List all of the numbers in the set
natural numbers.
whole numbers.
integers.
rational numbers.
irrational numbers.
real numbers.
In Exercises 2–5, state which property of the real numbers is being used.
In Exercises 6 and 7, write each interval in inequality notation and then graph each interval.
In Exercises 8 and 9, write each inequality in interval notation and then graph the interval.
In Exercises 10–13, rewrite each expression without absolute value bars.
In Exercises 14–37, evaluate each expression.
In Exercises 38–41, evaluate each expression for the given values of x and y.
In Exercises 42–49, simplify each expression. Write each answer with only positive exponents. Assume that all variables represent positive numbers.
In Exercises 50–66, simplify each expression. Assume that all variables represent positive numbers.
In Exercises 67–70, rationalize the denominator of each expression.
Write
Write
In Exercises 73–82, perform the indicated operations. Leave the resulting polynomial in standard form.
In Exercises 83–104, factor each polynomial completely.
In Exercises 105–118, perform the indicated operation. Simplify your answer.
Assuming that a right triangle has legs a and b of lengths 20 and 21, respectively, find the length of the hypotenuse.
One leg of a right triangle measures 5 inches. The hypotenuse is 1 inch longer than the other leg. Find the length of the hypotenuse.
Find the area A and the perimeter P of a right triangle with hypotenuse of length 20 and a leg of length 12.
Find the volume V of a box of length
Find the area of a rectangular rug if its width is 6 feet and its diagonal measures 10 feet.
The amount of alcohol in the body of a person who drinks x grams of alcohol every hour over a relatively long period is
Because of the earth's curvature, the maximum distance a person can see from a height h above the ground is
A contaminated reservoir contains 2% arsenic. The percentage (in decimal) of arsenic in the reservoir can be reduced by adding water. Assuming that the reservoir contains a million gallons of water, write a rational expression whose values give the percentage of arsenic in the reservoir when x gallons of water are added to it.
The height (in feet) of an open fruit crate that is three times as long as it is wide is given by
An object thrown down with an initial velocity of