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Home Question Bank Math Algebra Archive 2024 December 21

Algebra Questions from Dec 21,2024

Browse the Algebra Q&A Archive for Dec 21,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Question 2 Use the FOIL method to evaluate the expression: \( \begin{array}{l}(4+\sqrt{7})(8-\sqrt{7}) \\ 39+12 \sqrt{7} \\ 32+3 \sqrt{7} \\ 32+13 \sqrt{7} \\ 25+4 \sqrt{7}\end{array} \) Solve the following logarithmic equation. \( \begin{array}{l}\log _{10}(2 x)=3 \\ x=15 \\ x=50 \\ x=500 \\ x=5\end{array} \) Suppose \( \log _{d} x=3, \log _{a} y=7 \), and \( \log _{a} z=-2 \) Find the value of the following expression. \( \log _{a}\left(\frac{x^{3} y}{z^{4}}\right) \) 18 24 12 8 Suppose \( f(x)=4-x^{2} \) and \( g(x)=2 x+5 \) Find the value of \( f(g(-2)) \). 5 3 Simplify the rational expression by canceling common factors: \( \begin{array}{l}\frac{x^{2}+7 x+6}{x^{2}-3 x-4} \\ \frac{x+6}{x-4} \\ \frac{x+1}{x-4} \\ \frac{x-4}{x+6}\end{array} \) \( (2 x-3) \mathrm{cm} \), show that its breadth is \( (x-4) \mathrm{cm} \). (b) Factorise \( 15+7 x-2 x^{2} \) completely. Find the solution to the following equation. \[ \begin{array}{l}2^{3 x}=8^{1-x} \\ x=\frac{4}{7} \\ x=\frac{3}{2} \\ x=\frac{7}{4}\end{array} \] If the first 4 terms of a geometric sequence are \( \{7,21,63,189\} \), then the formula for the \( n^{t h} \) term in the sequence is \[ \begin{array}{ll}\text { b.) } a_{n}=3 \cdot(n-1)^{7} \\ \text { b.) } a_{n}=3 \cdot 7^{n-1} \\ \text { c.) } a_{n}=7 \cdot 3^{n-1} \\ \text { d.) } a_{n}=7 \cdot(n-1)^{3}\end{array} \] If \( \log _{2}(3 x-2)=4 \), then what is the value of \( x \) ? a.) 2 b.) 6 c.) 3 d.) 4 The equation \( y=2(3) \) shows the number of infected people from an outbreak of the Norovirus. The variable \( y \) represents the number of infected people, and \( t \) represents time in weeks. In how many weeks will the number of infected people roach 1,458? a.) 5 weeks b.) 10 weeks 6 weeks d.) 12 weeks
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