Exam 10: Math Exercises: Sets, Intervals, Absolute Value, and Properties

Write the given set in interval notation and graph the set on a number line. - $|x| x<-2 \mid$ $Write the given set in interval notation and graph the set on a number line. - |x| x<-2 \mid$

(Multiple Choice)

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Question 121

Completely factor the polynomial or state that the polynomial is prime. - $x ^ { 2 } - x - 63$

(Multiple Choice)

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Question 122

Simplify the rational expression. - $\frac { 4 x ^ { 2 } - 11 x - 3 } { 2 x ^ { 2 } - 9 x + 9 }$

(Multiple Choice)

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Question 123

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt { 36 y ^ { 18 } }$

(Multiple Choice)

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Question 124

Find the intersection of the given intervals. - $( \infty , 10 ] \cap [ - 8 , \infty ) \cap ( \infty , 1 )$

(Multiple Choice)

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Question 125

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { \frac { 5 } { x } + 3 } { \frac { 25 } { x ^ { 2 } } - 9 }$

(Multiple Choice)

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Question 126

Simplify the expression using the order of operations. -21 + (25 ·4)- 14

(Multiple Choice)

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Question 127

Find the quotient and the remainder. - $5 x ^ { 3 } - 7 x ^ { 2 } + 7 x - 8$ divided by $5 x - 2$

(Multiple Choice)

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Question 128

Find the intersection of the given intervals. - $( - \infty , \infty ) \cap [ - 9 , \infty )$

(Multiple Choice)

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Question 129

Write the given set in interval notation and graph the set on a number line. - $\left\{ x \mid - 5 < x < \frac { 1 } { 2 } \right\}$ $Write the given set in interval notation and graph the set on a number line. - \left\{ x \mid - 5 < x < \frac { 1 } { 2 } \right\}$

(Multiple Choice)

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Question 130

Write the interval in set-builder notation and graph the set on a number line. - $\left[ - \frac { 1 } { 2 } , 3 \right)$ $Write the interval in set-builder notation and graph the set on a number line. - \left[ - \frac { 1 } { 2 } , 3 \right)$

(Multiple Choice)

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Question 131

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. -(-2x + 7)(x + 8)

(Multiple Choice)

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Question 132

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 1 - \frac { 8 } { x } } { 1 + \frac { 8 } { x } }$

(Multiple Choice)

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Question 133

Use the associative property of multiplication to write an equivalent algebraic expression. - $5 ( 8 ( a + b ) )$

(Multiple Choice)

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Question 134

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $x ^ { 9 } x ^ { - 6 }$

(Multiple Choice)

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Question 135

Sets A, B, and C are given. Find the indicated set. A = {-8, -3, -1, 2, 5}, B = {-3, 2, 5, 7}, and C = {-1, 4, 9} - $A \cap B$

(Multiple Choice)

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Question 136

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt { 567 x ^ { 2 } }$

(Multiple Choice)

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Question 137

Use the distributive property to multiply the given expressions. - $( a + 2 ) 7$

(Multiple Choice)

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Question 138

Simplify the rational expression. - $\frac { y ^ { 2 } + 13 y + 42 } { y ^ { 2 } + 16 y + 63 }$

(Multiple Choice)

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Question 139

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - $( 13 x + 11 ) ( 13 x - 11 )$

(Multiple Choice)

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Question 140

Showing 121 - 140 of 298

Write the given set in interval notation and graph the set on a number line. - $|x| x<-2 \mid$ $Write the given set in interval notation and graph the set on a number line. - |x| x<-2 \mid$

Completely factor the polynomial or state that the polynomial is prime. - $x ^ { 2 } - x - 63$

Simplify the rational expression. - $\frac { 4 x ^ { 2 } - 11 x - 3 } { 2 x ^ { 2 } - 9 x + 9 }$

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt { 36 y ^ { 18 } }$

Find the intersection of the given intervals. - $( \infty , 10 ] \cap [ - 8 , \infty ) \cap ( \infty , 1 )$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { \frac { 5 } { x } + 3 } { \frac { 25 } { x ^ { 2 } } - 9 }$

Simplify the expression using the order of operations. -21 + (25 ·4)- 14

Find the quotient and the remainder. - $5 x ^ { 3 } - 7 x ^ { 2 } + 7 x - 8$ divided by $5 x - 2$

Find the intersection of the given intervals. - $( - \infty , \infty ) \cap [ - 9 , \infty )$

Write the given set in interval notation and graph the set on a number line. - $\left\{ x \mid - 5 < x < \frac { 1 } { 2 } \right\}$ $Write the given set in interval notation and graph the set on a number line. - \left\{ x \mid - 5 < x < \frac { 1 } { 2 } \right\}$

Write the interval in set-builder notation and graph the set on a number line. - $\left[ - \frac { 1 } { 2 } , 3 \right)$ $Write the interval in set-builder notation and graph the set on a number line. - \left[ - \frac { 1 } { 2 } , 3 \right)$

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. -(-2x + 7)(x + 8)

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 1 - \frac { 8 } { x } } { 1 + \frac { 8 } { x } }$

Use the associative property of multiplication to write an equivalent algebraic expression. - $5 ( 8 ( a + b ) )$

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $x ^ { 9 } x ^ { - 6 }$

Sets A, B, and C are given. Find the indicated set. A = {-8, -3, -1, 2, 5}, B = {-3, 2, 5, 7}, and C = {-1, 4, 9} - $A \cap B$

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt { 567 x ^ { 2 } }$

Use the distributive property to multiply the given expressions. - $( a + 2 ) 7$

Simplify the rational expression. - $\frac { y ^ { 2 } + 13 y + 42 } { y ^ { 2 } + 16 y + 63 }$

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - $( 13 x + 11 ) ( 13 x - 11 )$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Filters

Exam 10: Math Exercises: Sets, Intervals, Absolute Value, and Properties

Write the given set in interval notation and graph the set on a number line. - ∣x∣x<−2∣|x| x<-2 \mid∣x∣x<−2∣

Completely factor the polynomial or state that the polynomial is prime. - x2−x−63x ^ { 2 } - x - 63x2−x−63

Simplify the rational expression. - 4x2−11x−32x2−9x+9\frac { 4 x ^ { 2 } - 11 x - 3 } { 2 x ^ { 2 } - 9 x + 9 }2x2−9x+94x2−11x−3​

Simplify the radical expression. Assume all variables represent positive real numbers. - 36y18\sqrt { 36 y ^ { 18 } }36y18​

Find the intersection of the given intervals. - (∞,10]∩[−8,∞)∩(∞,1)( \infty , 10 ] \cap [ - 8 , \infty ) \cap ( \infty , 1 )(∞,10]∩[−8,∞)∩(∞,1)

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 5x+325x2−9\frac { \frac { 5 } { x } + 3 } { \frac { 25 } { x ^ { 2 } } - 9 }x225​−9x5​+3​

Simplify the expression using the order of operations. -21 + (25 ·4)- 14

Find the quotient and the remainder. - 5x3−7x2+7x−85 x ^ { 3 } - 7 x ^ { 2 } + 7 x - 85x3−7x2+7x−8 divided by 5x−25 x - 25x−2

Find the intersection of the given intervals. - (−∞,∞)∩[−9,∞)( - \infty , \infty ) \cap [ - 9 , \infty )(−∞,∞)∩[−9,∞)

Write the given set in interval notation and graph the set on a number line. - {x∣−5<x<12}\left\{ x \mid - 5 < x < \frac { 1 } { 2 } \right\}{x∣−5<x<21​}

Write the interval in set-builder notation and graph the set on a number line. - [−12,3)\left[ - \frac { 1 } { 2 } , 3 \right)[−21​,3)

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. -(-2x + 7)(x + 8)

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 1−8x1+8x\frac { 1 - \frac { 8 } { x } } { 1 + \frac { 8 } { x } }1+x8​1−x8​​

Use the associative property of multiplication to write an equivalent algebraic expression. - 5(8(a+b))5 ( 8 ( a + b ) )5(8(a+b))

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - x9x−6x ^ { 9 } x ^ { - 6 }x9x−6

Sets A, B, and C are given. Find the indicated set. A = {-8, -3, -1, 2, 5}, B = {-3, 2, 5, 7}, and C = {-1, 4, 9} - A∩BA \cap BA∩B

Simplify the radical expression. Assume all variables represent positive real numbers. - 567x2\sqrt { 567 x ^ { 2 } }567x2​

Use the distributive property to multiply the given expressions. - (a+2)7( a + 2 ) 7(a+2)7

Simplify the rational expression. - y2+13y+42y2+16y+63\frac { y ^ { 2 } + 13 y + 42 } { y ^ { 2 } + 16 y + 63 }y2+16y+63y2+13y+42​

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - (13x+11)(13x−11)( 13 x + 11 ) ( 13 x - 11 )(13x+11)(13x−11)

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Filters

Write the given set in interval notation and graph the set on a number line. - $|x| x<-2 \mid$ $Write the given set in interval notation and graph the set on a number line. - |x| x<-2 \mid$

Completely factor the polynomial or state that the polynomial is prime. - $x ^ { 2 } - x - 63$

Simplify the rational expression. - $\frac { 4 x ^ { 2 } - 11 x - 3 } { 2 x ^ { 2 } - 9 x + 9 }$

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt { 36 y ^ { 18 } }$

Find the intersection of the given intervals. - $( \infty , 10 ] \cap [ - 8 , \infty ) \cap ( \infty , 1 )$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { \frac { 5 } { x } + 3 } { \frac { 25 } { x ^ { 2 } } - 9 }$

Find the quotient and the remainder. - $5 x ^ { 3 } - 7 x ^ { 2 } + 7 x - 8$ divided by $5 x - 2$

Find the intersection of the given intervals. - $( - \infty , \infty ) \cap [ - 9 , \infty )$

Write the given set in interval notation and graph the set on a number line. - $\left\{ x \mid - 5 < x < \frac { 1 } { 2 } \right\}$ $Write the given set in interval notation and graph the set on a number line. - \left\{ x \mid - 5 < x < \frac { 1 } { 2 } \right\}$

Write the interval in set-builder notation and graph the set on a number line. - $\left[ - \frac { 1 } { 2 } , 3 \right)$ $Write the interval in set-builder notation and graph the set on a number line. - \left[ - \frac { 1 } { 2 } , 3 \right)$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 1 - \frac { 8 } { x } } { 1 + \frac { 8 } { x } }$

Use the associative property of multiplication to write an equivalent algebraic expression. - $5 ( 8 ( a + b ) )$

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $x ^ { 9 } x ^ { - 6 }$

Sets A, B, and C are given. Find the indicated set. A = {-8, -3, -1, 2, 5}, B = {-3, 2, 5, 7}, and C = {-1, 4, 9} - $A \cap B$

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt { 567 x ^ { 2 } }$

Use the distributive property to multiply the given expressions. - $( a + 2 ) 7$

Simplify the rational expression. - $\frac { y ^ { 2 } + 13 y + 42 } { y ^ { 2 } + 16 y + 63 }$

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - $( 13 x + 11 ) ( 13 x - 11 )$