91Ó°ÊÓ

Use the Quadratic Formula to solve the equation. (Round your answer to three decimal places.) $$ 12.67 x^{2}+31.55 x+8.09=0 $$

Use the Quadratic Formula to solve the equation. (Round your answer to three decimal places.) $$ -3.22 x^{2}-0.08 x+28.651=0 $$

Solve the equation using any convenient method. $$ a^{2} x^{2}-b^{2}=0, a \text { and } b \text { are real numbers } $$

Find all solutions of the equation. Check your solutions in the original equation. $$ x^{4}-81=0 $$

A river has risen 8 feet above its flood stage. The water begins to recede at a rate of 3 inches per hour. Write a mathematical model that shows the number of feet above flood stage after \(t\) hours. If the water continually recedes at this rate, when will the river be 1 foot above its flood stage?

An airline offers daily flights between Chicago and Denver. The total monthly cost \(C\) (in millions of dollars) of these flights is \(C=\sqrt{0.2 x+1}\) where \(x\) is the number of passengers (in thousands). The total cost of the flights for June is \(2.5\) million dollars. How many passengers flew in June?

True or False? Determine whether the statement is true or false. Justify your answer. Solve \(3(x+4)^{2}+(x+4)-2=0\) in two ways. (a) Let \(u=x+4\), and solve the resulting equation for \(u\). Then solve the \(u\)-solution for \(x\). (b) Expand and collect like terms in the equation, and solve the resulting equation for \(x\). (c) Which method is easier? Explain.