91Ó°ÊÓ

Identify each number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions will apply. ) $$\sqrt{24}$$

Solve each problem. Cylinder Dimensions A right circular cylinder has radius 6 in, and volume \(144 \pi\) in. \(^{3} .\) What is its height? (In the figure, \(h=\) height.)

The length of each side of a square is 3 in. more than the length of each side of a smaller square. The sum of the areas of the squares is 149 in. \(^{2} .\) Find the lengths of the sides of the two squares.

Solve each problem. Recycling Bin Dimensions A recycling bin is in the shape of a rectangular box. Find the height of the box if its length is \(18 \mathrm{ft}\), its width is \(8 \mathrm{ft}\), and its surface area is \(496 \mathrm{ft}^{2}\). ( In the figure, \(h=\) height. Assume that the given surface area includes that of the top lid of the box.)

Solve each problem. Distance between Cities On a vacation, Elwyn averaged 50 mph traveling from Denver to Minneapolis. Returning by a different route that covered the same number of miles, he averaged 55 mph. What is the distance between the two cities if his total traveling time was 32 hr?

A landscape architect has included a rectangular flower bed measuring 9 ft by 5 ft in her plans for a new building. She wants to use two colors of flowers in the bed, one in the center and the other for a border of the same width on all four sides. If she has enough plants to cover \(24 \mathrm{ft}^{2}\) for the border, how wide can the border be?

Solve each problem. Running Times Mary and Janet are running in the Apple Hill Fun Run. Mary runs at 7 mph, Janet at \(5 \mathrm{mph}\). If they start at the same time, how long will it be before they are \(1.5 \mathrm{mi}\) apart?

A rectangular piece of metal is 10 in. longer than it is wide. Squares with sides 2 in. long are cut from the four corners, and the flaps are folded upward to form an open box. If the volume of the box is 832 in. \(^{3}\), what were the original dimensions of the piece of metal?

Track Event Speeds At the 2008 Summer Olympics in Beijing. China, Usain Bolt (Jamaica) set a new Olympic and world record in the 100 -m dash with a time of 9.69 sec. If this pace could be maintained for an entire 26 -mi marathon, what would his time be? How would this time compare to the fastest time for a marathon, which is 2 hr, 3 min, 59 sec, also set in \(2008 ?\) (Hint: 1 m es 3.281 ft.) (Source: World Almanac and Book of Facts.)

Solve each inequality. Give the solution set using interval notation. $$|2 x+5|<3$$