91Ó°ÊÓ

Fill in each blank with the appropriate word or phrase. Carefully reread the section, if necessary. For rational equations, values that cause a zero denominator must be ______.

Fill in each blank with the appropriate word or phrase. Carefully reread the section, if necessary. "False solutions" to a rational or radical equation are also called ______ roots.

Simplify each radical (if possible). If imaginary, rewrite in terms of \(i\) and simplify. a. \(\sqrt{-16}\) b. \(\sqrt{-49}\) c. \(\sqrt{27}\) d. \(\sqrt{72}\)

Solve using the zero product property. Be sure each equation is in standard form and factor out any common factors before attempting to solve. Check all answers in the original equation. $$22 x=x^{3}-9 x^{2}$$

Identify the following equations as an identity, a contradiction, or a conditional equation, then state the solution. $$-3(4 z+5)=-15 z-20+3 z$$

Solve the compound inequalities and graph the solution set. $$\frac{2}{3} x-\frac{5}{6} \leq 0 \text { and } -3 x<-2$$

Mixture Exercises Give the total amount of the mix that results and the percent concentration or worth of the mix. Ten pints of a \(40 \%\) acid are combined with 10 pints of an \(80 \%\) acid.

The time \(T\) (in days) for a planet to make one revolution around the sun is modeled by \(T=0.407 R^{\frac{3}{2}},\) where \(R\) is the maximum radius of the planet's orbit in millions of miles (Kepler's third law of planetary motion). Use the equation to approximate the maximum radius of each orbit, given the number of days it takes for one revolution. (See Appendix I.F, Exercises 45 and \(46 .\) ) a. Mercury: 88 days b. Venus: 225 days c. Earth: 365 days d. Mars: 687 days e. Jupiter: 4,333 days f. Saturn: 10,759 days

Two jets take off on parallel runways going in opposite directions. The first travels at a rate of 250 mph and the second at 325 mph. How long until they are 980 miles apart?

Solve each equation using the most efficient method: factoring, square root property of equality, or the quadratic formula. Write your answer in both exact and approximate form (rounded to hundredths). Check one of the exact solutions in the original equation. $$\frac{5}{9} x^{2}-\frac{16}{15} x=\frac{3}{2}$$