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Home Question Bank Math Algebra Archive 2024 November 17

Algebra Questions from Nov 17,2024

Browse the Algebra Q&A Archive for Nov 17,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Questão 5) (1.0) Verifique que a equação \( x^{4}-3 x^{2}+5 x+4=0 \) tem solução real. What are the length and width of a rectangular traffic sign if the length exceeds the width by 10 inches and the perimeter is 160 inches? The length is 45 inches. (Type an integer or a decimal.) The width is \( \square \) inches. (Type an integer or a decimal.) Rationalize the denominator in the following: \( \frac{2 \sqrt{a}+2}{2+\sqrt{a}}=\square \) A line passes through the point \( (-8,6) \) and has a slope of \( -\frac{5}{2} \). Write an equation in point-slope form for this line. Suppose that the polynomial function \( f \) is defined as follows. \[ f(x)=(x+6)^{2}(x+9)(x-4)^{2} \] List each zero of \( f \) according to its multiplicity in the categories below. If there is more than one answer for a multiplicity, separate them with commas. If there is no answer, click on "None." Zero(s) of multiplicity one: Zero(s) of multiplicity three: What are the length and width of a rectangular traffic sign if the length exceeds the width by 10 inches and the perimeter is 160 inches? The length is \( \square \) inches. (Type an integer or a decimal.) Convert to a logarithmic equation. \( 10^{6}=1,000,000 \) (Use integers or fractions for any numbers in the equation.) Rationalize the denominator in the following and simplify completely. Assume all variables under the radicals are nonnegative. \( \frac{\sqrt{x}}{\sqrt{x}-2}=\square \) Two towns are 1100 miles apart. A group of hikers start from each town and walk the trail toward each other. They meet after a total hiking time of 200 hours. If one group travels \( 1 \frac{1}{2} \) mile per hour taster than the other group, find the rate of each group. The rate of the slower group is 2 mph . (Simplity your answer.) The rate of the laster group is (Simplity your answer.) Convert to a logarithmic equation. \( 10^{6}=1,000,000 \)
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