Chapter 1

Solve each equation using the quadratic formula. $$x^{2}-6 x=-7$$

Solve each equation or inequality. $$|-5 x+7|-4<-6$$

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? According to the problem, the revenue currently generated is \(\$ 35,000 .\) Substitute this value for revenue into the equation from Exercise \(53 .\) Solve for \(x\) to answer the question in the problem.

Solve each equation for \(x\). $$\frac{x-1}{2 a}=2 x-a$$

Solve each equation using the quadratic formula. $$x^{2}-4 x=-1$$

Solve each equation or inequality. $$|10-4 x| \geq-4$$

The cost of a charter flight to Miami is \(\$ 225\) each for 75 passengers, with a refund of \(\$ 5\) per passenger for each passenger in excess of \(75 .\) How many passengers must take the flight to produce a revenue of \(\$ 16,000 ?\)

Solve each equation for \(x\). $$a^{2} x+3 x=2 a^{2}$$

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

Solve each equation using the quadratic formula. $$x^{2}=2 x-5$$

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

A charter bus company charges a fare of \(\$ 40\) per person, plus \(\$ 2\) per person for each unsold seat on the bus. If the bus holds 100 passengers and \(x\) represents the number of unsold seats, how many passengers must ride the bus to produce revenue of \(\$ 5950 ?\) ( Note: Because of the company's commitment to efficient fuel use, the charter will not run unless filled to at least half-capacity.)

Find each product. Write the answer in standard form. $$(2+i)^{2}$$

Solve each equation for \(x\). $$a x+b^{2}=b x-a^{2}$$

Solve each equation. $$\sqrt{x}+2=\sqrt{4+7 \sqrt{x}}$$

Solve each equation using the quadratic formula. $$x^{2}=2 x-10$$

The manager of a cherry orchard wants to schedule the annual harvest. If the cherries are picked now, the average yield per tree will be \(100 \mathrm{lb},\) and the cherries can be sold for 40 cents per pound. Past experience shows that the yield per tree will increase about 5 lb per week, while the price will decrease about 2 cents per pound per week. How many weeks should the manager wait to get an average revenue of \(\$ 38.40\) per tree?

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

Solve each equation. $$\sqrt[3]{4 x+3}=\sqrt[3]{2 x-1}$$

Solve each equation using the quadratic formula. $$-4 x^{2}=-12 x+11$$

A local group of scouts has been collecting old aluminum cans for recycling. The group has already collected \(12,000\) Ib of cans, for which they could currently receive \(\$ 4\) per hundred pounds. The group can continue to collect cans at the rate of 400 lb per day. However, a glut in the old-can market has caused the recycling company to announce that it will lower its price, starting immediately, by \(\$ 0.10\) per hundred pounds per day. The scouts can make only one trip to the recycling center. How many days should they wait in order to get \(\$ 490\) for their cans?

Solve each equation. $$\sqrt[3]{2 x}=\sqrt[3]{5 x+2}$$

Solve each equation or inequality. $$|8 x+5|=0$$

Simple Interest Elmer Velasquez borrowed \(\$ 3150\) from his brother Julio to pay for books and tuition. He agreed to repay Julio in 6 months with simple annual interest at 4 \(\%\). (a) How much will the interest amount to? (b) What amount must Elmer pay Julio at the end of the 6 months?

Solve each equation. $$\sqrt[3]{5 x^{2}-6 x+2}-\sqrt[3]{x}=0$$

Solve each equation using the quadratic formula. $$\frac{1}{2} x^{2}+\frac{1}{4} x-3=0$$

Solve each equation or inequality. $$|7+2 x|=0$$

Find each product. Write the answer in standard form. $$(6-4 i)(6+4 i)$$

Simple Interest Levada Qualls borrows \(\$ 30,900\) from her bank to open a florist shop. She agrees to repay the money in 18 months with simple annual interest of \(5.5 \%\) (a) How much must she pay the bank in 18 months? (b) How much of the amount in part (a) is interest?

Solve each equation. $$\sqrt[3]{3 x^{2}-9 x+8}=\sqrt[3]{x}$$

Solve each equation using the quadratic formula. $$\frac{2}{3} x^{2}+\frac{1}{4} x=3$$

Sohe each equation or inequality. \(|4.3 x+9.8|<0\)

Find each product. Write the answer in standard form. $$(\sqrt{6}+i)(\sqrt{6}-i)$$

Celsius and Fahrenheit Temperatures In the met- ric system of weights and measures, temperature is measured in degrees Celsius (" \(^{\circ}\) C) instead of degrees Fahrenheit \(\left(^{\circ} \mathrm{F}\right) .\) To convert between the two systems, we use the equations $$ C=\frac{5}{9}(F-32) \quad \text { and } \quad F=\frac{9}{5} C+32 $$ In each exercise, convert to the other system. Round answers to the nearest tenth of a degree if necessary. $$40^{\circ} \mathrm{C}$$

Solve each equation. $$\sqrt[4]{x-15}=2$$

Solve each equation using the quadratic formula. $$0.2 x^{2}+0.4 x-0.3=0$$

Celsius and Fahrenheit Temperatures In the met- ric system of weights and measures, temperature is measured in degrees Celsius (" \(^{\circ}\) C) instead of degrees Fahrenheit \(\left(^{\circ} \mathrm{F}\right) .\) To convert between the two systems, we use the equations $$ C=\frac{5}{9}(F-32) \quad \text { and } \quad F=\frac{9}{5} C+32 $$ In each exercise, convert to the other system. Round answers to the nearest tenth of a degree if necessary. $$200^{\circ} \mathrm{C}$$

Solve each equation. $$\sqrt[4]{3 x+1}=1$$

Solve each equation using the quadratic formula. $$0.1 x^{2}-0.1 x=0.3$$

Solve each equation or inequality. $$|2 x+1| \leq 0$$

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

Celsius and Fahrenheit Temperatures In the met- ric system of weights and measures, temperature is measured in degrees Celsius (" \(^{\circ}\) C) instead of degrees Fahrenheit \(\left(^{\circ} \mathrm{F}\right) .\) To convert between the two systems, we use the equations $$ C=\frac{5}{9}(F-32) \quad \text { and } \quad F=\frac{9}{5} C+32 $$ In each exercise, convert to the other system. Round answers to the nearest tenth of a degree if necessary. $$50^{\circ} \mathrm{F}$$

Solve each equation. $$\sqrt[4]{x^{2}+2 x}=\sqrt[4]{3}$$

Solve each equation or inequality. $$|3 x+2| \leq 0$$

Celsius and Fahrenheit Temperatures In the met- ric system of weights and measures, temperature is measured in degrees Celsius (" \(^{\circ}\) C) instead of degrees Fahrenheit \(\left(^{\circ} \mathrm{F}\right) .\) To convert between the two systems, we use the equations $$ C=\frac{5}{9}(F-32) \quad \text { and } \quad F=\frac{9}{5} C+32 $$ In each exercise, convert to the other system. Round answers to the nearest tenth of a degree if necessary. $$77^{\circ} \mathrm{F}$$

Solve each equation. $$\sqrt[4]{x^{2}+6 x}=2$$

Solve each equation using the quadratic formula. $$(3 x+2)(x-1)=3 x$$

Solve each equation or inequality. $$|3 x+2|>0$$

Find each product. Write the answer in standard form. $$3 i(2-i)^{2}$$

Celsius and Fahrenheit Temperatures In the met- ric system of weights and measures, temperature is measured in degrees Celsius (" \(^{\circ}\) C) instead of degrees Fahrenheit \(\left(^{\circ} \mathrm{F}\right) .\) To convert between the two systems, we use the equations $$ C=\frac{5}{9}(F-32) \quad \text { and } \quad F=\frac{9}{5} C+32 $$ In each exercise, convert to the other system. Round answers to the nearest tenth of a degree if necessary. $$100^{\circ} \mathrm{F}$$