91Ó°ÊÓ

State whether each inequality is true or false. (a) \(\frac{7}{11} \geq \frac{8}{13}\) (b) \(-\frac{3}{5}>-\frac{3}{4}\)

Exponents Simplify each expression, and eliminate any negative exponents. (a) \(\frac{y^{-2} z^{-3}}{y^{-1}}\) (b) \(\left(\frac{x^{3} y^{-2}}{x^{-3} y^{2}}\right)^{-2}\)

The power \(P\) (measured in horsepower, hp) needed to propel a boat is directly proportional to the cube of the speed \(s\) (a) Write an equation that expresses this variation. (b) Find the constant of proportionality for a boat that needs an 80 -hp engine to propel the boat at 10 knots. (c) How much power is needed to drive this boat at 15 knots? (IMAGES CANNOT COPY)

Solving for a Variable Solve the equation for the indicated variable. $$\frac{a+1}{b}=\frac{a-1}{b}+\frac{b+1}{a} ; \quad \text { for } a$$

Inequalities Find the solutions of the inequality by drawing appropriate graphs. State each answer rounded to two decimals. $$\sqrt{0.5 x^{2}+1} \leq 2|x|$$

Perform the multiplication or division and simplify. $$\frac{x}{y / z}$$

Multiply the algebraic expressions using a Special Product Formula and simplify. $$(5-y)(5+y)$$

Evaluate the quotient, and write the result in the form \(a+b i\) $$\frac{1}{1+i}$$

Exponents Simplify each expression, and eliminate any negative exponents. (a) \(\left(\frac{a^{2}}{b}\right)^{5}\left(\frac{a^{3} b^{2}}{c^{3}}\right)^{3}\) (b) \(\frac{\left(u^{-1} v^{2}\right)^{2}}{\left(u^{3} v^{-2}\right)^{3}}\)

Inequalities Find the solutions of the inequality by drawing appropriate graphs. State each answer rounded to two decimals. $$(x+1)^{2}<(x-1)^{2}$$