Algebra Questions from Dec 17,2024

Browse the Algebra Q&A Archive for Dec 17,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Solve the following formula for the specified variable. Assume each variable is nonnegative and thus, list only the principal square root. If possible, simplify radicals or rationalize denominators. \( \mathrm{B}=\mathrm{Q}(1+\mathrm{w})^{2} \) for w \( \mathrm{w}=\square \) (Type an exact answer, using radicals as needed. Rationalize all denominators.) Solve the following formula for the specified variable. Assume each variable is nonnegative and thus, list only the principal square root. If possible, simplify radicals or rationalize denominators. \( \mathrm{d}=\frac{\mathrm{m}^{2}}{5 \mathrm{c}} \), for m \( \mathrm{m}=\square \) (Type an exact answer, using radicals as needed.) Three times the square of the difference between a number and 4 is -75 . Find the number(s). The number(s) are (Simplify your answer. Type an exact answer, using radicals and \( i \) as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) If \( \mathrm{h}(\mathrm{x})=3(\mathrm{x}-1)^{2} \), find all values of x for which \( \mathrm{h}(\mathrm{x})=-75 \). List all such values of x below. (Simplify your answer. Type an exact answer, using radicals and \( i \) as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) If \( \mathrm{g}(\mathrm{x})=\left(\mathrm{x}-\frac{1}{4}\right)^{2} \), find all values of x for which \( \mathrm{g}(\mathrm{x})=\frac{9}{16} \). List all such values of x below. \( \square \) (Simplify your answer. Type an exact answer, using radicals and \( i \) as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) Solve the following quadratic equation by completing the square. \[ 2 x^{2}-5 x+13=0 \] The solution set is \( \} \). (Simplify your answer. Type an exact answer, using radicals and \( i \) as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) Solve the quadratic equation by completing the square. \[ 8 x^{2}-8 x+4=0 \] The solution set is (Simplify your answer. Type an exact answer, using radicals and \( i \) as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) \( \left[\begin{array}{c}{(3^{2^{3}})\div (3^{1})^{5}+\sqrt {4^{3}}-39}\end{array}\right]+5^{0}= \) Solve the quadratic equation by completing the square. \( 3 x^{2}-5 x-7=0 \) The solution set is \( \{ \) (Simplify your answer. Type an exact answer, using radicals and \( i \) as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) Solve for \( u \) \( 6 u=54 \) \( u=\square \)
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