91Ó°ÊÓ

Solve the formula for the specified variable. Because each variable is non negative, list only the principal square root. If possible, simplify radicals or rationalize denominators. $$s=\frac{k w d^{2}}{l} \text { for } d$$

Solve: \(\frac{2}{x+5}+\frac{1}{x-5}=\frac{16}{x^{2}-25}\).

Determine whether statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The inequality \(\frac{x-2}{x+3}<2\) can be solved by multiplying both sides by \((x+3)^{2}, x \neq-3,\) resulting in the equivalent inequality \((x-2)(x+3)<2(x+3)^{2}\).

Solve the formula for the specified variable. Because each variable is non negative, list only the principal square root. If possible, simplify radicals or rationalize denominators. $$A=P(1+r)^{2} \text { for } r$$

Simplify: \(\frac{1+\frac{2}{x}}{1-\frac{4}{x^{2}}}\).

Solve the formula for the specified variable. Because each variable is non negative, list only the principal square root. If possible, simplify radicals or rationalize denominators. $$C=\frac{k P_{1} P_{2}}{d^{2}} \text { for } d$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Because I want to solve \(25 x^{2}-169=0\) fairly quickly, I'll use the quadratic formula.

Solve the system: $$\left\\{\begin{array}{r}2 x+3 y=6 \\\x-4 y=14\end{array}\right.$$

Write a quadratic inequality whose solution set is \([-3,5]\).

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Because I want to solve \(25 x^{2}-169=0\) fairly quickly, I'll use the quadratic formula.