Problem Set 11: Geometry
Practice Makes Perfect
Use the Properties of Angles In the following exercises, find ⓐ the supplement and ⓑ the complement of the given angle. [latex-display]\text{53^\circ }[/latex-display] ⓐ 127° ⓑ 37° [latex-display]\text{16^\circ }[/latex-display] [latex-display]\text{29^\circ }[/latex-display] ⓐ 151° ⓑ 61° [latex-display]\text{72^\circ }[/latex-display] In the following exercises, use the properties of angles to solve. Find the supplement of a [latex]\text{135^\circ }[/latex] angle. 45° Find the complement of a [latex]\text{38^\circ }[/latex] angle. Find the complement of a [latex]27.5^\circ [/latex] angle. 62.5° Find the supplement of a [latex]109.5^\circ [/latex] angle. Two angles are supplementary. The larger angle is [latex]\text{56^\circ }[/latex] more than the smaller angle. Find the measures of both angles. 62°, 118° Two angles are supplementary. The smaller angle is [latex]\text{36^\circ }[/latex] less than the larger angle. Find the measures of both angles. Two angles are complementary. The smaller angle is [latex]\text{34^\circ }[/latex] less than the larger angle. Find the measures of both angles. 62°, 28° Two angles are complementary. The larger angle is [latex]\text{52^\circ }[/latex] more than the smaller angle. Find the measures of both angles. Use the Properties of Triangles In the following exercises, solve using properties of triangles. The measures of two angles of a triangle are [latex]\text{26^\circ }[/latex] and [latex]\text{98^\circ }[/latex]. Find the measure of the third angle. 56° The measures of two angles of a triangle are [latex]\text{61^\circ }[/latex] and [latex]\text{84^\circ }[/latex]. Find the measure of the third angle. The measures of two angles of a triangle are [latex]\text{105^\circ }[/latex] and [latex]\text{31^\circ }[/latex]. Find the measure of the third angle. 44° The measures of two angles of a triangle are [latex]\text{47^\circ }[/latex] and [latex]\text{72^\circ }[/latex]. Find the measure of the third angle. One angle of a right triangle measures [latex]\text{33^\circ }[/latex]. What is the measure of the other angle? 57° One angle of a right triangle measures [latex]\text{51^\circ }[/latex]. What is the measure of the other angle? One angle of a right triangle measures [latex]22.5^\circ [/latex]. What is the measure of the other angle? 67.5° One angle of a right triangle measures [latex]36.5^\circ [/latex]. What is the measure of the other angle? The two smaller angles of a right triangle have equal measures. Find the measures of all three angles. 45°, 45°, 90° The measure of the smallest angle of a right triangle is [latex]\text{20^\circ }[/latex] less than the measure of the other small angle. Find the measures of all three angles. The angles in a triangle are such that the measure of one angle is twice the measure of the smallest angle, while the measure of the third angle is three times the measure of the smallest angle. Find the measures of all three angles. 30°, 60°, 90° The angles in a triangle are such that the measure of one angle is [latex]\text{20^\circ }[/latex] more than the measure of the smallest angle, while the measure of the third angle is three times the measure of the smallest angle. Find the measures of all three angles. Find the Length of the Missing Side In the following exercises, [latex]\Delta ABC[/latex] is similar to [latex]\Delta XYZ[/latex]. Find the length of the indicated side.

















Everyday Math
Building a scale model Joe wants to build a doll house for his daughter. He wants the doll house to look just like his house. His house is [latex]30[/latex] feet wide and [latex]35[/latex] feet tall at the highest point of the roof. If the dollhouse will be [latex]2.5[/latex] feet wide, how tall will its highest point be? 2.9 feet Measurement A city engineer plans to build a footbridge across a lake from point [latex]\text{X}[/latex] to point [latex]\text{Y}[/latex], as shown in the picture below. To find the length of the footbridge, she draws a right triangle [latex]\text{XYZ}[/latex], with right angle at [latex]\text{X}[/latex]. She measures the distance from [latex]\text{X}[/latex] to [latex]\text{Z},800[/latex] feet, and from [latex]\text{Y}[/latex] to [latex]\text{Z},1,000[/latex] feet. How long will the bridge be?
Writing Exercises
Write three of the properties of triangles from this section and then explain each in your own words. Answers will vary. Explain how the figure below illustrates the Pythagorean Theorem for a triangle with legs of length [latex]3[/latex] and [latex]4[/latex].
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
Use Properties of Angles, Triangles, and the Pythagorean Theorem
Use Properties of Angles In the following exercises, solve using properties of angles. What is the supplement of a [latex]\text{48^\circ }[/latex] angle? 132° What is the complement of a [latex]\text{61^\circ }[/latex] angle? Two angles are complementary. The smaller angle is [latex]\text{24^\circ }[/latex] less than the larger angle. Find the measures of both angles. 33°, 57° Two angles are supplementary. The larger angle is [latex]\text{45^\circ }[/latex] more than the smaller angle. Find the measures of both angles. Use Properties of Triangles In the following exercises, solve using properties of triangles. The measures of two angles of a triangle are [latex]22[/latex] and [latex]85[/latex] degrees. Find the measure of the third angle. 73° One angle of a right triangle measures [latex]41.5[/latex] degrees. What is the measure of the other small angle? One angle of a triangle is [latex]\text{30^\circ }[/latex] more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles. 30°, 60°, 90° One angle of a triangle is twice the measure of the smallest angle. The third angle is [latex]\text{60^\circ }[/latex] more than the measure of the smallest angle. Find the measures of all three angles. In the following exercises, [latex]\Delta ABC[/latex] is similar to [latex]\Delta XYZ[/latex]. Find the length of the indicated side.








Use Properties of Rectangles, Triangles, and Trapezoids
Understand Linear, Square, Cubic Measure In the following exercises, would you measure each item using linear, square, or cubic measure? amount of sand in a sandbag cubic height of a tree size of a patio square length of a highway In the following exercises, find ⓐ the perimeter ⓑ the area of each figure

Practice Makes Perfect
Understand Linear, Square, and Cubic Measure In the following exercises, determine whether you would measure each item using linear, square, or cubic units. amount of water in a fish tank cubic length of dental floss living area of an apartment square floor space of a bathroom tile height of a doorway linear capacity of a truck trailer In the following exercises, find the ⓐ perimeter and ⓑ area of each figure. Assume each side of the square is [latex]1[/latex] cm.





Everyday Math
Fence Jose just removed the children’s playset from his back yard to make room for a rectangular garden. He wants to put a fence around the garden to keep out the dog. He has a [latex]50[/latex] foot roll of fence in his garage that he plans to use. To fit in the backyard, the width of the garden must be [latex]10[/latex] feet. How long can he make the other side if he wants to use the entire roll of fence? 15 ft Gardening Lupita wants to fence in her tomato garden. The garden is rectangular and the length is twice the width. It will take [latex]48[/latex] feet of fencing to enclose the garden. Find the length and width of her garden. Fence Christa wants to put a fence around her triangular flowerbed. The sides of the flowerbed are [latex]6[/latex] feet, [latex]8[/latex] feet, and [latex]10[/latex] feet. The fence costs [latex]$10[/latex] per foot. How much will it cost for Christa to fence in her flowerbed? $24 Painting Caleb wants to paint one wall of his attic. The wall is shaped like a trapezoid with height [latex]8[/latex] feet and bases [latex]20[/latex] feet and [latex]12[/latex] feet. The cost of the painting one square foot of wall is about [latex]$0.05[/latex]. About how much will it cost for Caleb to paint the attic wall?
Writing Exercises
If you need to put tile on your kitchen floor, do you need to know the perimeter or the area of the kitchen? Explain your reasoning. Answers will vary. If you need to put a fence around your backyard, do you need to know the perimeter or the area of the backyard? Explain your reasoning. Look at the two figures.
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
Solve Geometry Applications: Circles and Irregular Figures
Use Properties of Circles In the following exercises, solve using the properties of circles. Round answers to the nearest hundredth. A circular mosaic has radius [latex]3[/latex] meters. Find the ⓐ circumference ⓑ area of the mosaic ⓐ 18.84 m ⓑ 28.26 sq. m A circular fountain has radius [latex]8[/latex] feet. Find the ⓐ circumference ⓑ area of the fountain Find the diameter of a circle with circumference [latex]150.72[/latex] inches. 48 in. Find the radius of a circle with circumference [latex]345.4[/latex] centimeters Find the Area of Irregular Figures In the following exercises, find the area of each shaded region.





Solve Geometry Applications: Volume and Surface Area
Find Volume and Surface Area of Rectangular Solids In the following exercises, find the ⓐ volume ⓑ surface area of the rectangular solid a rectangular solid with length [latex]14[/latex] centimeters, width [latex]4.5[/latex] centimeters, and height [latex]10[/latex] centimeters ⓐ 630 cu. cm ⓑ 496 sq. cm a cube with sides that are [latex]3[/latex] feet long a cube of tofu with sides [latex]2.5[/latex] inches ⓐ 15.625 cu. in. ⓑ 37.5 sq. in. a rectangular carton with length [latex]32[/latex] inches, width [latex]18[/latex] inches, and height [latex]10[/latex] inches Find Volume and Surface Area of Spheres In the following exercises, find the ⓐ volume ⓑ surface area of the sphere. a sphere with radius [latex]4[/latex] yards ⓐ 267.95 cu. yd. ⓑ 200.96 sq. yd. a sphere with radius [latex]12[/latex] meters a baseball with radius [latex]1.45[/latex] inches ⓐ 12.76 cu. in. ⓑ 26.41 sq. in. a soccer ball with radius [latex]22[/latex] centimeters Find Volume and Surface Area of Cylinders In the following exercises, find the ⓐ volume ⓑ surface area of the cylinder a cylinder with radius [latex]2[/latex] yards and height [latex]6[/latex] yards ⓐ 75.36 cu. yd. ⓑ 100.48 sq. yd. a cylinder with diameter [latex]18[/latex] inches and height [latex]40[/latex] inches a juice can with diameter [latex]8[/latex] centimeters and height [latex]15[/latex] centimeters ⓐ 753.6 cu. cm ⓑ 477.28 sq. cm a cylindrical pylon with diameter [latex]0.8[/latex] feet and height [latex]2.5[/latex] feet Find Volume of Cones In the following exercises, find the volume of the cone. a cone with height [latex]5[/latex] meters and radius [latex]1[/latex] meter 5.233 cu. m a cone with height [latex]24[/latex] feet and radius [latex]8[/latex] feet a cone-shaped water cup with diameter [latex]2.6[/latex] inches and height [latex]2.6[/latex] inches 4.599 cu. in. a cone-shaped pile of gravel with diameter [latex]6[/latex] yards and height [latex]5[/latex] yards Find the complement of a [latex]\text{52^\circ }[/latex] angle. 38° The measure of one angle of a triangle is twice the measure of the smallest angle. The measure of the third angle is [latex]14[/latex] more than the measure of the smallest angle. Find the measures of all three angles. The perimeter of an equilateral triangle is [latex]145[/latex] feet. Find the length of each side. 48.3 [latex]\Delta ABC[/latex] is similar to [latex]\Delta XYZ[/latex]. Find the length of side [latex]c[/latex].




Practice Makes Perfect
Use the Properties of Circles In the following exercises, solve using the properties of circles. The lid of a paint bucket is a circle with radius [latex]7[/latex] inches. Find the ⓐ circumference and ⓑ area of the lid. ⓐ 43.96 in. ⓑ 153.86 sq. in. An extra-large pizza is a circle with radius [latex]8[/latex] inches. Find the ⓐ circumference and ⓑ area of the pizza. A farm sprinkler spreads water in a circle with radius of [latex]8.5[/latex] feet. Find the ⓐ circumference and ⓑ area of the watered circle. ⓐ 53.38 ft ⓑ 226.865 sq. ft A circular rug has radius of [latex]3.5[/latex] feet. Find the ⓐ circumference and ⓑ area of the rug. A reflecting pool is in the shape of a circle with diameter of [latex]20[/latex] feet. What is the circumference of the pool? 62.8 ft A turntable is a circle with diameter of [latex]10[/latex] inches. What is the circumference of the turntable? A circular saw has a diameter of [latex]12[/latex] inches. What is the circumference of the saw? 37.68 in. A round coin has a diameter of [latex]3[/latex] centimeters. What is the circumference of the coin? A barbecue grill is a circle with a diameter of [latex]2.2[/latex] feet. What is the circumference of the grill? 6.908 ft The top of a pie tin is a circle with a diameter of [latex]9.5[/latex] inches. What is the circumference of the top? A circle has a circumference of [latex]163.28[/latex] inches. Find the diameter. 52 in. A circle has a circumference of [latex]59.66[/latex] feet. Find the diameter. A circle has a circumference of [latex]17.27[/latex] meters. Find the diameter. 5.5 m A circle has a circumference of [latex]80.07[/latex] centimeters. Find the diameter. In the following exercises, find the radius of the circle with given circumference. A circle has a circumference of [latex]150.72[/latex] feet. 24 ft A circle has a circumference of [latex]251.2[/latex] centimeters. A circle has a circumference of [latex]40.82[/latex] miles. 6.5 mi A circle has a circumference of [latex]78.5[/latex] inches. Find the Area of Irregular Figures In the following exercises, find the area of the irregular figure. Round your answers to the nearest hundredth.























Everyday Math
Area of a Tabletop Yuki bought a drop-leaf kitchen table. The rectangular part of the table is a [latex]\text{1-ft}[/latex] by [latex]\text{3-ft}[/latex] rectangle with a semicircle at each end, as shown. ⓐ Find the area of the table with one leaf up. ⓑ Find the area of the table with both leaves up.
Writing Exercises
Describe two different ways to find the area of this figure, and then show your work to make sure both ways give the same area.
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
Practice Makes Perfect
Find Volume and Surface Area of Rectangular Solids In the following exercises, find ⓐ the volume and ⓑ the surface area of the rectangular solid with the given dimensions. length [latex]2[/latex] meters, width [latex]1.5[/latex] meters, height [latex]3[/latex] meters ⓐ 9 cu. m ⓑ 27 sq. m length [latex]5[/latex] feet, width [latex]8[/latex] feet, height [latex]2.5[/latex] feet length [latex]3.5[/latex] yards, width [latex]2.1[/latex] yards, height [latex]2.4[/latex] yards ⓐ 17.64 cu. yd. ⓑ 41.58 sq. yd. length [latex]8.8[/latex] centimeters, width [latex]6.5[/latex] centimeters, height [latex]4.2[/latex] centimeters In the following exercises, solve. Moving van A rectangular moving van has length [latex]16[/latex] feet, width [latex]8[/latex] feet, and height [latex]8[/latex] feet. Find its ⓐ volume and ⓑ surface area. ⓐ 1,024 cu. ft ⓑ 640 sq. ft Gift box A rectangular gift box has length [latex]26[/latex] inches, width [latex]16[/latex] inches, and height [latex]4[/latex] inches. Find its ⓐ volume and ⓑ surface area. Carton A rectangular carton has length [latex]21.3[/latex] cm, width [latex]24.2[/latex] cm, and height [latex]6.5[/latex] cm. Find its ⓐ volume and ⓑ surface area. ⓐ 3,350.49 cu. cm ⓑ 1,622.42 sq. cm Shipping container A rectangular shipping container has length [latex]22.8[/latex] feet, width [latex]8.5[/latex] feet, and height [latex]8.2[/latex] feet. Find its ⓐ volume and ⓑ surface area. In the following exercises, find ⓐ the volume and ⓑ the surface area of the cube with the given side length. [latex]5[/latex] centimeters ⓐ 125 cu. cm ⓑ 150 sq. cm [latex]6[/latex] inches [latex]10.4[/latex] feet ⓐ 1124.864 cu. ft. ⓑ 648.96 sq. ft [latex]12.5[/latex] meters In the following exercises, solve. Science center Each side of the cube at the Discovery Science Center in Santa Ana is [latex]64[/latex] feet long. Find its ⓐ volume and ⓑ surface area. ⓐ 262,144 cu. ft ⓑ 24,576 sq. ft Museum A cube-shaped museum has sides [latex]45[/latex] meters long. Find its ⓐ volume and ⓑ surface area. Base of statue The base of a statue is a cube with sides [latex]2.8[/latex] meters long. Find its ⓐ volume and ⓑ surface area. ⓐ 21.952 cu. m ⓑ 47.04 sq. m Tissue box A box of tissues is a cube with sides 4.5 inches long. Find its ⓐ volume and ⓑ surface area. Find the Volume and Surface Area of Spheres In the following exercises, find ⓐ the volume and ⓑ the surface area of the sphere with the given radius. Round answers to the nearest hundredth. [latex]3[/latex] centimeters ⓐ 113.04 cu. cm ⓑ 113.04 sq. cm [latex]9[/latex] inches [latex]7.5[/latex] feet ⓐ 1,766.25 cu. ft ⓑ 706.5 sq. ft [latex]2.1[/latex] yards In the following exercises, solve. Round answers to the nearest hundredth. Exercise ball An exercise ball has a radius of [latex]15[/latex] inches. Find its ⓐ volume and ⓑ surface area. ⓐ 14,130 cu. in. ⓑ 2,826 sq. in. Balloon ride The Great Park Balloon is a big orange sphere with a radius of [latex]36[/latex] feet . Find its ⓐ volume and ⓑ surface area. Golf ball A golf ball has a radius of [latex]4.5[/latex] centimeters. Find its ⓐ volume and ⓑ surface area. ⓐ 381.51 cu. cm ⓑ 254.34 sq. cm Baseball A baseball has a radius of [latex]2.9[/latex] inches. Find its ⓐ volume and ⓑ surface area. Find the Volume and Surface Area of a Cylinder In the following exercises, find ⓐ the volume and ⓑ the surface area of the cylinder with the given radius and height. Round answers to the nearest hundredth. radius [latex]3[/latex] feet, height [latex]9[/latex] feet ⓐ 254.34 cu. ft ⓑ 226.08 sq. ft radius [latex]5[/latex] centimeters, height [latex]15[/latex] centimeters radius [latex]1.5[/latex] meters, height [latex]4.2[/latex] meters ⓐ 29.673 cu. m ⓑ 53.694 sq. m radius [latex]1.3[/latex] yards, height [latex]2.8[/latex] yards In the following exercises, solve. Round answers to the nearest hundredth. Coffee can A can of coffee has a radius of [latex]5[/latex] cm and a height of [latex]13[/latex] cm. Find its ⓐ volume and ⓑ surface area. ⓐ 1,020.5 cu. cm ⓑ 565.2 sq. cm Snack pack A snack pack of cookies is shaped like a cylinder with radius [latex]4[/latex] cm and height [latex]3[/latex] cm. Find its ⓐ volume and ⓑ surface area. Barber shop pole A cylindrical barber shop pole has a diameter of [latex]6[/latex] inches and height of [latex]24[/latex] inches. Find its ⓐ volume and ⓑ surface area. ⓐ 678.24 cu. in. ⓑ 508.68 sq. in. Architecture A cylindrical column has a diameter of [latex]8[/latex] feet and a height of [latex]28[/latex] feet. Find its ⓐ volume and ⓑ surface area. Find the Volume of Cones In the following exercises, find the volume of the cone with the given dimensions. Round answers to the nearest hundredth. height [latex]9[/latex] feet and radius [latex]2[/latex] feet 37.68 cu. ft height [latex]8[/latex] inches and radius [latex]6[/latex] inches height [latex]12.4[/latex] centimeters and radius [latex]5[/latex] cm 324.47 cu. cm height [latex]15.2[/latex] meters and radius [latex]4[/latex] meters In the following exercises, solve. Round answers to the nearest hundredth. Teepee What is the volume of a cone-shaped teepee tent that is [latex]10[/latex] feet tall and [latex]10[/latex] feet across at the base? 261.67 cu. ft Popcorn cup What is the volume of a cone-shaped popcorn cup that is [latex]8[/latex] inches tall and [latex]6[/latex] inches across at the base? Silo What is the volume of a cone-shaped silo that is [latex]50[/latex] feet tall and [latex]70[/latex] feet across at the base? 64,108.33 cu. ft Sand pile What is the volume of a cone-shaped pile of sand that is [latex]12[/latex] meters tall and [latex]30[/latex] meters across at the base?Everyday Math
Street light post The post of a street light is shaped like a truncated cone, as shown in the picture below. It is a large cone minus a smaller top cone. The large cone is [latex]30[/latex] feet tall with base radius [latex]1[/latex] foot. The smaller cone is [latex]10[/latex] feet tall with base radius of [latex]0.5[/latex] feet. To the nearest tenth, ⓐ find the volume of the large cone. ⓑ find the volume of the small cone. ⓒ find the volume of the post by subtracting the volume of the small cone from the volume of the large cone.
Writing Exercises
The formulas for the volume of a cylinder and a cone are similar. Explain how you can remember which formula goes with which shape. Answers will vary. Which has a larger volume, a cube of sides of [latex]8[/latex] feet or a sphere with a diameter of [latex]8[/latex] feet? Explain your reasoning.Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
Practice Makes Perfect
Make Unit Conversions in the U.S. System In the following exercises, convert the units. A park bench is [latex]6[/latex] feet long. Convert the length to inches. A floor tile is [latex]2[/latex] feet wide. Convert the width to inches. 24 inches A ribbon is [latex]18[/latex] inches long. Convert the length to feet. Carson is [latex]45[/latex] inches tall. Convert his height to feet. 3.75 feet Jon is [latex]6[/latex] feet [latex]4[/latex] inches tall. Convert his height to inches. Faye is [latex]4[/latex] feet [latex]10[/latex] inches tall. Convert her height to inches. 58 inches A football field is [latex]160[/latex] feet wide. Convert the width to yards. On a baseball diamond, the distance from home plate to first base is [latex]30[/latex] yards. Convert the distance to feet. 90 feet Ulises lives [latex]1.5[/latex] miles from school. Convert the distance to feet. Denver, Colorado, is [latex]5,183[/latex] feet above sea level. Convert the height to miles. 0.98 miles A killer whale weighs [latex]4.6[/latex] tons. Convert the weight to pounds. Blue whales can weigh as much as [latex]150[/latex] tons. Convert the weight to pounds. 300,000 pounds An empty bus weighs [latex]35,000[/latex] pounds. Convert the weight to tons. At take-off, an airplane weighs [latex]220,000[/latex] pounds. Convert the weight to tons. 110 tons The voyage of the Mayflower took [latex]2[/latex] months and [latex]5[/latex] days. Convert the time to days. Lynn’s cruise lasted [latex]6[/latex] days and [latex]18[/latex] hours. Convert the time to hours. 162 hours Rocco waited [latex]1\frac{1}{2}[/latex] hours for his appointment. Convert the time to seconds. Misty’s surgery lasted [latex]2\frac{1}{4}[/latex] hours. Convert the time to seconds. 8100 seconds How many teaspoons are in a pint? How many tablespoons are in a gallon? 256 tablespoons JJ’s cat, Posy, weighs [latex]14[/latex] pounds. Convert her weight to ounces. April’s dog, Beans, weighs [latex]8[/latex] pounds. Convert his weight to ounces. 128 ounces Baby Preston weighed [latex]7[/latex] pounds [latex]3[/latex] ounces at birth. Convert his weight to ounces. Baby Audrey weighed [latex]6[/latex] pounds [latex]15[/latex] ounces at birth. Convert her weight to ounces. 111 ounces Crista will serve [latex]20[/latex] cups of juice at her son’s party. Convert the volume to gallons. Lance needs [latex]500[/latex] cups of water for the runners in a race. Convert the volume to gallons. 31.25 gallons Use Mixed Units of Measurement in the U.S. System In the following exercises, solve and write your answer in mixed units. Eli caught three fish. The weights of the fish were [latex]2[/latex] pounds [latex]4[/latex] ounces, [latex]1[/latex] pound [latex]11[/latex] ounces, and [latex]4[/latex] pounds [latex]14[/latex] ounces. What was the total weight of the three fish? Judy bought [latex]1[/latex] pound [latex]6[/latex] ounces of almonds, [latex]2[/latex] pounds [latex]3[/latex] ounces of walnuts, and [latex]8[/latex] ounces of cashews. What was the total weight of the nuts? 4 lbs. 1 oz. One day Anya kept track of the number of minutes she spent driving. She recorded trips of [latex]45,10,8,65,20,\text{and 35 minutes.}[/latex] How much time (in hours and minutes) did Anya spend driving? Last year Eric went on [latex]6[/latex] business trips. The number of days of each was [latex]5,2,8,12,6,\text{and 3.}[/latex] How much time (in weeks and days) did Eric spend on business trips last year? 5 weeks and 1 day Renee attached a [latex]\text{6-foot - 6-inch}[/latex] extension cord to her computer’s [latex]\text{3-foot - 8-inch}[/latex] power cord. What was the total length of the cords? Fawzi’s SUV is [latex]6[/latex] feet [latex]4[/latex] inches tall. If he puts a [latex]\text{2-foot - 10-inch}[/latex] box on top of his SUV, what is the total height of the SUV and the box? 9 ft 2 in Leilani wants to make [latex]8[/latex] placemats. For each placemat she needs [latex]18[/latex] inches of fabric. How many yards of fabric will she need for the [latex]8[/latex] placemats? Mireille needs to cut [latex]24[/latex] inches of ribbon for each of the [latex]12[/latex] girls in her dance class. How many yards of ribbon will she need altogether? 8 yards Make Unit Conversions in the Metric System In the following exercises, convert the units. Ghalib ran [latex]5[/latex] kilometers. Convert the length to meters. Kitaka hiked [latex]8[/latex] kilometers. Convert the length to meters. 8000 meters Estrella is [latex]1.55[/latex] meters tall. Convert her height to centimeters. The width of the wading pool is [latex]2.45[/latex] meters. Convert the width to centimeters. 245 centimeters Mount Whitney is [latex]3,072[/latex] meters tall. Convert the height to kilometers. The depth of the Mariana Trench is [latex]10,911[/latex] meters. Convert the depth to kilometers. 10.911 kilometers June’s multivitamin contains [latex]1,500[/latex] milligrams of calcium. Convert this to grams. A typical ruby-throated hummingbird weights [latex]3[/latex] grams. Convert this to milligrams. 3000 milligrams One stick of butter contains [latex]91.6[/latex] grams of fat. Convert this to milligrams. One serving of gourmet ice cream has [latex]25[/latex] grams of fat. Convert this to milligrams. 25,000 milligrams The maximum mass of an airmail letter is [latex]2[/latex] kilograms. Convert this to grams. Dimitri’s daughter weighed [latex]3.8[/latex] kilograms at birth. Convert this to grams. 3800 grams A bottle of wine contained [latex]750[/latex] milliliters. Convert this to liters. A bottle of medicine contained [latex]300[/latex] milliliters. Convert this to liters. 0.3 liters Use Mixed Units of Measurement in the Metric System In the following exercises, solve and write your answer in mixed units. Matthias is [latex]1.8[/latex] meters tall. His son is [latex]89[/latex] centimeters tall. How much taller, in centimeters, is Matthias than his son? Stavros is [latex]1.6[/latex] meters tall. His sister is [latex]95[/latex] centimeters tall. How much taller, in centimeters, is Stavros than his sister? 65 centimeters A typical dove weighs [latex]345[/latex] grams. A typical duck weighs [latex]1.2[/latex] kilograms. What is the difference, in grams, of the weights of a duck and a dove? Concetta had a [latex]\text{2-kilogram}[/latex] bag of flour. She used [latex]180[/latex] grams of flour to make biscotti. How many kilograms of flour are left in the bag? 1.82 kilograms Harry mailed [latex]5[/latex] packages that weighed [latex]420[/latex] grams each. What was the total weight of the packages in kilograms? One glass of orange juice provides [latex]560[/latex] milligrams of potassium. Linda drinks one glass of orange juice every morning. How many grams of potassium does Linda get from her orange juice in [latex]30[/latex] days? 16.8 grams Jonas drinks [latex]200[/latex] milliliters of water [latex]8[/latex] times a day. How many liters of water does Jonas drink in a day? One serving of whole grain sandwich bread provides [latex]6[/latex] grams of protein. How many milligrams of protein are provided by [latex]7[/latex] servings of whole grain sandwich bread? 42,000 milligrams Convert Between U.S. and Metric Systems In the following exercises, make the unit conversions. Round to the nearest tenth. Bill is [latex]75[/latex] inches tall. Convert his height to centimeters. Frankie is [latex]42[/latex] inches tall. Convert his height to centimeters. 106.7 centimeters Marcus passed a football [latex]24[/latex] yards. Convert the pass length to meters. Connie bought [latex]9[/latex] yards of fabric to make drapes. Convert the fabric length to meters. 8.2 meters Each American throws out an average of [latex]1,650[/latex] pounds of garbage per year. Convert this weight to kilograms. An average American will throw away [latex]90,000[/latex] pounds of trash over his or her lifetime. Convert this weight to kilograms. 41,500 kilograms A [latex]\text{5K}[/latex] run is [latex]5[/latex] kilometers long. Convert this length to miles. Kathryn is [latex]1.6[/latex] meters tall. Convert her height to feet. 5.2 feet Dawn’s suitcase weighed [latex]20[/latex] kilograms. Convert the weight to pounds. Jackson’s backpack weighs [latex]15[/latex] kilograms. Convert the weight to pounds. 33 pounds Ozzie put [latex]14[/latex] gallons of gas in his truck. Convert the volume to liters. Bernard bought [latex]8[/latex] gallons of paint. Convert the volume to liters. 30.4 liters Convert between Fahrenheit and Celsius In the following exercises, convert the Fahrenheit temperature to degrees Celsius. Round to the nearest tenth. [latex-display]86\text{^\circ F}[/latex-display] [latex-display]77\text{^\circ F}[/latex-display] 25°C [latex-display]104\text{^\circ F}[/latex-display] [latex-display]14\text{^\circ F}[/latex-display] −10°C [latex-display]72\text{^\circ F}[/latex-display] [latex-display]4\text{^\circ F}[/latex-display] −15.5°C [latex-display]0\text{^\circ F}[/latex-display] [latex-display]120\text{^\circ F}[/latex-display] 48.9°C In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth. [latex-display]5\text{^\circ C}[/latex-display] [latex-display]25\text{^\circ C}[/latex-display] 77°F [latex-display]-10\text{^\circ C}[/latex-display] [latex-display]-15\text{^\circ C}[/latex-display] 5°F [latex-display]22\text{^\circ C}[/latex-display] [latex-display]8\text{^\circ C}[/latex-display] 46.4°F [latex-display]43\text{^\circ C}[/latex-display] [latex-display]16\text{^\circ C}[/latex-display] 60.8°FEveryday Math
Nutrition Julian drinks one can of soda every day. Each can of soda contains [latex]40[/latex] grams of sugar. How many kilograms of sugar does Julian get from soda in [latex]1[/latex] year? Reflectors The reflectors in each lane-marking stripe on a highway are spaced [latex]16[/latex] yards apart. How many reflectors are needed for a one-mile-long stretch of highway? 110 reflectorsWriting Exercises
Some people think that [latex]65\text{^\circ }[/latex] to [latex]75\text{^\circ }[/latex] Fahrenheit is the ideal temperature range. ⓐ What is your ideal temperature range? Why do you think so? ⓑ Convert your ideal temperatures from Fahrenheit to Celsius. ⓐ Did you grow up using the U.S. customary or the metric system of measurement? ⓑ Describe two examples in your life when you had to convert between systems of measurement. ⓒ Which system do you think is easier to use? Explain.Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
Chapter Review Exercises
Rational and Irrational Numbers
In the following exercises, write as the ratio of two integers. [latex-display]6[/latex-display] [latex-display]-5[/latex-display] [latex-display]\frac{-5}{1}[/latex-display] [latex-display]2.9[/latex-display] [latex-display]1.8[/latex-display] [latex-display]\frac{18}{10}[/latex-display] In the following exercises, determine which of the numbers is rational. [latex-display]0.42,0.\stackrel{\text{-}}{\text{3}},2.56813\dots [/latex-display] [latex-display]\text{0.75319\ldots },0.\stackrel{\text{-}}{16},1.95[/latex-display] [latex-display]0.\stackrel{\text{-}}{16},1.95[/latex-display] In the following exercises, identify whether each given number is rational or irrational. ⓐ [latex]\sqrt{49}[/latex] ⓑ [latex]\sqrt{55}[/latex] ⓐ [latex]\sqrt{72}[/latex] ⓑ [latex]\sqrt{64}[/latex] ⓐ irrational ⓑ rational In the following exercises, list the ⓐ whole numbers, ⓑ integers, ⓒ rational numbers, ⓓ irrational numbers, ⓔ real numbers for each set of numbers. [latex-display]-9,0,\text{0.361....},\frac{8}{9},\sqrt{16},9[/latex-display] [latex-display]-5,-2\frac{1}{4},-\sqrt{4},0.\stackrel{\text{-}}{25},\frac{13}{5},4[/latex-display] ⓐ [latex]4[/latex] ⓑ [latex]-5,-\sqrt{4},4[/latex] ⓒ [latex]-5,-2\frac{1}{4},-\sqrt{4},0.\stackrel{\text{-}}{25},\frac{13}{5},4[/latex] ⓓ none ⓔ [latex]-5,-2\frac{1}{4},-\sqrt{4},0.\stackrel{\text{-}}{25},\frac{13}{5},4[/latex]Commutative and Associative Properties
In the following exercises, use the commutative property to rewrite the given expression. [latex-display]6+4=____[/latex-display] [latex-display]-14\cdot 5=____[/latex-display] −14·5 = 5(−14) [latex-display]3n=____[/latex-display] [latex-display]a+8=____[/latex-display] a + 8 = 8 + a In the following exercises, use the associative property to rewrite the given expression. [latex-display]\left(13\cdot 5\right)\cdot 2=_____[/latex-display] [latex-display]\left(22+7\right)+3=_____[/latex-display] (22 + 7) + 3 = 22 + (7 + 3) [latex-display]\left(4+9x\right)+x=_____[/latex-display] [latex-display]\frac{1}{2}\left(22y\right)=_____[/latex-display] [latex-display]\frac{1}{2}\left(22y\right)=\left(\frac{1}{2}\cdot 22\right)y[/latex-display] In the following exercises, evaluate each expression for the given value. If [latex]y=\frac{11}{12}[/latex], evaluate: ⓐ [latex]y+0.7+\left(-y\right)[/latex] ⓑ [latex]y+\left(-y\right)+0.7[/latex] If [latex]z=-\frac{5}{3}[/latex], evaluate: ⓐ [latex]z+5.39+\left(-z\right)[/latex] ⓑ [latex]z+\left(-z\right)+5.39[/latex] ⓐ 5.39 ⓑ 5.39 If [latex]k=65[/latex], evaluate: ⓐ [latex]\frac{4}{9}\left(\frac{9}{4}k\right)[/latex] ⓑ [latex]\left(\frac{4}{9}\cdot \frac{9}{4}\right)k[/latex] If [latex]m=-13[/latex], evaluate: ⓐ [latex]-\frac{2}{5}\left(\frac{5}{2}m\right)[/latex] ⓑ [latex]\left(-\frac{2}{5}\cdot \frac{5}{2}\right)m[/latex] ⓐ 13 ⓑ 13 In the following exercises, simplify using the commutative and associative properties. [latex-display]6y+37+\left(-6y\right)[/latex-display] [latex-display]\frac{1}{4}+\frac{11}{15}+\left(-\frac{1}{4}\right)[/latex-display] [latex-display]\frac{11}{15}[/latex-display] [latex-display]\frac{14}{11}\cdot \frac{35}{9}\cdot \frac{14}{11}[/latex-display] [latex-display]-18\cdot 15\cdot \frac{2}{9}[/latex-display] −60 [latex-display]\left(\frac{7}{12}+\frac{4}{5}\right)+\frac{1}{5}[/latex-display] [latex-display]\left(3.98d+0.75d\right)+1.25d[/latex-display] 5.98 d [latex-display]-12\left(4m\right)[/latex-display] [latex-display]30\left(\frac{5}{6}q\right)[/latex-display] 25 q [latex-display]11x+8y+16x+15y[/latex-display] [latex-display]52m+\left(-20n\right)+\left(-18m\right)+\left(-5n\right)[/latex-display] 34 m + (−25 n)Distributive Property
In the following exercises, simplify using the distributive property. [latex-display]7\left(x+9\right)[/latex-display] [latex-display]9\left(u - 4\right)[/latex-display] 9y − 36 [latex-display]-3\left(6m - 1\right)[/latex-display] [latex-display]-8\left(-7a - 12\right)[/latex-display] 56a + 96 [latex-display]\frac{1}{3}\left(15n - 6\right)[/latex-display] [latex-display]\left(y+10\right)\cdot p[/latex-display] yp + 10p [latex-display]\left(a - 4\right)-\left(6a+9\right)[/latex-display] [latex-display]4\left(x+3\right)-8\left(x - 7\right)[/latex-display] −4x + 68 In the following exercises, evaluate using the distributive property. If [latex]u=2[/latex], evaluate ⓐ [latex]3\left(8u+9\right)\text{and}[/latex] ⓑ [latex]3\cdot 8u+3\cdot 9[/latex] to show that [latex]3\left(8u+9\right)=3\cdot 8u+3\cdot 9[/latex] If [latex]n=\frac{7}{8}[/latex], evaluate ⓐ [latex]8\left(n+\frac{1}{4}\right)[/latex] and ⓑ [latex]8\cdot n+8\cdot \frac{1}{4}[/latex] to show that [latex]8\left(n+\frac{1}{4}\right)=8\cdot n+8\cdot \frac{1}{4}[/latex] ⓐ 9 ⓑ 9 If [latex]d=14[/latex], evaluate ⓐ [latex]-100\left(0.1d+0.35\right)[/latex] and ⓑ [latex]-100\cdot \left(0.1d\right)+\left(-100\right)\left(0.35\right)[/latex] to show that [latex]-100\left(0.1d+0.35\right)=-100\cdot \left(0.1d\right)+\left(-100\right)\left(0.35\right)[/latex] If [latex]y=-18[/latex], evaluate ⓐ [latex]-\left(y - 18\right)[/latex] and ⓑ [latex]-y+18[/latex] to show that [latex]-\left(y - 18\right)=-y+18[/latex] ⓐ 36 ⓑ 36Properties of Identities, Inverses, and Zero
In the following exercises, identify whether each example is using the identity property of addition or multiplication. [latex-display]-35\left(1\right)=-35[/latex-display] [latex-display]29+0=29[/latex-display] identity property of addition [latex-display]\left(6x+0\right)+4x=6x+4x[/latex-display] [latex-display]9\cdot 1+\left(-3\right)=9+\left(-3\right)[/latex-display] identity property of multiplication In the following exercises, find the additive inverse. [latex-display]-32[/latex-display] [latex-display]19.4[/latex-display] −19.4 [latex-display]\frac{3}{5}[/latex-display] [latex-display]-\frac{7}{15}[/latex-display] [latex-display]\frac{7}{15}[/latex-display] In the following exercises, find the multiplicative inverse. [latex-display]\frac{9}{2}[/latex-display] [latex-display]-5[/latex-display] [latex-display]-\frac{1}{5}[/latex-display] [latex-display]\frac{1}{10}[/latex-display] [latex-display]-\frac{4}{9}[/latex-display] [latex-display]-\frac{9}{4}[/latex-display] In the following exercises, simplify. [latex-display]83\cdot 0[/latex-display] [latex-display]\frac{0}{9}[/latex-display] 0 [latex-display]\frac{5}{0}[/latex-display] [latex-display]0\div \frac{2}{3}[/latex-display] 0 [latex-display]43+39+\left(-43\right)[/latex-display] [latex-display]\left(n+6.75\right)+0.25[/latex-display] n + 7 [latex-display]\frac{5}{13}\cdot 57\cdot \frac{13}{5}[/latex-display] [latex-display]\frac{1}{6}\cdot 17\cdot 12[/latex-display] 34 [latex-display]\frac{2}{3}\cdot 28\cdot \frac{3}{7}[/latex-display] [latex-display]9\left(6x - 11\right)+15[/latex-display] 54x − 84Systems of Measurement
In the following exercises, convert between U.S. units. Round to the nearest tenth. A floral arbor is [latex]7[/latex] feet tall. Convert the height to inches. A picture frame is [latex]42[/latex] inches wide. Convert the width to feet. 3.5 feet Kelly is [latex]5[/latex] feet [latex]4[/latex] inches tall. Convert her height to inches. A playground is [latex]45[/latex] feet wide. Convert the width to yards. 15 yards The height of Mount Shasta is [latex]14,179[/latex] feet. Convert the height to miles. Shamu weighs [latex]4.5[/latex] tons. Convert the weight to pounds. 9000 pounds The play lasted [latex]1\frac{3}{4}[/latex] hours. Convert the time to minutes. How many tablespoons are in a quart? 64 tablespoons Naomi’s baby weighed [latex]5[/latex] pounds [latex]14[/latex] ounces at birth. Convert the weight to ounces. Trinh needs [latex]30[/latex] cups of paint for her class art project. Convert the volume to gallons. 1.9 gallons In the following exercises, solve, and state your answer in mixed units. John caught [latex]4[/latex] lobsters. The weights of the lobsters were [latex]1[/latex] pound [latex]9[/latex] ounces, [latex]1[/latex] pound [latex]12[/latex] ounces, [latex]4[/latex] pounds [latex]2[/latex] ounces, and [latex]2[/latex] pounds [latex]15[/latex] ounces. What was the total weight of the lobsters? Every day last week, Pedro recorded the amount of time he spent reading. He read for [latex]50,25,83,45,32,60,\text{and}135[/latex] minutes. How much time, in hours and minutes, did Pedro spend reading? 7 hours 10 minutes Fouad is [latex]6[/latex] feet [latex]2[/latex] inches tall. If he stands on a rung of a ladder [latex]8[/latex] feet [latex]10[/latex] inches high, how high off the ground is the top of Fouad’s head? Dalila wants to make pillow covers. Each cover takes [latex]30[/latex] inches of fabric. How many yards and inches of fabric does she need for [latex]4[/latex] pillow covers? 3 yards, 12 inches In the following exercises, convert between metric units. Donna is [latex]1.7[/latex] meters tall. Convert her height to centimeters. Mount Everest is [latex]8,850[/latex] meters tall. Convert the height to kilometers. 8.85 kilometers One cup of yogurt contains [latex]488[/latex] milligrams of calcium. Convert this to grams. One cup of yogurt contains [latex]13[/latex] grams of protein. Convert this to milligrams. 13,000 milligrams Sergio weighed [latex]2.9[/latex] kilograms at birth. Convert this to grams. A bottle of water contained [latex]650[/latex] milliliters. Convert this to liters. 0.65 liters In the following exercises, solve. Minh is [latex]2[/latex] meters tall. His daughter is [latex]88[/latex] centimeters tall. How much taller, in meters, is Minh than his daughter? Selma had a [latex]\text{1-liter}[/latex] bottle of water. If she drank [latex]145[/latex] milliliters, how much water, in milliliters, was left in the bottle? 855 milliliters One serving of cranberry juice contains [latex]30[/latex] grams of sugar. How many kilograms of sugar are in [latex]30[/latex] servings of cranberry juice? One ounce of tofu provides [latex]2[/latex] grams of protein. How many milligrams of protein are provided by [latex]5[/latex] ounces of tofu? 10,000 milligrams In the following exercises, convert between U.S. and metric units. Round to the nearest tenth. Majid is [latex]69[/latex] inches tall. Convert his height to centimeters. A college basketball court is [latex]84[/latex] feet long. Convert this length to meters. 25.6 meters Caroline walked [latex]2.5[/latex] kilometers. Convert this length to miles. Lucas weighs [latex]78[/latex] kilograms. Convert his weight to pounds. 171.6 pounds Steve’s car holds [latex]55[/latex] liters of gas. Convert this to gallons. A box of books weighs [latex]25[/latex] pounds. Convert this weight to kilograms. 11.4 kilograms In the following exercises, convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth. [latex-display]95\text{^\circ F}[/latex-display] [latex-display]23\text{^\circ F}[/latex-display] −5°C [latex-display]20\text{^\circ F}[/latex-display] [latex-display]64\text{^\circ F}[/latex-display] 17.8°C In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth. [latex-display]30\text{^\circ C}[/latex-display] [latex-display]-5\text{^\circ C}[/latex-display] 23°F [latex-display]-12\text{^\circ C}[/latex-display] [latex-display]24\text{^\circ C}[/latex-display] 75.2°FChapter Practice Test
For the numbers [latex]\text{0.18349\ldots },0.\stackrel{\text{-}}{\text{2}},1.67[/latex], list the ⓐ rational numbers and ⓑ irrational numbers. Is [latex]\sqrt{144}[/latex] rational or irrational? [latex-display]\sqrt{144}=12\text{therefore rational.}[/latex-display] From the numbers [latex]-4,-1\frac{1}{2},0,\frac{5}{8},\sqrt{2},7[/latex], which are ⓐ integers ⓑ rational ⓒ irrational ⓓ real numbers? Rewrite using the commutative property: [latex]x\cdot 14=_________[/latex] x·14 = 14·x Rewrite the expression using the associative property: [latex]\left(y+6\right)+3=_______________[/latex] Rewrite the expression using the associative property: [latex]\left(8\cdot 2\right)\cdot 5=___________[/latex] (8·2)·3 = 8·(2·3) Evaluate [latex]\frac{3}{16}\left(\frac{16}{3}n\right)[/latex] when [latex]n=42[/latex]. For the number [latex]\frac{2}{5}[/latex] find the ⓐ additive inverse ⓑ multiplicative inverse. ⓐ [latex]-\frac{2}{5}[/latex] ⓑ [latex]\frac{5}{2}[/latex] In the following exercises, simplify the given expression. [latex-display]\frac{3}{4}\left(-29\right)\left(\frac{4}{3}\right)[/latex-display] [latex-display]-3+15y+3[/latex-display] 15y [latex-display]\left(1.27q+0.25q\right)+0.75q[/latex-display] [latex-display]\left(\frac{8}{15}+\frac{2}{9}\right)+\frac{7}{9}[/latex-display] [latex-display]\frac{23}{15}[/latex-display] [latex-display]-18\left(\frac{3}{2}n\right)[/latex-display] [latex-display]14y+\left(-6z\right)+16y+2z[/latex-display] 30y − 4z [latex-display]9\left(q+9\right)[/latex-display] [latex-display]6\left(5x - 4\right)[/latex-display] 30x − 24 [latex-display]-10\left(0.4n+0.7\right)[/latex-display] [latex-display]\frac{1}{4}\left(8a+12\right)[/latex-display] 2a + 3 [latex-display]m\left(n+2\right)[/latex-display] [latex-display]8\left(6p - 1\right)+2\left(9p+3\right)[/latex-display] 66p − 2 [latex-display]\left(12a+4\right)-\left(9a+6\right)[/latex-display] [latex-display]\frac{0}{8}[/latex-display] 0 [latex-display]\frac{4.5}{0}[/latex-display] [latex-display]0\div \left(\frac{2}{3}\right)[/latex-display] 0 In the following exercises, solve using the appropriate unit conversions. Azize walked [latex]4\frac{1}{2}[/latex] miles. Convert this distance to feet. [latex]\text{(1 mile}=\text{5,280 feet).}[/latex] One cup of milk contains [latex]276[/latex] milligrams of calcium. Convert this to grams. [latex]\text{(1 milligram}=\text{0.001 gram)}[/latex] .276 grams Larry had [latex]5[/latex] phone customer phone calls yesterday. The calls lasted [latex]28,44,9,75,\text{and}55[/latex] minutes. How much time, in hours and minutes, did Larry spend on the phone? [latex]\text{(1 hour}=\text{60 minutes)}[/latex] Janice ran [latex]15[/latex] kilometers. Convert this distance to miles. Round to the nearest hundredth of a mile. [latex]\text{(1 mile}=\text{1.61 kilometers)}[/latex] 9.317 miles Yolie is [latex]63[/latex] inches tall. Convert her height to centimeters. Round to the nearest centimeter. [latex]\text{(1 inch}=\text{2.54 centimeters)}[/latex] Use the formula [latex]F=\frac{9}{5}C+32[/latex] to convert [latex]35\text{^\circ C}[/latex] to degrees [latex]\text{F}[/latex] 95°FLicenses & Attributions
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