91Ó°ÊÓ

Averaging Grades. A student has scores of \(70,77,\) and 85 on three government exams. What score does she need on a fourth exam to give her an average of 80 or better?

Factor out all common factors first including \(-1\) if the first term is negative. If an expression is prime, so indicate. $$ x^{2}+4 x-28 $$

Explain why the factorization is not complete. Factor: \(\quad 1-t^{8}=\left(1+t^{4}\right)\left(1-t^{4}\right)\)

In the following problems, simplify each expression by performing the indicated operations and solve each equation. $$\frac{18 m^{4}}{36 m^{4}-9 m^{3}}$$

For the typical "one-hour" prime-time television slot, the number of minutes of commercials is \(\frac{3}{7}\) of the number of minutes of the actual program. Determine how many minutes of the program are shown in that one hour.

Fundraising. A school PTA wants to rent a dunking tank for its annual school fundraising carnival. The cost is \(\$ 85.00\) for the first 3 hours and then \(\$ 19.50\) for each additional hour or part thereof. How long can the tank be rented if up to \(\$ 185\) is budgeted for this expense?

In the following problems, simplify each expression by performing the indicated operations and solve each equation. $$1+x-\frac{x}{x-5}$$

Factor out all common factors first including \(-1\) if the first term is negative. If an expression is prime, so indicate. $$ -r+3 r^{2}-10 $$

Solve: \(2^{|2 x-3|}=64\)

Work Schedules. A student works two part-time jobs. He earns \(\$ 8\) an hour for working at the college library and \(\$ 15\) an hour for construction work. To save time for study, he limits his work to 25 hours a week. If he enjoys the work at the library more, how many hours can he work at the library and still earn at least \(\$ 300\) a week?