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Home Question Bank Math Algebra Archive 2024 December 30

Algebra Questions from Dec 30,2024

Browse the Algebra Q&A Archive for Dec 30,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Write in logarithmic form. \( 9^{3}=729 \) The logarithmic form of \( 9^{3}=729 \) is (Use integers or fractions for any numbers in the equation.) A small business estimates that the value \( \mathrm{V}(\mathrm{t}) \) of a copy machine is decreasing according to the function \[ V(t)=5000(4)^{-0.24 t} \] where \( t \) is the number of years that have elapsed since the machine was purchased, and \( \mathrm{V}(\mathrm{t}) \) is in dollars. Use this information to answer parts (a)-(d). Ine onginai varue was \$ \$VUU. (Kound to the nearest oonar as neeged.) ee score (b) What is the value of the machine 5 yr after purchase, to the nearest dollar? The value of the machine 5 yr after purchase is approximately \( \$ 946 \). \( \square \) (Round to the nearest dollar as needed.) (c) What is the value of the machine 10 yr after purchase, to the nearest dollar? The value of the machine 10 yr after purchase is approximately \( \$ \) \( \square \) Determine whether the following function is one-to-one. If it is, find the inverse. \( f(x)=x^{3}-9 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. B. The function is one-to-one. The inverse function is \( \mathrm{f}^{-1}(\mathrm{x})=\square \) (Simplify your answer. Use integers or fractions for any numbers in the expression.) Use the tests for symmetry to decide whether the graph of the given relation is symmetric with respect to the \( x \)-axis, they-axis, or the origin. More than one of these symmetries may apply, and perhaps none apply. \( y=20|x| \) Select all that apply. \( \square \) A. It is symmetric with respect to the \( y \)-axis. \( \square \) B. It is symmetric with respect to the \( x \)-axis. \( \square \) C. It is symmetric with respect to the origin. \( \square \) D. It is not symmetric with respect to the \( x \)-axis, \( y \)-axis, or origin.
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