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Home Question Bank Math Algebra Archive 2024 December 04

Algebra Questions from Dec 04,2024

Browse the Algebra Q&A Archive for Dec 04,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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A corporation gave a university \( \$ 320,000 \) to support product safety research. The university deposited some of the money in a \( 11 \% \) simple interest account and the remainder in an \( 9.1 \% \) simple interest account. How much should be deposited in each account so that the annual interest earned is \( \$ 33,300 \) ? \( 11 \% \) \( 9.1 \% \) \( \left(\begin{array}{cccc}2 & 3 & 5 & 6 \\ 4 & 2 & -1 & 3 \\ 7 & 6 & 9 & 8 \\ 1 & 2 & -3 & 5\end{array}\right) \) inverso por gauss - Jor Which of the following equations represents a line that passes through the points \( (-6,10) \) and \( (-8,16) \) ? I. \( 3 x+y=-8 \) II. \( y=-3 x-7 \) Neither II only I I and II A university alumni association invested part of \( \$ 22,000 \) in preferred stock that earns \( 8 \% \) annual simple interest, and the remainder in a municipal bond that earns \( 7 \% \) annual simple interest. The amount of interest earned each year is \( \$ 1,610 \). How much was invested in each account? at \( 7 \% \quad \$ \square \) at \( 8 \% \)\( \$ \square \) (b) Solve for \( x \) in \( \log _{\frac{1}{2}}(3-x) \) Graph the solution set of the following system of inequalities. \( \begin{array}{c}x+y \leq 4 \\ y \geq x^{2}-3\end{array} \) Solve by the substitution method. (If there is no solution, enter NO SOLUTION. Use the parameters \( x \) and \( y \) as necessary.) \[ \begin{array}{r}y=3 x+1 \\ y=2 x+2\end{array} \] \( (x, y)=( \) Solve by the substitution method. (If there is no solution, enter NO SOLUTION. Use the parameters \( x \) and \( y \) as necessary.) \[ \begin{array}{r}5 x+2 y=17 \\ x=7-y\end{array} \] \( (x, y)=(\square \) A bottle of water costs \( \$ 1.50 \). Explain how you would make a graph of four ordered pairs to model the total cost of the water in terms of the number of bottles. (i) Intro Solve by the substitution method. (If there is no solution, enter NO SOLUTION. Use the parameters \( x \) and \( y \) as necessary.) \[ \begin{aligned} 2 x-3 y=4 \\ x=5 y+2\end{aligned} \] \( (x, y)=( \)
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