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Home Question Bank Math Algebra Archive 2024 December 29

Algebra Questions from Dec 29,2024

Browse the Algebra Q&A Archive for Dec 29,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Solve the simultaneous equations. You must show all your working. \( \begin{array}{l}4 x-3 y=26 \\ 5 x+6 y=13\end{array} \) 10 Solve the simultaneous equations. You must show all your working. \( \begin{array}{l}x-3 y=26 \\ 5 x+6 y=13\end{array} \) For the following quadratic function, tell whether the graph opens upward or downward and whether the graph is whder, narrower, or the same as \( f(x)=x^{2} \). \( F(x)=2 x^{2}+12 \) The graph opens A. downward. The graph is A. the same width as that of \( f(x)=x^{2} \) B. wider than \( f(x)=x^{2} \). Identify the vertex of the parabola. \( f(x)=(x+1)^{2}-1 \) The vertex of the parabola is the point (Type an ordered pair.) \( m^{-\frac{1}{4}}=27 m^{-1} \) Find the value of \( m \). 8 Simplify. \( y^{3} \div y^{5} \) \( 9^{x} \times 9^{2}=9^{12} \) Find the value of \( x \) Let \( f(x)=7 x+4 \) and \( g(x)=4 x-5 \). Find \( (f+g)(x),(f-g)(x),(f g)(x) \), and \( \left(\frac{1}{g}\right)(x) \). Give the domain of each. \( \left(\frac{f}{g}\right)(x)=\frac{7 x+4}{4 x-5} \) (Simplify your answer.) The domain of \( f+g \) is \( -\infty, \infty \). (Type your answer in interval notation.) The domain of \( f-g \) is \( -\infty, \infty \). (Type your answer in interval notation.) The domain of \( f g \) is \( -\infty, \infty \). (Type your answer in interval notation.) The domain of \( \frac{f}{g} \) is (Type your answer in interval notation.) 6 Simplify. \[ \frac{4 x^{2}-16 x}{x^{2}-16} \] Let \( f(\mathrm{x})=7 \mathrm{x}+4 \) and \( \mathrm{g}(\mathrm{x})=4 \mathrm{x}-5 \). Find \( (\mathrm{f}+\mathrm{g})(\mathrm{x}) \), \( (\mathrm{f}-\mathrm{g})(\mathrm{x}) \), \( (\mathrm{fg})(\mathrm{x}) \), and \( \left(\frac{\mathrm{f}}{\mathrm{g}}\right)(\mathrm{x}) \). Give the domain of each. \( (\mathrm{f}+\mathrm{g})(\mathrm{x})=\square \) (Simplify your answer.) \( (\mathrm{f}-\mathrm{g})(\mathrm{x})=\square \) (Simplify your answer.) \( (\mathrm{fg})(\mathrm{x})=\square \) (Simplify your answer.) \( \left(\frac{\mathrm{f}}{\mathrm{g}}\right)(\mathrm{x})=\square \) (Simplify your answer.) The domain of \( \mathrm{f}+\mathrm{g} \) is \( \square \). (Type your answer in interval notation.) The domain of \( \mathrm{f}-\mathrm{g} \) is \( \square \). (Type your answer in interval notation.) The domain of fg is \( \square \). (Type your answer in interval notation.)
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