91Ó°ÊÓ

The equations of two lines are given. Determine whether the lines are parallel, perpendicular, or neither. \(7 x-3 y=2 ; \quad 9 y+21 x=1\)

Simplify the fractional expression. (Expressions like these arise in calculus.) $$\sqrt{1+\left(\frac{x}{\sqrt{1-x^{2}}}\right)^{2}}$$

Absolute Value Inequalities Solve the absolute value inequality. Express the answer using interval notation and graph the solution set. $$|2 x| > 7$$

Radicals Simplify the expression, and eliminate any negative exponents(s). Assume that all letters denote positive numbers. (a) \(\sqrt[3]{y \sqrt{y}}\) (b) \(\sqrt{\frac{16 u^{3} v}{u v^{5}}}\)

Use a Special Factoring Formula to factor the expression. $$9 a^{2}-16$$

Radicals Simplify the expression, and eliminate any negative exponents(s). Assume that all letters denote positive numbers. (a) \(\sqrt{s \sqrt{s^{3}}}\) (b) \(\sqrt[3]{\frac{54 x^{2} y^{4}}{2 x^{5} y}}\)

The equations of two lines are given. Determine whether the lines are parallel, perpendicular, or neither. \(6 y-2 x=5 ; \quad 2 y+6 x=1\)

Simplify the fractional expression. (Expressions like these arise in calculus.) $$\sqrt{1+\left(x^{3}-\frac{1}{4 x^{3}}\right)^{2}}$$

Use a Special Factoring Formula to factor the expression. $$(x+3)^{2}-4$$

Recall that the symbol \(\bar{z}\) represents the complex conjugate of \(z .\) If \(z=a+b i\) and \(w=c+d i,\) show that each statement is true. $$\overline{z w}=\bar{z} \cdot \bar{w}$$