Algebra and Trigonometry Enhanced with Graphing Utilities (7th Edition)

Chapter 1

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Rational Numbers ; Rational Numbers are numbers ... more

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; Use the order of operations (PEMDAS = ... more

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Distributive ; The Distributive Property is ... more

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; The product (also known as the multiplication) ... more

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The intersection of two sets is denoted as . ; ... more

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Counting Numbers (also known as ‘Natural Numbers... more

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Rational numbers are defined as numbers that can ... more

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The Zero-Product Property states that if , then ... more

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The least common multiple of and is . would be ... more

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The set of rational numbers and irrational ... more

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; Take all elements from set and set . ; is ... more

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; Take all elements from set and set to find . ... more

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; Take the elements that are in both set and set... more

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; Take the elements that are in both set and set... more

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; Take all elements from set and set to find... more

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; Take all elements that are in both set and set... more

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; is the complement of set , meaning all the ... more

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; is the complement of set , meaning all the ... more

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; is the complement of set , meaning all the ... more

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; is the complement of set , meaning all the ... more

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; First, find the complement of sets and . is ... more

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; First, we will find the complement of sets and... more

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(a) (b) ; For rounding to three decimal places, ... more

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(a) (b) ; For rounding to three decimal places, ... more

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(a) (b) ; For rounding to three decimal places, ... more

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(a) (b) ; For rounding to three decimal places, ... more

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(a) (b) ; For rounding to three decimal places, ... more

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(a) (b) ; For rounding to three decimal places, ... more

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(a) (b) ; For rounding to three decimal places, ... more

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(a) (b) ; For rounding to three decimal places, ... more

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(a) (b) ; is approximately equal to . For ... more

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(a) (b) ; is approximately equal to . For ... more

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(a) (b) ; is approximately equal to . For ... more

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(a) (b) ; equates to . For rounding to the ... more

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; The word ‘sum’ always implies addition of terms... more

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; The word ‘product’ always implies ... more

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; The word ‘sum’ always implies addition of terms... more

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; The word ‘sum’ always implies addition of terms... more

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; The word ‘product’ always implies ... more

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; The word ‘product’ always implies ... more

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; The word ‘difference’ implies a subtraction of ... more

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; The word ‘difference’ implies a subtraction of ... more

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; The word ‘quotient’ implies a division of two ... more

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; The word ‘quotient’ implies a division of two ... more

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; Since addition is commutative, the order of the... more

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; Since addition is commutative, the order of the... more

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; Using the order of operations of PEMDAS, we ... more

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; Using the order of operations of PEMDAS, we ... more

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; Since addition is commutative, the order of the... more

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; Use the order of operations PEMDAS. Perform the... more

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; In order to add fractions, we need to make sure... more

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; In order to add/subtract fractions, we need to ... more

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; Using order of operations PEMDAS, we first look... more

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; Using order of operations PEMDAS, we first look... more

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; Using order of operations PEMDAS, we first look... more

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; Using order of operations PEMDAS, we first look... more

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; Using order of operations PEMDAS, we first look... more

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; Using order of operations PEMDAS, we first look... more

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; First, perform the operation inside the ... more

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; First, perform the operation inside the ... more

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; Perform the operations in the numerator and ... more

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; Perform the operations in the numerator and ... more

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; Multiply the fractions by taking the product of... more

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; Multiply the fractions by taking the product of... more

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; Since multiplication is commutative, we can ... more

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; Since multiplication is commutative, we can ... more

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; To add fractions, the denominators of the ... more

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; To add fractions, the denominators of the ... more

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; To add fractions, the denominators of the ... more

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; To add fractions, the denominators of the ... more

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; To add fractions, the denominators of the ... more

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; To add fractions, the denominators of the ... more

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; To add/subtract fractions, the denominators of ... more

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; To add/subtract fractions, the denominators of ... more

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; To add/subtract fractions, the denominators of ... more

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; To add/subtract fractions, the denominators of ... more

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; Since fractions are just division operators, we... more

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; Since fractions are just division operators, we... more

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; By the order of operations (PEMDAS), begin by ... more

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; By the order of operations (PEMDAS), begin by ... more

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; By the order of operations (PEMDAS), begin by ... more

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; By the order of operations (PEMDAS), begin by ... more

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; Use the Distributive Property. ; more

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; Use the Distributive Property. ; more

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; Use the Distributive Property. ; more

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; Use the Distributive Property. ; more

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; Use the Distributive Property to multiply. ; ... more

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; Use the Distributive Property. ; Simplify the ... more

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; Use the Distributive Property, also known as ... more

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; Use the Distributive Property, also known as ... more

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; Use the Distributive Property, also known as ... more

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; Use the Distributive Property, also known as ... more

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; Use the Distributive Property, also known as ... more

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; Use the Distributive Property, also known as ... more

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The distributive tells us that is equivalent to... more

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When two or more operations are present in the ... more

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since and . ; The distributive property states ... more

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The division of two additions is not the same as ... more

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Subtraction is not commutative since the order in ... more

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Subtraction is not associative since changing ... more

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Division is not commutative since the order in ... more

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Division is not associative because changing where... more

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Symmetric property ; The symmetric property states... more

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Symmetric property ; The symmetric property states... more

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There does not exist any number that is both ... more

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The sum of a rational number and an irrational ... more

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The pattern for fractions that have terminating ... more

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1:00 AM (CST) ; Here, we use the concept of Modulo... more

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is undefined since there exists no number  that ... more

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Variable ; Variables are used to denote an unknown... more

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Origin ; The origin of a line or a graph ... more

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Origin ; The origin of a line or a graph ... more

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Base ; The base of the expression is the number/... more

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; We move the decimal 3 places to the left, ... more

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This is one of the properties of multiplication. ... more

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Since distance is always positive and computed as ... more

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Since is a real number, and , this statement is ... more

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A number expressed in scientific notation is ... more

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To multiply two expressions with the same base, ... more

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defines the negative real numbers. ; defines the... more

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= ... n times. By multiplying the fractions n ... more

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Here are the points , and on the real number line... more

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; is farther to the right on the real number ... more

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; is farther to the left on the real number line... more

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; is farther to the right on the real number ... more

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; is farther to the left on the real number line... more

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; is farther to the right on the real number ... more

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; is farther to the right on the real number ... more

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; is equal to , so they occupy the same place on... more

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; is farther to the right on the real number ... more

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; is farther to the left on the real number line... more

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; is equal to , so they occupy the same place on... more

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; If is positive, then is not negative or ; more

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; If is negative, then is not positive or . ; more

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; This statement says that is to the left of on... more

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; This statement says that is to the right of ... more

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; This statement says that is either to the left... more

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; This statement says that is either to the ... more

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Write the inequality using interval notation. A ... more

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Write the inequality using interval notation. A ... more

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Write the inequality using interval notation. A ... more

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Write the inequality using interval notation. A ... more

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; To find the distance between two points on a ... more

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; To find the distance between two points on a ... more

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; To find the distance between two points on a ... more

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; To find the distance between two points on a ... more

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; To find the distance between two points on a ... more

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; To find the distance between two points on a ... more

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; Use the Principle of Substitution to plug in ... more

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; Use the principle of substitution to plug in ... more

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; Use the principle of substitution to plug in ... more

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; Use the principle of substitution to plug in ... more

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; Use the principle of substitution to plug in ... more

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; Use the principle of substitution to plug in ... more

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; Use the principle of substitution to plug in ... more

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; Use the principle of substitution to plug in ... more

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; Use the principle of substitution to plug in ... more

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; Use the principle of substitution to plug in ... more

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; Use the principle of substitution to plug in ... more

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; Use the principle of substitution to plug in ... more

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; Use the principle of substitution to plug in ... more

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; Use the principle of substitution to plug in ... more

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; Use the principle of substitution to plug in ... more

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; Use the principle of substitution to plug in ... more

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; Use the principle of substitution to plug in ... more

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; Use the principle of substitution to plug in ... more

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c ; The domain of the variable is defined as the ... more

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c ; The domain of the variable is defined as the ... more

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a ; The domain of a variable is defined as the set... more

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No exclusions ; The domain of the variable is ... more

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No exclusions ; The domain of the variable is ... more

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b, d ; The domain of a variable is defined as the ... more

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b, c, d ; The domain of the variable is defined as... more

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c ; The domain of the variable is defined as the ... more

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; The domain of the variable is defined as the ... more

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; The domain of the variable is defined as the ... more

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; The domain of the variable is defined as the ... more

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; The domain of the variable is defined as the ... more

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; Plug in the value of the temperature in ... more

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; Plug in the value of the temperature in ... more

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; Plug in the value of the temperature in ... more

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; Plug in the value of the temperature in ... more

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; Perform the operations and make sure to use the... more

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; Perform the operations and make sure to use the... more

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; Perform the operations and make sure to use the... more

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; Perform the operations and make sure to use the... more

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; The multiplication of terms with matching bases... more

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; The multiplication of terms with matching bases... more

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; Simplify the expression using the Laws of ... more

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; Simplify the expression using the Laws of ... more

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; Simplify the radical. ; more

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; Simplify the radical. ; more

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; Perform the operations inside the radical. ; ... more

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; Perform the operations inside the radical. ; ... more

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; Square the expression. Use the commutative ... more

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; Take the reciprocal of the expression based on ... more

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; Rewrite the expression so that all exponents ... more

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; Rewrite the expression so that all exponents ... more

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; Rewrite the expression so that the common ... more

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; Rewrite the expression so that all exponents ... more

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; Rewrite the expression so that the common ... more

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; Rewrite the expression so that all exponents ... more

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; Rewrite the expression so that all exponents ... more

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; Rewrite the expression so that all exponents ... more

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; Rewrite the expression so that all exponents ... more

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; Rewrite the expression so that all exponents ... more

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; Plug in the values for the given variables. ; more

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; Plug in the values for the given variables. ; more

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; Plug in the values for the given variables. ; more

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; Plug in the values for the given variables. ; more

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; Plug in the values for the given variables. ; more

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; Plug in the values for the given variables. ; more

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; Plug in the values for the given variables. ; more

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; Plug in the values for the given variables. ; more

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; Plug in the values for the given variables. ; more

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; Plug in the values for the given variables. ; more

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if if ; Plug in . ; Plug in . ; more

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if if ; Plug in . ; Plug in . ; more

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; Use the Laws of Exponents to write the quotient... more

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; Instead of plugging into a calculator, use the ... more

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; Plug the expression into a calculator. ; more

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; Plug the expression into a calculator. ; more

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; Plug the expression into a calculator. ; more

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; Plug the expression into a calculator. ; more

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; Plug the expression into a calculator. ; more

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; Plug the expression into a calculator. ; more

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or  if rounded to three decimals ; Plug the ... more

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or  if rounded to three decimals ; Plug the ... more

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; To write a number in scientific notation, have ... more

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; To write a number in scientific notation, have ... more

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; To write a number in scientific notation, have ... more

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; To write a number in scientific notation, have ... more

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; To write a number in scientific notation, have ... more

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; To write a number in scientific notation, have ... more

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; To write a number in scientific notation, have ... more

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; To write a number in scientific notation, we ... more

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; Perform the calculation. ; more

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; Perform the calculation. ; more

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; Perform the calculation. ; more

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; Perform the calculation. ; more

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; Perform the calculation. ; more

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; Perform the calculation. ; more

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; Perform the calculation. ; more

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; Perform the calculation. ; more

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; The product of two terms implies a ... more

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; The perimeter, , is twice the sum of the length... more

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; The product of two terms implies a ... more

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; The product of two terms implies a ... more

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; An equilateral triangle has 3 congruent side ... more

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; An equilateral triangle has 3 congruent side ... more

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; The radius is the only variable needed to find ... more

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; The radius is the only variable needed to find ... more

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; Cubes have equal lengths for length, width, and... more

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; Cubes have equal lengths for length, width, and... more

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; Treat deposits as additions to the account, and... more

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; being 'at least' 6 units away means that the ... more

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; being 'more than' 6 units away means that the ... more

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; Perform the calculation to write the expression... more

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; To write a number in scientific notation, we ... more

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; Perform the calculation to write the expression... more

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; Perform the calculation to write the expression... more

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; To write a number in scientific notation, have ... more

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; To write a number in scientific notation, have ... more

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; First, find the number of seconds in year. ; ... more

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seconds ; Write the numbers in scientific ... more

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larger by ; Since , the fraction does not ... more

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larger by ; Since , the fraction does not ... more

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There is not a positive real number closest to... more

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; Test the conditions for the number found, . ... more

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There are a lot of similarities between the two ... more

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On the real number line, we find that is to the ... more

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Right ; A right triangle is a triangle that ... more

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; The formula for the area of a triangle is ... more

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; The formula for the circumference of a circle ... more

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Similar ; Similar triangles have equivalent ... more

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Angle-Side-Angle (ASA) is one of the methods for ... more

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Since a sphere is a 3-dimensional object, the ... more

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The Pythagorean theorem states that the square of ... more

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The converse of the Pythagorean theorem states ... more

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The surface area of a sphere is found using the ... more

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These two triangles have 3 congruent corresponding... more

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These two triangles have 2 equal corresponding ... more

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The two corresponding sides given for these ... more

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; Since the problem states that the triangle is a... more

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; Since the problem states that the triangle is a... more

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; Since the problem states that the triangle is a... more

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; Since the problem states that the triangle is a... more

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; Since the problem states that the triangle is a... more

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; Since the problem states that the triangle is a... more

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Right triangle ; Use the converse of the ... more

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Right triangle ; Use the converse of the ... more

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Not a right triangle ; Use the converse of the ... more

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Not a right triangle ; Use the converse of the ... more

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Right triangle ; Use the converse of the ... more

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Right triangle ; Use the converse of the ... more

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Not a right triangle ; Use the converse of the ... more

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Not a right triangle ; Use the converse of the ... more

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in ; Recall the formula for the area of a ... more

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cm ; Recall the formula for the area of a ... more

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in ; Recall the formula for the area of a ... more

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cm ; Recall the formula for the area of a ... more

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m m ; Recall the formula for the area and ... more

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ft ft ; Recall the formula for the area and ... more

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ft ft ; Recall the formula for the Volume of a ... more

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in in ; Recall the formula for the Volume of a ... more

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cm cm ; Recall the formula for the Volume of a ... more

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ft ft ; Recall the formula for the Volume of a ... more

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in in ; Recall the formula for the Volume of a ... more

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in in ; Recall the formula for the Volume of a ... more

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; Find the radius of the inscribed circle. Use ... more

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; Find the radius of the inscribed circle. Use ... more

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; Find the diameter, , of the circumscribed ... more

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; Find the diameter, , of the circumscribed ... more

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; Find angle A using the corresponding angle for ... more

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; Find angle A using the corresponding angle for ... more

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; Find angle A using the corresponding angle for ... more

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; Find angle A using the corresponding angle for ... more

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ft. ; To perform one revolution, a wheel must ... more

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or revolutions. ; To perform one revolution, a ... more

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; Find the area of square . ; Find the side ... more

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; Find the side length for square . ; Find the ... more

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; To find the area of the window, find the area ... more

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; To find the area of the deck, take the ... more

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paces ; Use the properties of similar triangles to... more

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; Use the properties of similar triangles to find... more

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Approximately ; Convert the height in feet to ... more

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; Convert the height in feet to miles. ; Use the ... more

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; Convert the height of 100 feet to miles. ; Use ... more

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; If a, b, c are the lengths of the sides of a ... more

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Largest rectangle area Circle encloses the most ... more

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The light from the lighthouse can be seen The ... more

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; The degree of a polynomial is the degree of the... more

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; The multiplication of these two binomials is a ... more

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; The multiplication of these two polynomials ... more

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The 'terms' of a polynomial are defined as the ... more

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In this monomial, would be the coefficient, not ... more

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is not considered a monomial since it has a ... more

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Recall that multiplying terms with exponents ... more

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To verify whether this statement is true, perform ... more

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Yes, the expression is a monomial. Variable: ; ... more

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Yes, the expression is a monomial. Variable: ; ... more

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No, the expression is not a monomial. ; A monomial... more

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No, the expression is not a monomial. ; A monomial... more

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Yes, the expression is a monomial. Variables: ; ... more

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Yes, the expression is a monomial. Variables: ; ... more

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No, the expression is not a monomial. ; A monomial... more

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No, the expression is not a monomial. ; A monomial... more

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No, the expression is not a monomial. ; A monomial... more

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No, the expression is not a monomial. ; A monomial... more

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No, the expression is not a monomial. ; A monomial... more

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Yes, the expression is a polynomial of degree . ; ... more

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Yes, the expression is a polynomial of degree . ; ... more

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Yes, the expression is a polynomial of degree . ; ... more

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No, the expression is not a polynomial. ; A ... more

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No, the expression is not a polynomial. ; A ... more

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Yes, the expression is a polynomial of degree . ; ... more

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Yes, the expression is a polynomial of degree . ; ... more

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No, the expression is not a polynomial. ; A ... more

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No, the expression is not a polynomial. ; A ... more

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; Group the like terms together. Recall that ... more

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; Group the like terms together. Recall that ... more

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; Remove the parentheses. Remember to distribute ... more

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; Remove the parentheses.Remember to distribute ... more

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; Group the like terms together. Remember that ... more

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; Group the like terms together. Remember that ... more

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; Use the Distributive Property. ; Remove the ... more

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; Use the Distributive Property. ; Group the like... more

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; Use the Distributive Property. Be sure to ... more

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; Use the Distributive Property. Remember to ... more

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; Remove the parentheses. Remember to distribute ... more

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; Remove the parentheses. Remember to distribute ... more

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; Use the Distributive Property.Remember to ... more

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; Use the Distributive Property. ; Group the like... more

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; Use the Distributive Property. ; more

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; Use the Distributive Property. ; more

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; Use the Distributive Property. ; more

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; Use the Distributive Property. ; more

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; Use the Distributive Property. This method is ... more

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; Use the Distributive Property. This method is ... more

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; Use the FOIL method to multiply the binomials. ... more

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; Use the FOIL method to multiply the binomials. ... more

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; Use the FOIL method to multiply the binomials. ... more

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; Use the FOIL method to multiply the binomials. ... more

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; Use the FOIL method to multiply the binomials. ... more

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; Use the FOIL method to multiply the binomials. ... more

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; Use the FOIL method to multiply the binomials. ... more

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; Use the FOIL method to multiply the binomials. ... more

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; Use the FOIL method to multiply the binomials. ... more

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; Use the FOIL method to multiply the binomials. ... more

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; Use the FOIL method to multiply the binomials. ... more

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; Use the FOIL method to multiply the binomials. ... more

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; Use the FOIL method to multiply the binomials. ... more

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; Use the FOIL method to multiply the binomials. ... more

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; Use the FOIL method to multiply the binomials. ... more

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; Use the FOIL method to multiply the binomials. ... more

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; Use the FOIL method to multiply the binomials. ... more

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; Use the FOIL method to multiply the binomials. ... more

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; Recognize that this is the special product of a... more

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; Recognize that this is the special product of a... more

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; Recognize that this is the special product of a... more

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; Recognize that this is the special product of a... more

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; Recognize that this is the special product ... more

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; Recall the formula for the perfect cube. ; ... more

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Recall that exponents are a shorthand for ... more

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prime ; A polynomial is prime when there are no ... more

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could not be factored into a perfect square. ... more

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; Recall the formula for factoring a polynomial... more

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; To sum together the two terms, find the Least ... more

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; Rewrite the expression using the Negative ... more

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; Rewrite the expression using the Negative ... more

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; Find the Least Common Denominator of all terms ... more

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  ; Find the Least Common Denominator of all terms... more

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; Reduce the complex expression by multiplying ... more

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; Reduce the complex expression by multiplying ... more

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; Use the negative exponent rule to express all ... more

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; Use the negative exponent rule to express all ... more

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; Reduce the complex expression by multiplying ... more

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; Use the negative exponent rule to express all ... more

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; Reduce the complex expression by multiplying ... more

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; Use the negative exponent rule to express all ... more

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; Factor out the common binomial. ; Combine like ... more

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; Factor out the common binomial. ; Combine like ... more

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; Factor out the common factor. ; Distribute ... more

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  ; Factor out the common factor. ; Distribute ... more

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; Factor out the common factor. ; Distribute ... more

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;  Factor out the common factor.  ; Distribute ... more

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;  Factor out the common factors. ;   ;  ... more

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  ;   Factor out the common factors. ;  Combine ... more

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  ;  Use the negative exponent rule to express all... more

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  ;  Use the negative exponent rule to express all... more

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   ;  Use a calculator. Round to two decimal ... more

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; Use a calculator. Round to two decimal places... more

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  ; Use a calculator. Round to two decimal places... more

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  ;   Use a calculator. Round to two decimal ... more

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    ; Use a calculator. Round to two decimal ... more

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   ; Use a calculator. Round to two decimal places... more

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   ;  Use a calculator. Round to two decimal ... more

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  ;  Use a calculator. Round to two decimal places... more

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   ; Plug in the value for length $l=64$ into the ... more

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  ; Plug in the value for length $l=16$ into the ... more

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    ; The reason that is because any real value ... more

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