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

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { x ^ { 2 } - 10 x + 25 } { 11 x - 55 } \div \frac { 9 x - 45 } { 99 }$

(Multiple Choice)

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Question 41

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $49 ^ { 1 / 2 }$

(Multiple Choice)

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Question 42

Completely factor the polynomial or state that the polynomial is prime. - $\mathrm { x } ^ { 2 } + 64$

(Multiple Choice)

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Question 43

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 8 } { x ^ { 2 } } - \frac { 6 } { x }$

(Multiple Choice)

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Question 44

Completely factor the polynomial or state that the polynomial is prime. - $64 x ^ { 2 } + 144 x + 81$

(Multiple Choice)

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Question 45

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 9 x ^ { 4 } - 72 x } { 3 x ^ { 2 } - 12 } \cdot \frac { x ^ { 2 } + x - 2 } { 4 x ^ { 3 } + 8 x ^ { 2 } + 16 x }$

(Multiple Choice)

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Question 46

Completely factor the polynomial or state that the polynomial is prime. - $12 x ^ { 2 } + 17 x + 6$

(Multiple Choice)

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Question 47

Use the associative property of addition to write an equivalent algebraic expression. - $( n p + f ) + m$

(Multiple Choice)

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Question 48

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 9 x } { x - 6 } + \frac { 2 } { 6 - x }$

(Multiple Choice)

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Question 49

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { x ^ { 2 } + 11 x + 30 } { x ^ { 2 } + 12 x + 36 } \cdot \frac { x ^ { 2 } + 6 x } { x ^ { 2 } - 3 x - 40 }$

(Multiple Choice)

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Question 50

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 4 + \frac { 2 } { x } } { \frac { x } { 3 } + \frac { 1 } { 6 } }$

(Multiple Choice)

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Question 51

Use the distributive property to multiply the given expressions. - $2 ( 7 x + 3 )$

(Multiple Choice)

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Question 52

Use the commutative property of multiplication to write an equivalent algebraic expression. - $4 \cdot x$

(Multiple Choice)

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Question 53

$\left. (- 7 x ^ { 3 } y ^ { 4 } \right) ^ { 2 }$

(Multiple Choice)

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Question 54

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. -(x + 6)(x - 2)

(Multiple Choice)

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Question 55

Completely factor the polynomial or state that the polynomial is prime. - $1000 x ^ { 3 } - 343$

(Multiple Choice)

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Question 56

Find the intersection of the given intervals. - $( - 3,9 ] \cap ( - 8,4 ]$

(Multiple Choice)

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Question 57

List all the elements of B that belong to the given set. - $B = \left\{ 2 , \sqrt { 6 } , - 17,0 , \frac { 0 } { 8 } , 0.33 \right\}$ Irrational numbers

(Multiple Choice)

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Question 58

Simplify the rational expression. - $\frac { x ^ { 2 } + 10 x + 24 } { x ^ { 2 } + 14 x + 48 }$

(Multiple Choice)

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Question 59

Completely factor the polynomial or state that the polynomial is prime. - $12 z ^ { 2 } - 7 z - 12$

(Multiple Choice)

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Question 60

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { x ^ { 2 } - 10 x + 25 } { 11 x - 55 } \div \frac { 9 x - 45 } { 99 }$

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $49 ^ { 1 / 2 }$

Completely factor the polynomial or state that the polynomial is prime. - $\mathrm { x } ^ { 2 } + 64$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 8 } { x ^ { 2 } } - \frac { 6 } { x }$

Completely factor the polynomial or state that the polynomial is prime. - $64 x ^ { 2 } + 144 x + 81$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 9 x ^ { 4 } - 72 x } { 3 x ^ { 2 } - 12 } \cdot \frac { x ^ { 2 } + x - 2 } { 4 x ^ { 3 } + 8 x ^ { 2 } + 16 x }$

Completely factor the polynomial or state that the polynomial is prime. - $12 x ^ { 2 } + 17 x + 6$

Use the associative property of addition to write an equivalent algebraic expression. - $( n p + f ) + m$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 9 x } { x - 6 } + \frac { 2 } { 6 - x }$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { x ^ { 2 } + 11 x + 30 } { x ^ { 2 } + 12 x + 36 } \cdot \frac { x ^ { 2 } + 6 x } { x ^ { 2 } - 3 x - 40 }$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 4 + \frac { 2 } { x } } { \frac { x } { 3 } + \frac { 1 } { 6 } }$

Use the distributive property to multiply the given expressions. - $2 ( 7 x + 3 )$

Use the commutative property of multiplication to write an equivalent algebraic expression. - $4 \cdot x$

$\left. (- 7 x ^ { 3 } y ^ { 4 } \right) ^ { 2 }$

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. -(x + 6)(x - 2)

Completely factor the polynomial or state that the polynomial is prime. - $1000 x ^ { 3 } - 343$

Find the intersection of the given intervals. - $( - 3,9 ] \cap ( - 8,4 ]$

List all the elements of B that belong to the given set. - $B = \left\{ 2 , \sqrt { 6 } , - 17,0 , \frac { 0 } { 8 } , 0.33 \right\}$ Irrational numbers

Simplify the rational expression. - $\frac { x ^ { 2 } + 10 x + 24 } { x ^ { 2 } + 14 x + 48 }$

Completely factor the polynomial or state that the polynomial is prime. - $12 z ^ { 2 } - 7 z - 12$

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

Perform the indicated operations and simplify the result. Leave the answer in factored form. - x2−10x+2511x−55÷9x−4599\frac { x ^ { 2 } - 10 x + 25 } { 11 x - 55 } \div \frac { 9 x - 45 } { 99 }11x−55x2−10x+25​÷999x−45​

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - 491/249 ^ { 1 / 2 }491/2

Completely factor the polynomial or state that the polynomial is prime. - x2+64\mathrm { x } ^ { 2 } + 64x2+64

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 8x2−6x\frac { 8 } { x ^ { 2 } } - \frac { 6 } { x }x28​−x6​

Completely factor the polynomial or state that the polynomial is prime. - 64x2+144x+8164 x ^ { 2 } + 144 x + 8164x2+144x+81

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 9x4−72x3x2−12⋅x2+x−24x3+8x2+16x\frac { 9 x ^ { 4 } - 72 x } { 3 x ^ { 2 } - 12 } \cdot \frac { x ^ { 2 } + x - 2 } { 4 x ^ { 3 } + 8 x ^ { 2 } + 16 x }3x2−129x4−72x​⋅4x3+8x2+16xx2+x−2​

Completely factor the polynomial or state that the polynomial is prime. - 12x2+17x+612 x ^ { 2 } + 17 x + 612x2+17x+6

Use the associative property of addition to write an equivalent algebraic expression. - (np+f)+m( n p + f ) + m(np+f)+m

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 9xx−6+26−x\frac { 9 x } { x - 6 } + \frac { 2 } { 6 - x }x−69x​+6−x2​

Perform the indicated operations and simplify the result. Leave the answer in factored form. - x2+11x+30x2+12x+36⋅x2+6xx2−3x−40\frac { x ^ { 2 } + 11 x + 30 } { x ^ { 2 } + 12 x + 36 } \cdot \frac { x ^ { 2 } + 6 x } { x ^ { 2 } - 3 x - 40 }x2+12x+36x2+11x+30​⋅x2−3x−40x2+6x​

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 4+2xx3+16\frac { 4 + \frac { 2 } { x } } { \frac { x } { 3 } + \frac { 1 } { 6 } }3x​+61​4+x2​​

Use the distributive property to multiply the given expressions. - 2(7x+3)2 ( 7 x + 3 )2(7x+3)

Use the commutative property of multiplication to write an equivalent algebraic expression. - 4⋅x4 \cdot x4⋅x

(−7x3y4)2\left. (- 7 x ^ { 3 } y ^ { 4 } \right) ^ { 2 }(−7x3y4)2

Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. -(x + 6)(x - 2)

Completely factor the polynomial or state that the polynomial is prime. - 1000x3−3431000 x ^ { 3 } - 3431000x3−343

Find the intersection of the given intervals. - (−3,9]∩(−8,4]( - 3,9 ] \cap ( - 8,4 ](−3,9]∩(−8,4]

List all the elements of B that belong to the given set. - B={2,6,−17,0,08,0.33}B = \left\{ 2 , \sqrt { 6 } , - 17,0 , \frac { 0 } { 8 } , 0.33 \right\}B={2,6​,−17,0,80​,0.33} Irrational numbers

Simplify the rational expression. - x2+10x+24x2+14x+48\frac { x ^ { 2 } + 10 x + 24 } { x ^ { 2 } + 14 x + 48 }x2+14x+48x2+10x+24​

Completely factor the polynomial or state that the polynomial is prime. - 12z2−7z−1212 z ^ { 2 } - 7 z - 1212z2−7z−12

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

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { x ^ { 2 } - 10 x + 25 } { 11 x - 55 } \div \frac { 9 x - 45 } { 99 }$

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $49 ^ { 1 / 2 }$

Completely factor the polynomial or state that the polynomial is prime. - $\mathrm { x } ^ { 2 } + 64$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 8 } { x ^ { 2 } } - \frac { 6 } { x }$

Completely factor the polynomial or state that the polynomial is prime. - $64 x ^ { 2 } + 144 x + 81$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 9 x ^ { 4 } - 72 x } { 3 x ^ { 2 } - 12 } \cdot \frac { x ^ { 2 } + x - 2 } { 4 x ^ { 3 } + 8 x ^ { 2 } + 16 x }$

Completely factor the polynomial or state that the polynomial is prime. - $12 x ^ { 2 } + 17 x + 6$

Use the associative property of addition to write an equivalent algebraic expression. - $( n p + f ) + m$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 9 x } { x - 6 } + \frac { 2 } { 6 - x }$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { x ^ { 2 } + 11 x + 30 } { x ^ { 2 } + 12 x + 36 } \cdot \frac { x ^ { 2 } + 6 x } { x ^ { 2 } - 3 x - 40 }$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 4 + \frac { 2 } { x } } { \frac { x } { 3 } + \frac { 1 } { 6 } }$

Use the distributive property to multiply the given expressions. - $2 ( 7 x + 3 )$

Use the commutative property of multiplication to write an equivalent algebraic expression. - $4 \cdot x$

$\left. (- 7 x ^ { 3 } y ^ { 4 } \right) ^ { 2 }$

Completely factor the polynomial or state that the polynomial is prime. - $1000 x ^ { 3 } - 343$

Find the intersection of the given intervals. - $( - 3,9 ] \cap ( - 8,4 ]$

List all the elements of B that belong to the given set. - $B = \left\{ 2 , \sqrt { 6 } , - 17,0 , \frac { 0 } { 8 } , 0.33 \right\}$ Irrational numbers

Simplify the rational expression. - $\frac { x ^ { 2 } + 10 x + 24 } { x ^ { 2 } + 14 x + 48 }$

Completely factor the polynomial or state that the polynomial is prime. - $12 z ^ { 2 } - 7 z - 12$