91Ó°ÊÓ

Solve the quadratic equation by the method of your choice. $$2 x^{2}+5 x=3$$

Simplify each exponential expression. Assume that variables represent nonzero real numbers. $$\left(3 x^{-4} y z^{-7}\right)(3 x)^{-3}$$

Evaluate each expression. $$\sqrt[3]{\sqrt{\sqrt{169}+\sqrt{9}}+\sqrt{\sqrt[3]{1000}}+\sqrt[3]{216}}$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The rational expressions $$ \frac{7}{14 x} \text { and } \frac{7}{14+x} $$ can both be simplified by dividing each numerator and each denominator by 7

Factor completely. $$x^{4}-10 x^{2} y^{2}+9 y^{4}$$

Simplify: \(\left(y^{n}+2\right)\left(y^{n}-2\right)-\left(y^{n}-3\right)^{2}\)

The formula for converting Celsius temperature, \(C,\) to Fahrenheit temperature, \(F\), is $$F=\frac{9}{5} C+32$$ If Fahrenheit temperature ranges from \(41^{\circ}\) to \(50^{\circ},\) inclusive, what is the range for Celsius temperature? Use interval notation to express this range.

Simplify each expression. Assume that all variables represent positive numbers. $$\left(49 x^{-2} y^{4}\right)^{-\frac{1}{2}}\left(x y^{\frac{1}{2}}\right)$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When performing the division $$ \frac{7 x}{x+3} \div \frac{(x+3)^{2}}{x-5} $$ I began by dividing the numerator and the denominator by the common factor, \(x+3\)

In Exercises \(111-120,\) use the order of operations to simplify each expression. $$8^{2}-16 \div 2^{2} \cdot 4-3$$