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Home Question Bank Math Algebra Archive 2024 November 02

Algebra Questions from Nov 02,2024

Browse the Algebra Q&A Archive for Nov 02,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Simplify \( 3 m+4 m^{2} n-2 m+6 m^{2} \) Write the given expression as a single logarithm: \( 2 \log (2 x+3)+\frac{1}{2} \log (x+1) \). Simplify, if possible. Note: As a reference, consider using the Power Property, \( p \log _{a}(M)=\log _{a}\left(M^{p}\right) \). Provide your answer below: \( \log (\square) \) sion: \( \log _{2}(80)-\log _{2}(5) \) Solve the following system of equations. \[ \begin{array}{l}y=x^{2}+7 x-3 \\ y=-4 x-21\end{array} \] If there is more than one solution, use the "or" button. \( (x, y)=(\square, \square) \quad \frac{\square}{\square} \square \frac{\square}{\square} \) Solve the exponential equation. Approximate your answer to the nearest thousandth. \( 8^{x+3}=5^{x} \) \( x \approx \square \) (Round to the nearest thousandth as needed.) ․ Resuelve: \( 2^{\frac{x-2}{2}} \cdot 2^{\frac{3-2 x}{3}} \cdot-2^{\frac{x-1}{5}}=2 \) \( \sqrt{2}^{x-2} \cdot \sqrt[3]{2}^{3-2 x} \cdot \sqrt[5]{2}^{x-1}=1 \) \( \begin{array}{lll}\text { a) } 2 & \text { b) } 4 & \text { c) } 5 \\ \text { d) } 6 & \text { e) } 8 & \end{array} \) Solve the following system of equations. \[ x^{2}+y^{2}=\frac{34}{9} \] \( y+3 x=-\frac{4}{3} \) If there is more than one solution, enter additional solutions with the "or" button. If there is no real solution, use the "No solution" button. \( (x, y)=(\square . \square) \) 1. Calcular \( p \) si el polinomio es homogéneo de grado 70 \( Q(x, y)=2 x^{3 n-1} y^{n+3}+x^{n} y^{m+2 n}+x^{p+m} \) Solve the exponential equation. Approximate your answer to the nearest thousandth. \( e^{3.3 x}=8.37 \) \( x \approx \square \) an integer or decimal rounded to the nearest thousandth as needed.) (Type and Find the domain of the following rational function. \( H(x)=\frac{20 x^{2}+x}{x^{2}+9} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain of \( \mathrm{H}(\mathrm{x}) \) is restricted to (Type your answer in interval notation.) B. There are no restrictions on the domain of \( \mathrm{H}(\mathrm{x}) \).
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