Question 1

Evaluate the expression $| | - 14 | - | - 1 | |$

Accepted Answer

A)  13 
B) -15 
C)  0 
D)  15 
E)  - 13 
A)  13 
B) -15 
C)  0 
D)  15 
E)  - 13 A

Question 2

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)  $22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 }$ A

Question 3

Factor the expression by grouping terms. $2 x ^ { 3 } + x ^ { 2 } - 6 x - 3$

Accepted Answer

$\left( x ^ { 2 } - 3 \right) ( 2 x + 1 )$

Question 4

Simplify the expression. Assume the letters denote any real numbers. $\sqrt [ 3 ] { a ^ { 2 } b } \cdot \sqrt [ 3 ] { a ^ { 10 } b }$

Accepted Answer

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

Question 5

Evaluate the expression $| | - 14 | - | - 1 | |$

Accepted Answer

A)  13 
B)  -15 
C)  0 
D)  15 
E)  - 13 
A)  13 
B)  -15 
C)  0 
D)  15 
E)  - 13

Question 6

Simplify the expression. $\left( 15 x ^ { 6 } y ^ { 3 } \right) \left( \frac { 1 } { 5 } x ^ { 7 } y ^ { 3 } \right)$

Accepted Answer

The answer of Simplify the expression. \(\left( 15 x ^...

Question 7

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 8

Express the inequality $- 3 < x < 0$ in interval notation

Accepted Answer

A)  $[ - 3,0 )$ 
B)  $[ - 3,0 ]$ 
C)  $( 0,3 )$ 
D)  $( - \infty , - 3 ) \cup ( 0 , \infty )$ 
E)  $( - 3,0 )$ 
A)  $[ - 3,0 )$ 
B)  $[ - 3,0 ]$ 
C)  $( 0,3 )$ 
D)  $( - \infty , - 3 ) \cup ( 0 , \infty )$ 
E)  $( - 3,0 )$

Question 9

Evaluate the expression. $\left( \frac { 3 } { 4 } \right) ^ { - 2 }$

Accepted Answer

The answer of Evaluate the expression. \(\left( \frac { 3...

Question 10

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 11

Use a Factoring Formula to factor the expression. $$27 s ^ { 3 } - 125 t ^ { 3 }$$

Accepted Answer

A)  $( 3 s - 5 t ) \left( 9 s ^ { 2 } + 15 s t + 25 t ^ { 2 } \right)$ 
B)  $( 3 s + 5 t ) \left( 9 s ^ { 2 } - 15 s t + 25 t ^ { 2 } \right)$ 
C)  $( 3 s - 5 t ) \left( 9 s ^ { 2 } + 16 s t + 25 t ^ { 2 } \right)$ 
D)  $( 3 s + 5 t ) \left( 9 s ^ { 2 } - 17 s t + 25 t ^ { 2 } \right)$ 
E)  $( 3 s - 5 t ) \left( 9 s ^ { 2 } + 17 s t + 25 t ^ { 2 } \right)$ 
A)  $( 3 s - 5 t ) \left( 9 s ^ { 2 } + 15 s t + 25 t ^ { 2 } \right)$ 
B)  $( 3 s + 5 t ) \left( 9 s ^ { 2 } - 15 s t + 25 t ^ { 2 } \right)$ 
C)  $( 3 s - 5 t ) \left( 9 s ^ { 2 } + 16 s t + 25 t ^ { 2 } \right)$ 
D)  $( 3 s + 5 t ) \left( 9 s ^ { 2 } - 17 s t + 25 t ^ { 2 } \right)$ 
E)  $( 3 s - 5 t ) \left( 9 s ^ { 2 } + 17 s t + 25 t ^ { 2 } \right)$

Question 12

Perform the indicated operation and simplify. $\left( 2 x ^ { 6 } + 3 y ^ { 4 } \right) ^ { 2 }$

Accepted Answer

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

Question 13

Factor the expression. $64 s ^ { 2 } - y ^ { 2 }$

Accepted Answer

The answer of Factor the expression. \(64 s ^ {...

Question 14

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

Accepted Answer

A)  $\frac { 801 } { 902 }$ 
B)  $\frac { 4 } { 5 }$ 
C)  $\frac { 111 } { 125 }$ 
D)  $\frac { 1143 } { 1286 }$ 
E) none of these 
A)  $\frac { 801 } { 902 }$ 
B)  $\frac { 4 } { 5 }$ 
C)  $\frac { 111 } { 125 }$ 
D)  $\frac { 1143 } { 1286 }$ 
E) none of these

Question 15

Evaluate the expression $| | 14 | - | - 1 | |$

Accepted Answer

A)  15 
B)  - 13 
C)  13 
D)  -15 
E)  0 
A)  15 
B)  - 13 
C)  13 
D)  -15 
E)  0

Question 16

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

Accepted Answer

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

Question 17

Perform the indicated operation and simplify. $\left( 5 x ^ { 4 } + 6 y ^ { 6 } \right) ^ { 2 }$

Accepted Answer

A)  $25 x ^ { 8 } - 60 x ^ { 4 } y ^ { 6 } - 36 y ^ { 12 }$ 
B)  $25 x ^ { 8 } + 60 x ^ { 4 } y ^ { 6 } + 36 y ^ { 12 }$ 
C)  $25 x ^ { 8 } + 30 x ^ { 4 } y ^ { 6 } + 36 y ^ { 12 }$ 
D)  $25 x ^ { 8 } - 30 x ^ { 4 } y ^ { 6 } + 36 y ^ { 12 }$ 
E)  $25 x ^ { 8 } - 60 x ^ { 4 } y ^ { 6 } + 36 y ^ { 12 }$ 
A)  $25 x ^ { 8 } - 60 x ^ { 4 } y ^ { 6 } - 36 y ^ { 12 }$ 
B)  $25 x ^ { 8 } + 60 x ^ { 4 } y ^ { 6 } + 36 y ^ { 12 }$ 
C)  $25 x ^ { 8 } + 30 x ^ { 4 } y ^ { 6 } + 36 y ^ { 12 }$ 
D)  $25 x ^ { 8 } - 30 x ^ { 4 } y ^ { 6 } + 36 y ^ { 12 }$ 
E)  $25 x ^ { 8 } - 60 x ^ { 4 } y ^ { 6 } + 36 y ^ { 12 }$

Question 18

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

Accepted Answer

The answer of Evaluate the arithmetic expression. \(( 6 +...

Question 19

Evaluate the arithmetic expression. $\frac { 2 + 7 } { 3 } - 6 [ 15 - ( 17 - 2 \cdot 3 ) ]$

Accepted Answer

A) 20 
B) 27 
C) -36 
D)  36 
E)  none of these 
A) 20 
B) 27 
C) -36 
D)  36 
E)  none of these

Question 20

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

Accepted Answer

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

Evaluate the expression $| | - 14 | - | - 1 | |$

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

Factor the expression by grouping terms. $2 x ^ { 3 } + x ^ { 2 } - 6 x - 3$

Simplify the expression. Assume the letters denote any real numbers. $\sqrt [ 3 ] { a ^ { 2 } b } \cdot \sqrt [ 3 ] { a ^ { 10 } b }$

Evaluate the expression $| | - 14 | - | - 1 | |$

Simplify the expression. $\left( 15 x ^ { 6 } y ^ { 3 } \right) \left( \frac { 1 } { 5 } x ^ { 7 } y ^ { 3 } \right)$

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

Express the inequality $- 3 < x < 0$ in interval notation

Evaluate the expression. $\left( \frac { 3 } { 4 } \right) ^ { - 2 }$

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

Use a Factoring Formula to factor the expression. $27 s ^ { 3 } - 125 t ^ { 3 }$

Perform the indicated operation and simplify. $\left( 2 x ^ { 6 } + 3 y ^ { 4 } \right) ^ { 2 }$

Factor the expression. $64 s ^ { 2 } - y ^ { 2 }$

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

Evaluate the expression $| | 14 | - | - 1 | |$

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

Perform the indicated operation and simplify. $\left( 5 x ^ { 4 } + 6 y ^ { 6 } \right) ^ { 2 }$

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

Evaluate the arithmetic expression. $\frac { 2 + 7 } { 3 } - 6 [ 15 - ( 17 - 2 \cdot 3 ) ]$

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

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Exam 14: Counting and Probability

Evaluate the expression ∣∣−14∣−∣−1∣∣| | - 14 | - | - 1 | |∣∣−14∣−∣−1∣∣

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​}

Factor the expression by grouping terms. 2x3+x2−6x−32 x ^ { 3 } + x ^ { 2 } - 6 x - 32x3+x2−6x−3

Simplify the expression. Assume the letters denote any real numbers. a2b3⋅a10b3\sqrt [ 3 ] { a ^ { 2 } b } \cdot \sqrt [ 3 ] { a ^ { 10 } b }3a2b​⋅3a10b​

Evaluate the expression ∣∣−14∣−∣−1∣∣| | - 14 | - | - 1 | |∣∣−14∣−∣−1∣∣

Simplify the expression. (15x6y3)(15x7y3)\left( 15 x ^ { 6 } y ^ { 3 } \right) \left( \frac { 1 } { 5 } x ^ { 7 } y ^ { 3 } \right)(15x6y3)(51​x7y3)

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​

Express the inequality −3<x<0- 3 < x < 0−3<x<0 in interval notation

Evaluate the expression. (34)−2\left( \frac { 3 } { 4 } \right) ^ { - 2 }(43​)−2

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​

Use a Factoring Formula to factor the expression. 27s3−125t327 s ^ { 3 } - 125 t ^ { 3 }27s3−125t3

Perform the indicated operation and simplify. (2x6+3y4)2\left( 2 x ^ { 6 } + 3 y ^ { 4 } \right) ^ { 2 }(2x6+3y4)2

Factor the expression. 64s2−y264 s ^ { 2 } - y ^ { 2 }64s2−y2

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

Evaluate the expression ∣∣14∣−∣−1∣∣| | 14 | - | - 1 | |∣∣14∣−∣−1∣∣

Perform the indicated operations 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)

Perform the indicated operation and simplify. (5x4+6y6)2\left( 5 x ^ { 4 } + 6 y ^ { 6 } \right) ^ { 2 }(5x4+6y6)2

Evaluate the arithmetic expression. (6+9)/5−3[15−(17−2⋅3)]( 6 + 9 ) / 5 - 3 [ 15 - ( 17 - 2 \cdot 3 ) ](6+9)/5−3[15−(17−2⋅3)]

Evaluate the arithmetic expression. 2+73−6[15−(17−2⋅3)]\frac { 2 + 7 } { 3 } - 6 [ 15 - ( 17 - 2 \cdot 3 ) ]32+7​−6[15−(17−2⋅3)]

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​

Equations and Graphs

Functions

Polynomial and Rational Functions

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Systems of Equations and Inequalities

Matrices and Determinants

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Sequences and Series

Filters

Evaluate the expression $| | - 14 | - | - 1 | |$

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

Factor the expression by grouping terms. $2 x ^ { 3 } + x ^ { 2 } - 6 x - 3$

Simplify the expression. Assume the letters denote any real numbers. $\sqrt [ 3 ] { a ^ { 2 } b } \cdot \sqrt [ 3 ] { a ^ { 10 } b }$

Evaluate the expression $| | - 14 | - | - 1 | |$

Simplify the expression. $\left( 15 x ^ { 6 } y ^ { 3 } \right) \left( \frac { 1 } { 5 } x ^ { 7 } y ^ { 3 } \right)$

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

Express the inequality $- 3 < x < 0$ in interval notation

Evaluate the expression. $\left( \frac { 3 } { 4 } \right) ^ { - 2 }$

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

Use a Factoring Formula to factor the expression. $27 s ^ { 3 } - 125 t ^ { 3 }$

Perform the indicated operation and simplify. $\left( 2 x ^ { 6 } + 3 y ^ { 4 } \right) ^ { 2 }$

Factor the expression. $64 s ^ { 2 } - y ^ { 2 }$

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

Evaluate the expression $| | 14 | - | - 1 | |$

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

Perform the indicated operation and simplify. $\left( 5 x ^ { 4 } + 6 y ^ { 6 } \right) ^ { 2 }$

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

Evaluate the arithmetic expression. $\frac { 2 + 7 } { 3 } - 6 [ 15 - ( 17 - 2 \cdot 3 ) ]$

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