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Home Question Bank Math Algebra Archive 2024 November 25

Algebra Questions from Nov 25,2024

Browse the Algebra Q&A Archive for Nov 25,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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If \( \log _{2}(3 x-2)=4 \), then what is the value of \( x \) ? In psychology, it has been suggested that the number \( S \) of nonsense syllables that a person can repeat consecutively depends on his or her IQ score I according to the equation \( S=2 \sqrt{1}-9 \). Use this relationship to estimate the IQ of a person who can repeat 7 nonsense syllables consecutively. \( I=\square \) (Round to the nearest integer as needed.) The equation \( y=5\left(2^{t}\right) \) shows the number of infected people from an outbreak of influenza. 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 reach 1,280? What is the value of \( \log \left(\frac{x^{3} y}{z^{2}}\right) \) when given the following: \( \log (x)=-1 \) \( \log (y)=6 \) \( \log (z)=2 \) Solve the equation. \[ x^{2}+11=60 \] The term \( \log _{9}\left(\frac{6}{11}\right) \) can also be written as \( 1 \leftarrow \quad \) Solve the equation. \[ \sqrt{7 x}=21 \] Solve the logarithmic equation \( \log _{10}(1,000)=x \) 3) \( 8 m^{6}-27 n^{9} \) 1. Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function \( h(t)=-16 t^{2}+16 t+480 \), where \( t \) is the time in seconds and \( h \) is the height in feet. a. How long did it take for Jason to reach his maximum height? b. What was the highest point that Jason reached? c. What was Jason's initial height?
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