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Home Question Bank Math Algebra Archive 2024 December 05

Algebra Questions from Dec 05,2024

Browse the Algebra Q&A Archive for Dec 05,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\( 7 a - 7 b + a c + 5 \) Graph this inequality: \[ y<-\frac{1}{2} x+1 \] Plot points on the boundary line. Select the line to switch between solid and dotted. Select a region to shade it. Which expressions are equivalent to \( \frac{5^{2}}{5^{8}} ? \) Choose 2 answers: A \( \frac{1}{5^{6}} \) B \( 1^{-6} \) C \( \left(5^{2}\right)^{-3} \) D \( \left(5^{2}\right)^{-8} \) Select the equivalent expression. \( \left(\frac{x^{4}}{7^{-8}}\right)^{-7}=? \) Choose 1 answer: (A) \( \frac{x^{28}}{7^{-56}} \) (B) \( \frac{x^{28}}{7^{56}} \) (C) \( x^{-28} \cdot 7^{-56} \) Question Graph the parabola \( y=-x^{2}-2 x-5 \) by plotting the vertex, the \( y \)-intercept, and the point symmetric to the \( y \)-intercept across the axis of symmetry. Move the key points to create the parabola. Use the orange key point as the vertex. Place the vertex point before the other key points. Lös ekvationen och svara exakt. \( \left(x^{3}-5\right)^{\frac{1}{5}}=4^{\frac{1}{10}} \) Which expressions are equivalent to \( 4^{-2} \cdot 7^{-2} ? \) Choose 2 answers: A \( (4 \cdot 7)^{-4} \) B \( \frac{1}{28^{2}} \) C \( \frac{7^{-2}}{4^{2}} \) D \( (4 \cdot 7)^{4} \) Question Graph the parabola \( y=x^{2}+2 x+5 \) by plotting the vertex, the \( y \)-intercept, and the point symmetric to the \( y \)-intercept across the axis of symmetry. Move the key points to plot the parabola. Use the orange key point as the vertex. Plot the vertex before plotting the other key points. Solve the following absolute value inequality. \[ \begin{array}{c}\frac{|x-3|}{2}>1 \\ x>[?] \\ x<\square\end{array} \] If \( f(x)=3 x+k \) and \( f f(2)=12 \), find the value of \( k \)
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