91Ó°ÊÓ

The formula $$ N=\frac{t^{2}-t}{2} $$ describes the number of football games, \(N\), that must be played in a league with t teams if each team is to play every other team once. Use this information to solve Exercises 83-84. If a league has 36 games scheduled, how many teams belong to the league, assuming that each team plays every other team once?

On two examinations, you have grades of 86 and 88 . There is an optional final examination, which counts as one grade. You decide to take the final in order to get a course grade of \(A\), meaning a final average of at least 90 . a. What must you get on the final to earn an \(A\) in the course? b. By taking the final, if you do poorly, you might risk the B that you have in the course based on the first two exam grades. If your final average is less than 80 , you will lose your B in the course. Describe the grades on the final that will cause this to happen.

Solve each equation. Use set notation to express solution sets for equations with no solution or equations that are true for all real numbers. \(\frac{x}{a}=\frac{x}{a}\)

Explain how to multiply two binomials using the FOIL method. Give an example with your explanation.

A car can be rented from Basic Rental for \(\$ 60\) per week plus 50 cents for each mile driven. How many miles can you travel if you can spend at most \(\$ 600\) for the week?

When graphing the solutions of an inequality, what is the difference between an open dot and a closed dot?

When solving an inequality, when is it necessary to change the direction of the inequality symbol? Give an example.

Describe ways in which solving a linear inequality is similar to solving a linear equation.

Describe ways in which solving a linear inequality is different than solving a linear equation.

Solve each equation. \(0.7 x+0.4(20)=0.5(x+20)\)