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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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Solve the logarithmic equation \( \log _{4}(256)=x \). a.) \( x=3 \) b.) \( x=64 \) c.) \( x=16 \) d.) \( x=4 \) If \( 9^{2 x-1}=3^{-x+8} \), then \( x \) equals a.) 3 b.) 7 c.) 9 d.) 2 For the exponential function \( f(x)=5 \cdot 2^{x} \), what is the value of \( f(3) \) ? \[ \begin{array}{ll}\text { a.) } 1,000 \\ \text { b.) } 40 \\ \text { d.) } 250\end{array} \] 3.2. The first three terms of an arithmetic geometric sequence are 16,8 and 4 respectively. 3.2 .1 Determine the nth term of the sequence 3.2 .2 Determine all possihle values of \( n \) for which the sum of the first \( n \) terms of this sequence is greater than 31 3.2 .3 Calculate the sum to infinity of this sequence 6. Given a linepr function \( f \) such that \( f(2)=1 \), and \( f(-3)=11 \). What is the \( y \)-intercep of \( f \) ? A. 3 B. 5 C. 6 D. 9 To solve the rational equation \( \frac{2}{x}+\frac{3-x}{6}=\frac{5}{x+2} \), how can the expression \( \frac{5}{x+2} \) be rewritten using the least common denominator? a.) \( \frac{5-x}{(x+2)} \) b.) \( \frac{30 x}{6 x(x+2)} \) c.) \( \frac{5 x}{x(x+2)} \) d.) \( \frac{30}{6(x+2)} \) Write the following as a single rational expression. \( \frac{200+35 x}{x}+\frac{250+40 x}{x} \) a.) \( \frac{50+5 x}{x^{2}} \) b.) \( \frac{5(10+x)}{x^{2}} \) c.) \( \frac{40+7 x}{50+8 x} \) d.) \( \frac{250+40 x}{200+35 x} \) The rational expression \( \frac{2 x+3}{x+4}+\frac{8}{x} \) is equivalent to a.) \( \frac{2 x^{2}+11 x+32}{x(x+4)} \) b.) \( \frac{2 x+11}{2 x+4} \) c.) \( \frac{2 x^{2}-5 x-32}{x(x+4)} \) d.) \( \frac{2 x-11}{2 x-4} \) The rational expression \( \frac{x^{2}-8 x+15}{x^{2}-5 x+6} \) simplifies to a.) \( \frac{x-3}{x-2} \) b.) \( \frac{x-5}{x-3} \) c.) \( \frac{x-2}{x-5} \) d.) \( \frac{x-5}{x-2} \) Which of the following rational expressions has the domain restrictions \( x=4 \) and \( x=-2 \) ? a.) \( \frac{(x+1)(x-3)}{(x-4)(x+2)} \) b.) \( \frac{(x+2)(x-4)}{(x+5)(x-3)} \) c.) \( \frac{(x-4)(x+2)}{(x+8)(x+1)} \) d.) \( \frac{(x-3)(x-1)}{(x+4)(x-2)} \)
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