)  $a ^ { 2 } + b ^ { 2 }$ 
B)  $a - b ^ { 2 }$ 
C)  $a + b ^ { 2 }$ 
D)  $a - 2 a \sqrt { b } + b ^ { 2 }$ 
E)  $a - 2 \sqrt { a b } - b ^ { 2 }$

Question 19

List the elements of the given set that are
a) natural numbers
b) integers
c) rational numbers
d) irrational numbers $\left\{ 0 , - 7,50,22 / 7 , \sqrt { 3 } , 1 . \overline { 23 } , - \frac { 1 } { 3 } , \sqrt [ 3 ] { 9 } \right\}$

Accepted Answer

The answer of List the elements of the given set...

Question 20

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

Accepted Answer

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

Simplify the expression. $\frac { 2 y ^ { 2 } - 3 y - 5 } { 4 y ^ { 2 } - 25 } \div \frac { y ^ { 2 } - 6 y - 7 } { 2 y ^ { 2 } - 9 y - 35 }$

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

Simplify the expression. $\frac { 1 + \frac { 1 } { x - 3 } } { 1 - \frac { 1 } { x - 3 } }$

Evaluate the expression using $x = 4 , y = 5 , \text { and } z = - 2$ . $\sqrt [ 4 ] { x ^ { 3 } + 40 y + 4 z }$

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

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

Simplify the expression. Eliminate any negative exponents. $\frac { \left( x ^ { 7 } y ^ { 8 } \right) ^ { 5 } \left( x ^ { 2 } y ^ { 6 } \right) ^ { - 5 } } { x ^ { 2 } y ^ { 18 } }$

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 operations and simplify. $2 ( 4 t - 1 ) - \left( t ^ { 2 } + 1 \right) - 4 t ( t - 5 )$

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

Simplify the expression. $\frac { 1 + \frac { 1 } { x - 5 } } { 1 - \frac { 1 } { x - 5 } }$

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

Evaluate the expression using $x = 4 , y = 5 , \text { and } z = - 2$ . $\sqrt [ 4 ] { x ^ { 3 } + 40 y + 4 z }$

Perform the indicated operations and simplify. $3 ( 3 t - 5 ) - \left( t ^ { 2 } + 3 \right) - 5 t ( t - 2 )$

Factor the trinomial. $5 x ^ { 2 } - 29 x + 20$

Perform the indicated operation and simplify. $\left( x ^ { 2 } + x - 10 \right) \left( x ^ { 3 } - x + 5 \right)$

Multiply the algebraic expressions using a Special Product Formula and simplify. $( \sqrt { a } - b ) ( \sqrt { a } + b )$

List the elements of the given set that are a) natural numbers b) integers c) rational numbers d) irrational numbers $\left\{ 0 , - 7,50,22 / 7 , \sqrt { 3 } , 1 . \overline { 23 } , - \frac { 1 } { 3 } , \sqrt [ 3 ] { 9 } \right\}$

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

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Trigonometric Functions: Unit Circle Approach

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Exam 14: Counting and Probability

Simplify the expression. 2y2−3y−54y2−25÷y2−6y−72y2−9y−35\frac { 2 y ^ { 2 } - 3 y - 5 } { 4 y ^ { 2 } - 25 } \div \frac { y ^ { 2 } - 6 y - 7 } { 2 y ^ { 2 } - 9 y - 35 }4y2−252y2−3y−5​÷2y2−9y−35y2−6y−7​

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

Simplify the expression. 1+1x−31−1x−3\frac { 1 + \frac { 1 } { x - 3 } } { 1 - \frac { 1 } { x - 3 } }1−x−31​1+x−31​​

Evaluate the expression using x=4,y=5, and z=−2x = 4 , y = 5 , \text { and } z = - 2x=4,y=5, and z=−2 . x3+40y+4z4\sqrt [ 4 ] { x ^ { 3 } + 40 y + 4 z }4x3+40y+4z​

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)

Simplify the expression. Eliminate any negative exponents. (x7y8)5(x2y6)−5x2y18\frac { \left( x ^ { 7 } y ^ { 8 } \right) ^ { 5 } \left( x ^ { 2 } y ^ { 6 } \right) ^ { - 5 } } { x ^ { 2 } y ^ { 18 } }x2y18(x7y8)5(x2y6)−5​

Perform the indicated operations and simplify. 2(4t−1)−(t2+1)−4t(t−5)2 ( 4 t - 1 ) - \left( t ^ { 2 } + 1 \right) - 4 t ( t - 5 )2(4t−1)−(t2+1)−4t(t−5)

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

Simplify the expression. 1+1x−51−1x−5\frac { 1 + \frac { 1 } { x - 5 } } { 1 - \frac { 1 } { x - 5 } }1−x−51​1+x−51​​

Evaluate the expression using x=4,y=5, and z=−2x = 4 , y = 5 , \text { and } z = - 2x=4,y=5, and z=−2 . x3+40y+4z4\sqrt [ 4 ] { x ^ { 3 } + 40 y + 4 z }4x3+40y+4z​

Perform the indicated operations and simplify. 3(3t−5)−(t2+3)−5t(t−2)3 ( 3 t - 5 ) - \left( t ^ { 2 } + 3 \right) - 5 t ( t - 2 )3(3t−5)−(t2+3)−5t(t−2)

Factor the trinomial. 5x2−29x+205 x ^ { 2 } - 29 x + 205x2−29x+20

Perform the indicated operation and simplify. (x2+x−10)(x3−x+5)\left( x ^ { 2 } + x - 10 \right) \left( x ^ { 3 } - x + 5 \right)(x2+x−10)(x3−x+5)

Multiply the algebraic expressions using a Special Product Formula and simplify. (a−b)(a+b)( \sqrt { a } - b ) ( \sqrt { a } + b )(a​−b)(a​+b)

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

Equations and Graphs

Functions

Polynomial and Rational Functions

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Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Filters

Simplify the expression. $\frac { 2 y ^ { 2 } - 3 y - 5 } { 4 y ^ { 2 } - 25 } \div \frac { y ^ { 2 } - 6 y - 7 } { 2 y ^ { 2 } - 9 y - 35 }$

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

Simplify the expression. $\frac { 1 + \frac { 1 } { x - 3 } } { 1 - \frac { 1 } { x - 3 } }$

Evaluate the expression using $x = 4 , y = 5 , \text { and } z = - 2$ . $\sqrt [ 4 ] { x ^ { 3 } + 40 y + 4 z }$

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

Simplify the expression. Eliminate any negative exponents. $\frac { \left( x ^ { 7 } y ^ { 8 } \right) ^ { 5 } \left( x ^ { 2 } y ^ { 6 } \right) ^ { - 5 } } { x ^ { 2 } y ^ { 18 } }$

Perform the indicated operations and simplify. $2 ( 4 t - 1 ) - \left( t ^ { 2 } + 1 \right) - 4 t ( t - 5 )$

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

Simplify the expression. $\frac { 1 + \frac { 1 } { x - 5 } } { 1 - \frac { 1 } { x - 5 } }$

Evaluate the expression using $x = 4 , y = 5 , \text { and } z = - 2$ . $\sqrt [ 4 ] { x ^ { 3 } + 40 y + 4 z }$

Perform the indicated operations and simplify. $3 ( 3 t - 5 ) - \left( t ^ { 2 } + 3 \right) - 5 t ( t - 2 )$

Factor the trinomial. $5 x ^ { 2 } - 29 x + 20$

Perform the indicated operation and simplify. $\left( x ^ { 2 } + x - 10 \right) \left( x ^ { 3 } - x + 5 \right)$

Multiply the algebraic expressions using a Special Product Formula and simplify. $( \sqrt { a } - b ) ( \sqrt { a } + b )$