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Home Question Bank Math Algebra Archive 2024 December 01

Algebra Questions from Dec 01,2024

Browse the Algebra Q&A Archive for Dec 01,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\( \left. \begin{array} { l } { 5 x \cdot \square \cdot 2 = \Delta \cdot y ^ { 2 } \cdot 20 } \\ { \square = 2 y ^ { 2 } } \\ { \Delta = x } \end{array} \right. \) Simplify. \( \quad \sqrt{3 w^{2} v} \sqrt{15 w v^{8}} \) Assume that all variables represent positive real numbers. simplify. \( \sqrt{20 v^{3} x^{2}} \sqrt{5 v^{3} x^{2}} \) Assume that all variables represent positive real numbers. 12 Reduza os termos semelhantes. a) \( 10 x^{2}-(5 x+6)-\left[2 x-\left(3 x^{2}-2\right)\right] \) b) \( 5 a-[3 b+7-(4 a-5 b)+(2-a)] \) c) \( x^{2}+\left(\frac{1}{2} x-2\right)-\left(-\frac{1}{2}+x+\frac{1}{3} x^{2}\right) \) Express as a trinomial. \[ (2 x+3)(3 x-2) \] Two buses leave a station at the same time and travel in opposite directions. One bus travels \( 19 \frac{\mathrm{~km}}{\mathrm{~h}} \mathrm{slower} \) than the other. If the two buses are 1785 kilometers apart after 7 hours, what is the rate of each bus? Note that the ALEKs graphing calculator can be used to make computations easier. Rate of the slower bus: Rate of the faster bus: A motorboat takes 4 hours to travel 128 miles going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current? Note that the ALEKS graphing calculator can be used to make computations easier. Rate of the boat in still water: Express as a trinomial. \[ (3 x+3)(2 x+8) \] Simplify. \( \quad \sqrt{6 u^{7} w^{4}} \sqrt{3 u^{4} w^{8}} \) Assume that all variables represent positive real numbers. Two buses leave towns 369 miles apart at the same time and travel toward each other. One bus travels \( 9 \frac{\mathrm{mi}}{\mathrm{h}} \) faster than the other. If they meet in 3 hours, what is the rate of each bus? Note that the Alexs graphing calculator can be used to make computations easier. Rate of the faster bus:
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