Exam 1: Algebraic Concepts

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Rationalize the denominator of the fraction and simplify. ​ Rationalize the denominator of the fraction and simplify. ​   ​ ​

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Use the rules of exponents to simplify the expression so that only positive exponents remain. ​ Use the rules of exponents to simplify the expression so that only positive exponents remain. ​   ​ ​

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Choose the graph that represents this subset of the real numbers. ​ Choose the graph that represents this subset of the real numbers. ​   and  and Choose the graph that represents this subset of the real numbers. ​   and

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Use your calculator to approximate the following expression. ​ Use your calculator to approximate the following expression. ​   ​ Round your answer to eight decimal places. ​ ​ Round your answer to eight decimal places. ​

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Perform the indicated operations and simplify. ​ Perform the indicated operations and simplify. ​   ​ ​

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Assume that Assume that   ,   and that U is the universal set of natural numbers less than 11. Find   . ​ , Assume that   ,   and that U is the universal set of natural numbers less than 11. Find   . ​ and that U is the universal set of natural numbers less than 11. Find Assume that   ,   and that U is the universal set of natural numbers less than 11. Find   . ​ . ​

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Factor the expression completely. ​ Factor the expression completely. ​   ​ ​

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Determine the missing factor. ​ Determine the missing factor. ​   ​ ​

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Simplify the expression by using the properties of radicals. Assume nonnegative variables. ​ Simplify the expression by using the properties of radicals. Assume nonnegative variables. ​   ​ ​

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Cell Pro makes cell phones and has total weekly costs of $1,000 for rent, utilities, and equipment, in addition to labor and material costs of $18.50 for each phone it makes. If Cell Pro makes cell phones and has total weekly costs of $1,000 for rent, utilities, and equipment, in addition to labor and material costs of $18.50 for each phone it makes. If   represents the number of phones produced and sold, choose the expression for Cell Pro's weekly costs. ​ represents the number of phones produced and sold, choose the expression for Cell Pro's weekly costs. ​

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Evaluate the expression. ​ Evaluate the expression. ​   ​ ​

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Evaluate the algebraic expression at the indicated value of the variable. ​ Evaluate the algebraic expression at the indicated value of the variable. ​   at   ​ at Evaluate the algebraic expression at the indicated value of the variable. ​   at   ​ ​

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Evaluate the following expression. ​ Evaluate the following expression. ​   ​ ​

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Assume that Assume that   and that U is the universal set of natural numbers less than 11. Find A'. ​ and that U is the universal set of natural numbers less than 11. Find A'. ​

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Use the properties of exponents to simplify the expression so that only positive exponents remain. ​ Use the properties of exponents to simplify the expression so that only positive exponents remain. ​   ​ ​

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Perform the indicated operations and simplify. ​ Perform the indicated operations and simplify. ​   ​ ​

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Use the rules of exponents to simplify the expression. ​ Use the rules of exponents to simplify the expression. ​   ​ ​

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Factor the expression as a product of binomials. ​ Factor the expression as a product of binomials. ​   ​ ​

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Perform the indicated operations and simplify. ​ Perform the indicated operations and simplify. ​   ​ ​

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Express the inequality using interval notation. ​ Express the inequality using interval notation. ​   ​ ​

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