RENTING AN APARTMENT Three students are planning to rent an apartment for a year and

Fill in the blanks. The equation is a ________ equation in written in general form.

Fill in the blanks. Squaring each side of an equation, multiplying each side of an equation by a variable quantity, and raising each side of an equation to a rational power are all operations that can introduce ________ solutions to a given equation.

Fill in the blanks. The equation is of ________ ________.

Fill in the blanks. To clear the equation of fractions, multiply each side of the equation by the least common denominator ________.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 530, find all solutions of the equation. Check your solutions in the original equation.

GRAPHICAL ANALYSIS In Exercises 3134, (a) use a graphing utility to graph the equation, (b) use the graph to approximate any -intercepts of the graph, (c) set and solve the resulting equation, and (d) compare the result of part (c) with the -intercepts of the graph.

GRAPHICAL ANALYSIS In Exercises 3134, (a) use a graphing utility to graph the equation, (b) use the graph to approximate any -intercepts of the graph, (c) set and solve the resulting equation, and (d) compare the result of part (c) with the -intercepts of the graph.

GRAPHICAL ANALYSIS In Exercises 3134, (a) use a graphing utility to graph the equation, (b) use the graph to approximate any -intercepts of the graph, (c) set and solve the resulting equation, and (d) compare the result of part (c) with the -intercepts of the graph.

GRAPHICAL ANALYSIS In Exercises 3134, (a) use a graphing utility to graph the equation, (b) use the graph to approximate any -intercepts of the graph, (c) set and solve the resulting equation, and (d) compare the result of part (c) with the -intercepts of the graph.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 3558, find all solutions of the equation. Check your solutions in the original equation.

GRAPHICAL ANALYSIS In Exercises 5962, (a) use a graphing utility to graph the equation, (b) use the graph to approximate any -intercepts of the graph, (c) set and solve the resulting equation, and (d) compare the result of part (c) with the -intercepts of the graph.

GRAPHICAL ANALYSIS In Exercises 5962, (a) use a graphing utility to graph the equation, (b) use the graph to approximate any -intercepts of the graph, (c) set and solve the resulting equation, and (d) compare the result of part (c) with the -intercepts of the graph.

GRAPHICAL ANALYSIS In Exercises 5962, (a) use a graphing utility to graph the equation, (b) use the graph to approximate any -intercepts of the graph, (c) set and solve the resulting equation, and (d) compare the result of part (c) with the -intercepts of the graph.

GRAPHICAL ANALYSIS In Exercises 5962, (a) use a graphing utility to graph the equation, (b) use the graph to approximate any -intercepts of the graph, (c) set and solve the resulting equation, and (d) compare the result of part (c) with the -intercepts of the graph.

In Exercises 6376, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 6376, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 6376, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 6376, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 6376, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 6376, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 6376, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 6376, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 6376, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 6376, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 6376, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 6376, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 6376, find all solutions of the equation. Check your solutions in the original equation.

In Exercises 6376, find all solutions of the equation. Check your solutions in the original equation.

GRAPHICAL ANALYSIS In Exercises 77 80, (a) use a graphing utility to graph the equation, (b) use the graph to approximate any -intercepts of the graph, (c) set and solve the resulting equation, and (d) compare the result of part (c) with the -intercepts of the graph.

GRAPHICAL ANALYSIS In Exercises 77 80, (a) use a graphing utility to graph the equation, (b) use the graph to approximate any -intercepts of the graph, (c) set and solve the resulting equation, and (d) compare the result of part (c) with the -intercepts of the graph.

GRAPHICAL ANALYSIS In Exercises 77 80, (a) use a graphing utility to graph the equation, (b) use the graph to approximate any -intercepts of the graph, (c) set and solve the resulting equation, and (d) compare the result of part (c) with the -intercepts of the graph.

GRAPHICAL ANALYSIS In Exercises 77 80, (a) use a graphing utility to graph the equation, (b) use the graph to approximate any -intercepts of the graph, (c) set and solve the resulting equation, and (d) compare the result of part (c) with the -intercepts of the graph.

In Exercises 8188, find the real solutions of the equation algebraically. (Round your answers to three decimal places.)

In Exercises 8188, find the real solutions of the equation algebraically. (Round your answers to three decimal places.)

In Exercises 8188, find the real solutions of the equation algebraically. (Round your answers to three decimal places.)

In Exercises 8188, find the real solutions of the equation algebraically. (Round your answers to three decimal places.)

In Exercises 8188, find the real solutions of the equation algebraically. (Round your answers to three decimal places.)

In Exercises 8188, find the real solutions of the equation algebraically. (Round your answers to three decimal places.)

In Exercises 8188, find the real solutions of the equation algebraically. (Round your answers to three decimal places.)

In Exercises 8188, find the real solutions of the equation algebraically. (Round your answers to three decimal places.)

THINK ABOUT IT In Exercises 8998, find an equation that has the given solutions. (There are many correct answers.)

THINK ABOUT IT In Exercises 8998, find an equation that has the given solutions. (There are many correct answers.)

THINK ABOUT IT In Exercises 8998, find an equation that has the given solutions. (There are many correct answers.)

THINK ABOUT IT In Exercises 8998, find an equation that has the given solutions. (There are many correct answers.)

THINK ABOUT IT In Exercises 8998, find an equation that has the given solutions. (There are many correct answers.)

THINK ABOUT IT In Exercises 8998, find an equation that has the given solutions. (There are many correct answers.)

THINK ABOUT IT In Exercises 8998, find an equation that has the given solutions. (There are many correct answers.)

THINK ABOUT IT In Exercises 8998, find an equation that has the given solutions. (There are many correct answers.)

THINK ABOUT IT In Exercises 8998, find an equation that has the given solutions. (There are many correct answers.)

THINK ABOUT IT In Exercises 8998, find an equation that has the given solutions. (There are many correct answers.)

CHARTERING A BUS A college charters a bus for $1700 to take a group to a museum. When six more students join the trip, the cost per student drops by $7.50. How many students were in the original group?

RENTING AN APARTMENT Three students are planning to rent an apartment for a year and share equally in the cost. By adding a fourth person, each person could save $75 a month. How much is the monthly rent?

AIRSPEED An airline runs a commuter flight between Portland, Oregon and Seattle, Washington, which are 145 miles apart. If the average speed of the plane could be increased by 40 miles per hour, the travel time would be decreased by 12 minutes. What airspeed is required to obtain this decrease in travel time?

AVERAGE SPEED A family drove 1080 miles to their vacation lodge. Because of increased traffic density, their average speed on the return trip was decreased by 6 miles per hour and the trip took hours longer. Determine their average speed on the way to the lodge.

MUTUAL FUNDS A deposit of $2500 in a mutual fund reaches a balance of $3052.49 after 5 years. What annual interest rate on a certificate of deposit compounded monthly would yield an equivalent return?

MUTUAL FUNDS A sales representative for a mutual funds company describes a guaranteed investment fund that the company is offering to new investors. You are told that if you deposit $10,000 in the fund you will be guaranteed a return of at least $25,000 after 20 years. (Assume the interest is compounded quarterly.) (a) What is the annual interest rate if the investment only meets the minimum guaranteed amount? (b) After 20 years, you receive $32,000. What is the annual interest rate?

NUMBER OF DOCTORS The number of medical doctors (in thousands) in the United States from 1998 through 2006 can be modeled by where represents the year, with corresponding to 1998. (Source: American Medical Association) (a) In which year did the number of medical doctors reach 875,000? (b) Use the model to predict when the number of medical doctors will reach 1,000,000. Is this prediction reasonable? Explain.

VOTING POPULATION The total voting-age population (in millions) in the United States from 1990 through 2006 can be modeled by where represents the year, with corresponding to 1990. (Source: U.S. Census Bureau) (a) In which year did the total voting-age population reach 210 million? (b) Use the model to predict when the total voting-age population will reach 245 million. Is this prediction reasonable? Explain.

SATURATED STEAM The temperature (in degrees Fahrenheit) of saturated steam increases as pressure increases. This relationship is approximated by the model where is the absolute pressure (in pounds per square inch). (a) Use the model to complete the table. (b) The temperature of steam at sea level is Use the table in part (a) to approximate the absolute pressure at this temperature. (c) Solve part (b) algebraically. (d) Use a graphing utility to verify your solutions for parts (b) and (c).

AIRLINE PASSENGERS An airline offers daily flights between Chicago and Denver. The total monthly cost (in millions of dollars) of these flights is where 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?

DEMAND The demand equation for a video game is modeled by where is the number of units demanded per day and is the price per unit. Approximate the demand when the price is $37.55.

DEMAND The demand equation for a high definition television set is modeled by where is the number of units demanded per month and is the price per unit. Approximate the demand when the price is $750.

BASEBALL A baseball diamond has the shape of a square in which the distance from home plate to second base is approximately feet. Approximate the distance between the bases.

METEOROLOGY A meteorologist is positioned 100 feet from the point where a weather balloon is launched. When the balloon is at height the distance (in feet) between the meteorologist and the balloon is (a) Use a graphing utility to graph the equation. Use the trace feature to approximate the value of when (b) Complete the table. Use the table to approximate the value of when (c) Find algebraically when (d) Compare the results of the three methods. In each case, what information did you gain that was not apparent in another solution method?

GEOMETRY You construct a cone with a base radius of 8 inches. The lateral surface area of the cone can be represented by the equation where is the height of the cone. (a) Use a graphing utility to graph the equation. Use the trace feature to approximate the value of when square inches. (b) Complete the table. Use the table to approximate the value of when (c) Find algebraically when (d) Compare the results of the three methods. In each case, what information did you gain that was not apparent in another solution method?

LABOR Working together, two people can complete a task in 8 hours. Working alone, one person takes 2 hours longer than the other to complete the task. How long would it take for each person to complete the task?

LABOR Working together, two people can complete a task in 12 hours. Working alone, one person takes 3 hours longer than the other to complete the task. How long would it take for each person to complete the task?

POWER LINE A power station is on one side of a river that is mile wide, and a factory is 8 miles downstream on the other side of the river, as shown in the figure. It costs $24 per foot to run power lines over land and $30 per foot to run them under water. (a) Write the total cost of running power lines in terms of (see figure). (b) Find the total cost when (c) Find the length when (d) Use a graphing utility to graph the equation from part (a). (e) Use your graph from part (d) to find the value of that minimizes the cost.

In Exercises 117 and 118, solve for the indicated variable. A PERSONS TANGENTIAL SPEED IN A ROTOR Solve for

In Exercises 117 and 118, solve for the indicated variable. INDUCTANCE Solve for

TRUE OR FALSE? In Exercises 119121, determine whether the statement is true or false. Justify your answer. An equation can never have more than one extraneous solution.

TRUE OR FALSE? In Exercises 119121, determine whether the statement is true or false. Justify your answer. When solving an absolute value equation, you will always have to check more than one solution.

TRUE OR FALSE? In Exercises 119121, determine whether the statement is true or false. Justify your answer. The equation has no solution.

CAPSTONE When solving an equation, list three operations that can introduce an extraneous solution. Write an equation that has an extraneous solution

In Exercises 123 and 124, find such that the distance between the given points is 13. Explain your results.

In Exercises 123 and 124, find such that the distance between the given points is 13. Explain your results.

In Exercises 125 and 126, find such that the distance between the given points is 17. Explain your results.

In Exercises 125 and 126, find such that the distance between the given points is 17. Explain your results.

Find and when the solution of the equation is (There are many correct answers.)

WRITING Write a short paragraph listing the steps required to solve this equation involving absolute values and explain why it is important to check your solutions.

Find and when the solution of the equation is (There are many correct answers.)

WRITING Write a short paragraph listing the steps required to solve this equation involving radicals and explain why it is important to check your solutions.