Algebra and Trigonometry Enhanced with Graphing Utilities (7th Edition)
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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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Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
; Recognize that this is the special product ... 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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; Multiply the divisor by to cancel the leading ... more
Verified Answer ✓
; Multiply the divisor by to cancel the leading ... more
Verified Answer ✓
; Multiply the divisor by to cancel the leading ... more
Verified Answer ✓
; Multiply the divisor by to cancel the leading ... more
Verified Answer ✓
; Multiply the divisor by to cancel the leading ... more
Verified Answer ✓
; Multiply the divisor by to cancel the leading ... more
Verified Answer ✓
; Multiply the divisor by to cancel the leading ... more
Verified Answer ✓
; Multiply the divisor by to cancel the leading ... more
Verified Answer ✓
; Multiply the divisor by to cancel the leading ... more
Verified Answer ✓
; Multiply the divisor by to cancel the leading ... more
Verified Answer ✓
; Multiply the divisor by to cancel the leading ... more
Verified Answer ✓
; Multiply the divisor by to cancel the leading ... more
Verified Answer ✓
; Multiply the divisor by to cancel the leading ... more
Verified Answer ✓
; Multiply the divisor by to cancel the leading ... more
Verified Answer ✓
; Multiply the divisor by to cancel the leading ... more
Verified Answer ✓
; Multiply the divisor by to cancel the leading ... more
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Recall that exponents are a shorthand for ... more
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For the sum of two polynomials, we can only ... more
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The degree would not change. When adding ... more
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I prefer the vertical method for adding two ... more
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I prefer to memorize the square of a binomial. ; ... more
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; Both terms have a factor of and a factor of... more
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prime ; A polynomial is prime when there are no ... more
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Using the distributive method, constant terms a ... more
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A 'prime' polynomial is a polynomial with integer ... more
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Distributing these terms would give us , which is ... more
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could not be factored into a perfect square. ... more
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Any polynomial in the form , where a is a real ... more
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Expand the right side of the equation with FOIL... more
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; Identify the common factor of the polynomial... more
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; Identify the common factor of the polynomial... more
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; Identify the common factor of the polynomial... more
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; Identify the common factor of the polynomial... more
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; Identify the common factor of the polynomial... more
Verified Answer ✓
; Identify the common factor of the polynomial... more
Verified Answer ✓
; Identify the common factor of the polynomial... more
Verified Answer ✓
; Identify the common factor of the polynomial... more
Verified Answer ✓
; Identify the common factor of the polynomial... more
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; Identify the common factor of the polynomial... more
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; Recall the formula for the difference of ... more
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; Recall the formula for the difference of ... more
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; Recall the formula for the difference of ... more
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; Recall the formula for perfect squares. ; Take ... more
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; Recall the formula for perfect squares. ; Take ... more
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; Recall the formula for perfect squares. ; Take ... more
Verified Answer ✓
; Recall the formula for perfect squares. ; Take ... more
Verified Answer ✓
; Recall the formula for perfect squares. ; Take ... more
Verified Answer ✓
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Verified Answer ✓
; Recall the formula for perfect squares. ; Take ... more
Verified Answer ✓
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Verified Answer ✓
; Recall the formula for perfect squares. ; Take ... more
Verified Answer ✓
; Recall the formula for perfect squares. ; Take ... more
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; Recall the formula for factoring a difference ... more
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; Recall the formula for factoring a sum of cubes... more
Verified Answer ✓
; Recall the formula for factoring a sum of cubes... more
Verified Answer ✓
; Recall the formula for factoring a sum of cubes... more
Verified Answer ✓
; Recall the formula for factoring a sum of cubes... more
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; Recall the formula for factoring the sum of ... more
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; Polynomials of the form where are factored ... more
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; Polynomials of the form where are factored ... more
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; Polynomials of the form where are factored ... more
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; Polynomials of the form where are factored ... more
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; Polynomials of the form where are factored ... more
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; Polynomials of the form where are factored ... more
Verified Answer ✓
; Polynomials of the form where are factored ... more
Verified Answer ✓
; Polynomials of the form where are factored ... more
Verified Answer ✓
; Polynomials of the form where are factored ... more
Verified Answer ✓
; Polynomials of the form where are factored ... more
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; Polynomials of the form where are factored ... more
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; Polynomials of the form where are factored ... more
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; Group together terms with common factors. ; ... more
Verified Answer ✓
; Group together terms with common factors. ; ... more
Verified Answer ✓
; Group together terms with common factors. ; ... more
Verified Answer ✓
; Group together terms with common factors. ; ... more
Verified Answer ✓
; Group together terms with common factors. ; ... more
Verified Answer ✓
; Group together terms with common factors. ; ... more
Verified Answer ✓
; Recall the formula for factoring a polynomial... more
Verified Answer ✓
; Recall the formula for factoring a polynomial... more
Verified Answer ✓
; Recall the formula for factoring a polynomial... more
Verified Answer ✓
; Recall the formula for factoring a polynomial... more
Verified Answer ✓
N ; Recall the formula for factoring a polynomial... more
Verified Answer ✓
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Verified Answer ✓
; Recall the formula for factoring a polynomial... more
Verified Answer ✓
; Recall the formula for factoring a polynomial... more
Verified Answer ✓
; Recall the formula for factoring a polynomial... more
Verified Answer ✓
; Recall the formula for factoring a polynomial... more
Verified Answer ✓
; Recall the formula for factoring a polynomial... more
Verified Answer ✓
; Recall the formula for factoring a polynomial... more
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; Identify , the coefficient of x, for the ... more
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; Identify , the coefficient of x, for the ... more
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; Identify , the coefficient of x, for the ... more
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; Identify the term for the binomial of the form... more
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; Identify the term for the binomial of the form... more
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; Identify the term for the binomial of the form... more
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; This polynomial is a Difference of squares. ; ... more
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; This polynomial is a Difference of squares. ; ... more
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; Factor the polynomial and Rewrite. ; This ... more
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; Factor the polynomial and Rewrite. ; This ... more
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; Polynomials of the form where are factored ... more
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; Polynomials of the form where are factored ... more
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; Polynomials of the form where are factored ... more
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; Polynomials of the form where are factored ... more
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; Factor the polynomial so that the leading ... more
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; Factor the polynomial so that the leading ... more
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The polynomial is prime ; Polynomials of the form... more
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; Polynomials of the form where are factored ... more
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; Factor the polynomial and Reorder the terms so ... more
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; Factor the polynomial and Reorder the terms so ... more
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; Factor the polynomial and Reorder the terms so ... more
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; Polynomials of the form where are factored ... more
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; Factor the polynomial for the common terms ; ... more
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; Factor the polynomial for the common terms. ; ... more
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; Recall the formula for factoring a polynomial... more
Verified Answer ✓
; Recall the formula for factoring a polynomial... more
Verified Answer ✓
; Recall the formula for factoring a polynomial... more
Verified Answer ✓
; Recall the formula for factoring a polynomial... more
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; Recall the formula for the difference of ... more
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; Recall the formula for the difference of ... more
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; Polynomials of the form where are factored ... more
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; Polynomials of the form where are factored ... more
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; Factor out the common factor. ; Recall the ... more
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; Factor out the common factor. ; Recall the ... more
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; Recall the formula for factoring a polynomial... more
Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
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; Recall the formula for factoring a polynomial. ... more
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; Notice that both terms are already factored by ... more
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; Notice that both terms are already factored by ... more
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; Rewrite the expression so that both terms have ... more
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; Since both terms are perfect cubes, this ... more
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; Since both terms have a cube root, this ... more
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; To be able to factor this expression, factor ... more
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; Group together terms with common factors. ; ... more
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; Group together terms with common factors. ; ... more
Verified Answer ✓
; Group together terms with common factors. ; ... more
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; Group together terms with common factors. ; ... more
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; Factor the constant from both terms. ; Factor ... more
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; Factor out from both terms. ; Distribute the ... more
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; Factor out from both terms. ; Factor out from... more
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; Factor out the constant from both terms. ; ... more
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; Factor out from both terms. ; Perform the ... more
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; The factor pairs for are and . Since is a ... more
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; Since is the constant term, the only factor ... more
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; Perfect squares are polynomials of the form . ... more
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Step 1: Factor out common monomial factors.Step 2... more
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Divisor ; Just as with dividing integers, the ... more
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; Divisor is written as , so in this case, . Then... more
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This division problem can be performed using ... more
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The divisor of the form has a synthetic division ... more
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The divisor has the form of in synthetic division... more
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Perform the synthetic division of the polynomial ... more
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; Use Synthetic Division to find the Quotient and... more
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; Use Synthetic Division to find the Quotient and... more
Verified Answer ✓
; Use Synthetic Division to find the Quotient and... more
Verified Answer ✓
; Use Synthetic Division to find the Quotient and... more
Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
; Use Synthetic Division to find the Quotient and... more
Verified Answer ✓
; Use Synthetic Division to find the Quotient and... more
Verified Answer ✓
; Use the result from Step 1 to find the Quotient... more
Verified Answer ✓
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Verified Answer ✓
; Use Synthetic Division to find the Quotient and... more
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is not a factor of . ; Use Synthetic Division to ... more
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is a factor of . ; Use Synthetic Division to find ... more
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is a factor of . ; Use Synthetic Division to find ... more
Verified Answer ✓
is a factor of . ; Use Synthetic Division to find ... more
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is not a factor of . ; Use Synthetic Division to ... more
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is a factor of . ; Use Synthetic Division to find... more
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is a factor of . ; Use Synthetic Division to find ... more
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is not a factor of . ; Use Synthetic Division to ... more
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; Use Synthetic Division. ; Write the result of ... more
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Synthetic division is very useful when dividing a ... more
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Lowest terms ; Lowest or simplest terms are ... more
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Least Common Multiple ; Least Common Multiple is ... more
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The numerator and denominator both have a common ... more
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Use the distributive property to factor out from... more
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To test whether this expression is in lowest terms... more
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To find the LCM of these two terms, factor each ... more
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; Factor the numerator. ; Factor the denominator... more
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; Factor the numerator by grouping. ; Continue ... more
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; Since all terms have matching denominators, we ... more
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; To take the sum of fractions, the denominators ... more
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; To find the LCM of two polynomials, write the ... more
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; To find the LCM of two polynomials, write the ... more
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; Start by finding the Least Common Multiple (LCM... more
Verified Answer ✓
; Start by finding the Least Common Multiple (LCM... more
Verified Answer ✓
; Start by finding the Least Common Multiple (LCM... more
Verified Answer ✓
; Start by finding the Least Common Multiple (LCM... more
Verified Answer ✓
; Start by finding the Least Common Multiple (LCM... more
Verified Answer ✓
; Start by finding the Least Common Multiple (LCM... more
Verified Answer ✓
; Start by finding the Least Common Multiple (LCM... more
Verified Answer ✓
; Start by finding the Least Common Multiple (LCM... more
Verified Answer ✓
; Start by finding the Least Common Multiple (LCM... more
Verified Answer ✓
; Start by finding the Least Common Multiple (LCM... more
Verified Answer ✓
; Start by finding the Least Common Multiple (LCM... more
Verified Answer ✓
; Start by finding the Least Common Multiple (LCM... more
Verified Answer ✓
; To simplify a complex rational expression, use ... more
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; To simplify a complex rational expression, use ... more
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; Start by manipulating the complex rational ... more
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; Using the properties of negative exponents, ... more
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; Using the properties of negative exponents, ... more
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; Expand the numerator by distributing the terms... more
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The coefficients for the continued fractions ... more
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I find the method of finding the LCM for all ... more
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I find the method of finding the LCM for all ... more
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; Since the is inside the parentheses, we square... more
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; . ; This operation can be written as . By order... more
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index ; Definition of radicals. ; more
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cube ; Cube because the index is 3. ; root ; The ... more
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This is a property of Radicals. ; Let , , and . If... more
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; An exponent is not equivalent to a radical... more
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By definition, for radicals to be like radicals, ... more
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. This resultant expression still has a radical in... more
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The result of an even indexed radical must be ... more
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; Find the value that results in when taken to ... more
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; Find the nonnegative value that results in ... more
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; Find the value that results in when taken to ... more
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; Find the value that results in when taken to ... more
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; Find a factorization of that contains a ... more
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; Factor out the perfect square from the radicand... more
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; Factor out the perfect square from the radicand... more
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; Factor out the perfect squares from the ... more
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; Factor out the perfect cube from the radicand... more
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; Find a factorization of that contains a ... more
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; Find a factorization of that contains a ... more
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; Factor out the perfect cubes from the radicand... more
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; Find a factorization of that contains a fourth... more
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; Find a factorization of that contains a fourth... more
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; Find a factorization of that contains a fifth ... more
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; Reduce the quotient inside the radical. ; ... more
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; Reduce the quotient inside the radical. ; ; ... more
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; Rewrite the radical expression as a product of ... more
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; Rewrite the radical expression as a product of ... more
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; Find a factorization for all radicals to ... more
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; Find a factorization for all radicals to ... more
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; Distribute the exponent. ; Simplify the ... more
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; Distribute the exponent. ; Simplify the ... more
Verified Answer ✓
; Take the product. ; Find a factorization for ... more
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; Take the product. ; Find a factorization for ... more
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; Since both radicals have the same index and ... more
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; Since both radicals have the same index and ... more
Verified Answer ✓
; Factor both radicals and write as a product of ... more
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; Factor both radicals and write as a product of ... more
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; FOIL the binomials. ; Combine like terms and ... more
Verified Answer ✓
; FOIL the binomials. ; Combine like terms and ... more
Verified Answer ✓
; Factor the radicals to simplify and write as a ... more
Verified Answer ✓
; Factor the radicals to simplify and write as a ... more
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; Write as a product of binomials and FOIL. ; ... more
Verified Answer ✓
; Write as a product of binomials and FOIL. ; ... more
Verified Answer ✓
; Factor the radicals to simplify and write as a ... more
Verified Answer ✓
; Factor the radicals to simplify and write as a ... more
Verified Answer ✓
; Factor the radicals to simplify and write as a ... more
Verified Answer ✓
; Simplify and write as a product of radicals. ; ... more
Verified Answer ✓
; Simplify and write as a product of radicals. ; ... more
Verified Answer ✓
; Simplify and write as a product of radicals. ; ... more
Verified Answer ✓
; To rationalize the denominator, multiply the ... more
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Verified Answer ✓
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; To rationalize the denominator, multiply the ... more
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; Exponents written with fractions can be ... more
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; Exponents written with fractions can be ... more
Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
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; Rewrite the expression with positive exponents... more
Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
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Verified Answer ✓
; Rewrite the expression with positive exponents... more
Verified Answer ✓
; Since all terms have the same base, we can ... more
Verified Answer ✓
; Since all terms have the same base, we can ... more
Verified Answer ✓
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Verified Answer ✓
; Distribute the exponent multiplication in the ... more
Verified Answer ✓
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Verified Answer ✓
; Distribute the exponent multiplication in the ... more
Verified Answer ✓
; To sum together the two terms, find the Least ... 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