Solving Equations Examples And Worksheet (Page 14 of 14) in pdf

A62

Appendix A

Review of Fundamental Concepts of Algebra

165. THINK ABOUT IT What is meant by equivalent

156. From the foot bones of an adult human male, an

anthropologist estimates that the person’s height was

equations? Give an example of two equivalent

69 inches. A few feet away from the site where the

equations.

foot bones were discovered, the anthropologist

166. Solve

3 x

in two ways.

discovers a male adult femur that is 19 inches long. Is

(a) Let

and solve the resulting equation

it likely that both the foot bones and the thigh bone

for

Then solve the -solution for

came from the same person?

(b) Expand and collect like terms in the equation, and

157. VOLUME OF A BILLIARD BALL A billiard ball has

solve the resulting equation for

a volume of 5.96 cubic inches. Find the radius of a

billiard ball.

158. LENGTH OF A TANK The diameter of a cylindrical

THINK ABOUT IT In Exercises 167–170, write a quadratic

propane gas tank is 4 feet. The total volume of the tank

equation that has the given solutions. (There are many

is 603.2 cubic feet. Find the length of the tank.

correct answers.)

159. GEOMETRY A “Slow Moving Vehicle” sign has the

167.

and 6

shape of an equilateral triangle. The sign has a

168.

and

perimeter of 129 centimeters. Find the length of each

169.

and

side of the sign. Find the area of the sign.

160. GEOMETRY

170.

and

The radius of a traffic cone is

14 centimeters and the lateral surface area of the cone is

In Exercises 171 and 172, consider an equation of the form

1617 square centimeters. Find the height of the cone.

where and are constants.

161. VOTING POPULATION

The total voting-age

population

(in millions) in the United States from

171. Find

and

when the solution of the equation is

1990 through 2006 can be modeled by

(There are many correct answers.)

172. WRITING Write a short paragraph listing the steps

182.17

1.542t

required to solve this equation involving absolute values,

0.018t

and explain why it is important to check your solutions.

where represents the year, with

corresponding

to 1990.

(Source: U.S. Census Bureau)

In Exercises 173 and 174, consider an equation of the form

where and are constants.

(a) In which year did the total voting-age population

reach 200 million?

173. Find

and

when the solution of the equation is

(b) Use the model to predict the year in which the

20.

(There are many correct answers.)

total voting-age population will reach 241 million.

174. WRITING Write a short paragraph listing the steps

Is this prediction reasonable? Explain.

required to solve this equation involving radicals, and

162. AIRLINE PASSENGERS

An airline offers daily

explain why it is important to check your solutions.

flights between Chicago and Denver. The total monthly

175. Solve each equation, given that and are not zero.

cost

(in millions of dollars) of these flights is

0.2x

where is the number of passengers

(a)

(in thousands). The total cost of the flights for June is

(b) ax

2.5 million dollars. How many passengers flew in

June?

CAPSTONE

176.

EXPLORATION

(a) Explain the difference between a conditional

equation and an identity.

TRUE OR FALSE? In Exercises 163 and 164, determine

(b) Give an example of an absolute value equation

whether the statement is true or false. Justify your answer.

that has only one solution.

163. An equation can never have more than one extraneous

solution.

(d) Does raising each side of an equation to the th

164. When solving an absolute value equation, you will

power always yield an equivalent equation? Explain.

always have to check more than one solution.

Solving Equations Examples And Worksheet Page 14

Related Articles

Related forms

Related Categories