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Home Question Bank Math Algebra Archive 2024 November 06

Algebra Questions from Nov 06,2024

Browse the Algebra Q&A Archive for Nov 06,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Solve the system by back substitution. \( \begin{array}{l}7)+4 y+5 z=3 \\ 4 y+3 z=0 \\ 2 z=8 \text { B) }(-5,-3,4) \\ \text { A) }(-6,-3,4)\end{array} \) For the function below, (a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or a minimum value and find that value; and (d) graph the function. \( f(x)=2 x^{2}+6 x+6 \) (a) The vertex is (Type an ordered pair, using integers or fractions:) \( \Delta = \left[ \begin{array} { c c } { x - 2 } & { 2 } \\ { - 3 } & { x + 1 } \end{array} \right] = 34 \) For the function below, (a) find the vertex; (b) find the axis of symmetry, (c) determine whether there is a maximum or a minimum value and find that value; and (d) graph the function \( f(x)=2 x^{2}+6 x+6 \) Solve using the Quadratic Formula. \( 2 x^{2}+6 x+3=0 \) \( x=\frac{-3 \pm \sqrt{6}}{2} \) \( x=\frac{-3 \pm 2 \sqrt{3}}{2} \) \( x=\frac{-3 \pm \sqrt{15}}{2} \) \( x=\frac{-3 \pm \sqrt{3}}{2} \) \( 3^{3} \cdot 3^{4} \) simplified in exponent form is \( \square \) Solving using the Quadratic Formula. \( x^{2}+3 x-3=0 \) \( x=\frac{-3 \pm \sqrt{21}}{2} \) \( x=\frac{-3 \pm i}{2} \) \( x=\frac{3 \pm 2 \sqrt{5}}{2} \) \( x=\frac{3 \pm \sqrt{21}}{2} \) Solving using the Quadratic Formula. \( \begin{array}{l}x^{2}-13 x-48=0 \\ x=3, x=-4 \\ x=-2, x=-4 \\ x=-3, x=16 \\ x=-3, x=-4\end{array} \) Determine the number and type of solutions of the quadratic equation. \( -4 x^{2}-4 x-1=0 \) two real solutions two imaginary solutions one imaginary solution one real solution (a) Rewrite \( 4^{4}=256 \) as a logarithmic equation: (b) Rewrite \( \log 0.0001=-4 \) as an exponential equation:
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