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Home Question Bank Math Algebra Archive 2024 December 12

Algebra Questions from Dec 12,2024

Browse the Algebra Q&A Archive for Dec 12,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Which expression is equivalent to \( \sqrt[4]{16 c^{2}} \) ? \( 16 c^{\frac{1}{2}} 2 c^{\frac{1}{2}} \) \( 16 c^{2}-\frac{16}{c^{2}} \) PART 4 - Mathematical Knowledge \[ \text { Factor: } 3 z^{4}+6 z \] For the polynomial function below: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the \( x \)-axis at each \( x \)-intercept. (c) Determine the end behavior. \( f(x)=(x-4)^{2}(x+2)^{3} \) (a) Find any real zeros of \( f \). The real zero(s) of \( f \) is/are The multiplicity of the smaller zero is (Type a whole number.) The multiplicity of the larger zero is (Type a whole number.) (b) The graph \( \square \) the \( x \)-axis at the smaller \( x \)-intercept. The graph \( \square \) the \( x \)-axis at the larger \( x \)-intercept. (c) Select the end behavior of the graph. A. Falls left and rises right B. Falls left and right C. Rises left and right D. Rises left and falls right 19. Find the slope of a line which is perpendicular to the line given by \( 3 x-6 y=12 \). \( \begin{array}{llll}\text { A. } 2 & \text { B. }-2 & \text { C. } \frac{1}{2} & \text { D. }-\frac{1}{2}\end{array} \) the domain \( =(x-1)^{2}-9 \) Which expression is equivalent to \( 7 f^{\frac{3}{5}} \) ? \( 35 \sqrt{f^{3}} \sqrt[5]{7 f^{3}} \) \( 7 \sqrt[5]{f^{3}} \sqrt[5]{(7 f)^{3}} \) The one-to-one functions \( g \) and \( h \) are defined as follows. \begin{tabular}{c}\( g=\{(0,6),(2,3),(3,1),(6,-2),(9,5)\} \) \\ \( h(x)=3 x+13 \) \\ Find the following. \\ \hline\( g^{-1}(3)=\square \) \\ \( h^{-1}(x)=\square \) \\ \( \left(h^{-1} \circ h\right)(-7)=\square \)\end{tabular} Which expression is equivalent to \( (\sqrt[3]{x})^{5} \) ? \( 3 x^{5} \frac{x^{5}}{3} \) \( x^{\frac{5}{3}} x^{\frac{3}{5}} \) Factor the following expression: \( 7 \mathrm{x}^{3}+28 \mathrm{x}^{2}+21 \mathrm{x} \) \( -4.5 y-3.2 y=5.6 y+42.80 \) for \( y \)
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