91Ó°ÊÓ

If p units of an item are sold for \(x\) dollars per unit, the revenue is \(R=p x\). Use this idea to analyze the following problem. Number of Apartments Rented The manager of an 80-unit apartment complex knows from experience that at a rent of \(\$ 300,\) all the units will be full. On the average, one additional unit will remain vacant for each \(\$ 20\) increase in rent over \(\$ 300 .\) Furthermore, the manager must keep at least 30 units rented due to other financial considerations. Currently, the revenue from the complex is \(\$ 35,000 .\) How many apartments are rented? Suppose that \(x\) represents the number of \(\$ 20\) increases over \(\$ 300 .\) Represent the number of apartment units that will be rented in terms of \(x .\)

Find each product. Write the answer in standard form. $$(-2+3 i)(4-2 i)$$

Solve each quadratic inequality. Write each solution set in interval notation. $$x^{2}+4 x>-1$$

Solve each equation for \(x\). $$4 a-a x=3 b+b x$$

Solve each equation or inequality. $$|12-6 x|+3 \geq 9$$

Solve each equation using the quadratic formula. $$x^{2}-3 x-2=0$$

Solve each equation. $$\sqrt{2 x-5}=2+\sqrt{x-2}$$

Solve each equation. $$\sqrt{2 \sqrt{7 x+2}}=\sqrt{3 x+2}$$

Which one of the following inequalities has solution set \((-\infty, \infty) ?\) A. \((x-3)^{2} \geq 0\) B. \((5 x-6)^{2} \leq 0\) C. \((6 x+4)^{2}>0\) D. \((8 x+7)^{2}<0\)

Find each product. Write the answer in standard form. $$(2+4 i)(-1+3 i)$$