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mathematics
contemporary mathematics

Contemporary Mathematics 1st Edition OpenStax - Solutions

You want to install a tinted protective shield on this window. How many square feet do you order? 6 ft 4 ft
Find the area of the shaded region in the given figure. d = 20 cm L = 42 cm
Find the surface area of a hexagonal prism with side length \(5 \mathrm{~cm}\), apothem \(3.1 \mathrm{~cm}\), and height \(15 \mathrm{~cm}\).
Find the surface area of the triangular prism.A triangular prism has an equilateral base and side lengths of 15 in, triangle height of 10 in, and prism length of 25 in.
Find the volume of the triangular prism.A triangular prism has an equilateral base and side lengths of 15 in, triangle height of 10 in, and prism length of 25 in.
Find the volume of a right cylinder with radius equal to \(1.5 \mathrm{~cm}\) and height equal to \(5 \mathrm{~cm}\).
Find the surface area of the right cylinder.A right cylinder has a radius of \(6 \mathrm{~cm}\) and a height of \(10 \mathrm{~cm}\).
Find the volume of the right cylinder.A right cylinder has a radius of \(6 \mathrm{~cm}\) and a height of \(10 \mathrm{~cm}\).
Find the lengths of the missing sides in the figure shown. b C 12 60
Find the measure of the unknown side and angle. C 3.44 7
For the following exercises, use this line (Figure 10.4).1. Define \(\overline{D E}\).2. Define \(F\).3. Define \(\overleftrightarrow{D F}\)4. Define \(\overline{E F}\). D E Figure 10.4 F
View the street map (Figure 10.6) as a series of line segments from point to point. For example, we have vertical line segments \(\overline{A B}, \overline{B C}\), and \(\overline{C D}\) on the right. On the left side of the map, we have vertical line segments \(\overline{H I}, \overline{F G}\).
Identify the sets of parallel and perpendicular lines in Figure 10.9. G E E M B A F C H K D Figure 10.9
Use the line (Figure 10.10) for the following exercises. Draw each answer over the main drawing.1. Find \(\overrightarrow{B D} \cap \overleftarrow{C A}\)2. Find \(\overline{A B} \cup \overline{A D}\).3. Find \(\overleftrightarrow{A D} \cup \overrightarrow{B C}\).4. Find \(\overleftrightarrow{A D}
For the following exercises, refer to Figure 10.19 7 y 9 5. 4- 3. 2 B 1 D AT -7 -6 -5 -4 3-2-10 -1 2- 1 2 3 4 5 6 7 -3- C -4- -5- -6 -7 Figure 10.19
Name two pairs of intersecting planes on the shower enclosure illustration (Figure 10.20).1. Identify the location of points \(A, B, C\), and \(D\).2. Describe the line from point \(A\) to point \(D\).3. Describe the line from point \(C\) containing point \(B\).4. Does this figure represent a
Determine which angles are acute, right, obtuse, or straight on the graph (Figure 10.26). You may want to use a protractor for this one. L K Figure 10.26 10 H G F E
Solve for the angle measurements in Figure 10.29. 32x-7 Figure 10.29 5x+2
Solve for the angle measurements in Figure 10.31. 9x - 5 4x 7x-5 Figure 10.31
In Figure 10.33, one angle measures \(40^{\circ}\). Find the measures of the remaining angles. 2 3 40 Figure 10.33
You live on the corner of First Avenue and Linton Street. You want to plant a garden in the far corner of your property (Figure 10.38) and fence off the area. However, the corner of your property does not form the traditional right angle. You learned from the city that the streets cross at an angle
In Figure 10.39 given that angle 3 measures \(40^{\circ}\), find the measures of the remaining angles and give a reason for your solution. 2 angle 3-40/4 7 5 6 00 8 Figure 10.39 12
In Figure 10.40 given that angle 2 measures \(23^{\circ}\), find the measure of the remaining angles and state the reason for your solution. 3. 4 5 6 8 Figure 10.40 23 -12 angle 2
Find the measures of the angles \(1,2,4,11,12\), and 14 in Figure 10.41 and the reason for your answer given that \(l_{1}\) and \(l_{2}\) are parallel. 62 9 14/62 -12 7 8 11/12 5 6 4 1 62 Figure 10.41
Find the measure of each angle in the triangle shown (Figure 10.46). We know that the sum of the angles must equal \(180^{\circ}\). to (x+17) Figure 10.46 (3x-62)
Find the measure of angles numbered 1-5 in Figure 10.47. 89 30 2 4 3. Figure 10.47 5 75 134
In Figure 10.48 , is the triangle \(A B C\) congruent to triangle \(D E F\) ? B A F Figure 10.48 E
What congruence theorem is illustrated in Figure 10.53? Figure 10.53
What congruence theorem is illustrated in Figure 10.54? Figure 10.54
Are the two triangles shown in Figure 10.56 similar? 4 57 8.06 33 7 Triangle (a) 3.5 33 4.03 57 Triangle () Figure 10.56 2
In Figure 10.57, is triangle \(\delta\) (delta) similar to triangle \(\varepsilon\) (epsilon)? Find the lengths of sides \(x\) and \(y\) as part of your answer. x 6 2.375 Triangle (5) Figure 10.57 2.475 Triangle (e) 1.069
A person who is 5 feet tall is standing 50 feet away from the base of a tree (Figure 10.58). The tree casts a 57 -foot shadow. The person casts a 7-foot shadow. What is the height of the tree? X 57 ft Figure 10.58 5 ft 7 ft
At a certain time of day, a radio tower casts a shadow 180 feet long (Figure 10.59). At the same time, a 9 -foot truck casts a shadow 15 feet long. What is the height of the tower? Tower (ft) Truck 9 ft 180 ft 15 ft Figure 10.59
Identify each polygon. 1. 2. 3. 4.
What polygons make up Figure 10.66? 2 1 19. 16 8 10 3 15 11 5 12 13 14 7 17 4 Figure 10.66
Find the perimeter of a regular pentagon with a side length of \(7 \mathrm{~cm}\) (Figure 10.67). 7 cm Figure 10.67
Find the perimeter of a regular octagon with a side length of \(14 \mathrm{~cm}\) (Figure 10.68). 14 cm 14 cm Figure 10.68
Find the measure of an interior angle in a regular octagon using the formula, and then find the sum of all the interior angles using the sum formula.
Use algebra to calculate the measure of each interior angle of the five-sided polygon (Figure 10.70). B 120 A 5(x+7) 6x+25 5(3x-5) 5(2x+5) D E Figure 10.70
Find the sum of the measure of the exterior angles of the pentagon (Figure 10.72). B Figure 10.72
Find the circumference of a circle with diameter \(10 \mathrm{~cm}\).
Find the radius of a circle with a circumference of \(12 \mathrm{in}\).
You decide to make a trim for the window in Figure 10.74. How many feet of trim do you need to buy? T 6 ft- Figure 10.74 12 ft
Suppose you have a hexagon on a grid as in Figure 10.81. Translate the hexagon 5 units to the right and 3 units up. B C D A F E Figure 10.81
Figure 10.84 illustrates a tessellation begun with an equilateral triangle. Explain how this pattern is produced. Figure 10.84
An obtuse triangle is reflected about the dashed line, and the two shapes are joined together. How does the tessellation shown in Figure 10.87 materialize? Figure 10.87
Show how this tessellation (Figure 10.88) can be achieved. B' C' B C D' A D Figure 10.88
Do regular pentagons tessellate the plane by themselves (Figure 10.94)? Figure 10.94
Do regular octagons tessellate the plane by themselves (Figure 10.95)? Figure 10.95
Create a tessellation using two colors and two shapes.
Find the area of this triangle that has a base of \(4 \mathrm{~cm}\) and the height is \(6 \mathrm{~cm}\) (Figure 10.105). h = 6 cm! h=6 b=4 cm Figure 10.105
You have a garden with an area of 196 square feet. How wide can the garden be if the length is 28 feet?
Jennifer is planning to install vinyl floor tile in her rectangular-shaped basement, which measures \(29 \mathrm{ft}\) by \(16 \mathrm{ft}\). How many boxes of floor tile should she buy and how much will it cost if one box costs \(\$ 50\) and covers \(20 \mathrm{ft}^{2}\) ?
In the parallelogram (Figure 10.109), if \(F B=10, A D=15\), find the exact area of the parallelogram. B 110 cm A F 15 cm Figure 10.109 D C
The boundaries of a city park form a parallelogram (Figure 10.110). The park takes up one city block, which is contained by two sets of parallel streets. Each street measures 55 yd long. The perpendicular distance between streets is 39 yd. How much sod, sold by the square foot, should the city
\(A B C D\) (Figure 10.112) is a regular trapezoid with \(\overline{A B} \| \overline{C D}\). Find the exact perimeter of \(A B C D\), and then find the area. A 11 in B 13.5 in I ih = 10 in D 31 in Figure 10.112 C
Find the measurement of the diagonal \(d_{1}\) if the area of the rhombus is \(240 \mathrm{~cm}^{2}\), and the measure of \(d_{2}=24 \mathrm{~cm}\).
You notice a child flying a rhombus-shaped kite on the beach. When it falls to the ground, it falls on a beach towel measuring 36 in by 72 in. You notice that one of the diagonals of the kite is the same length as the 36 in width of the towel. The second diagonal appears to be 2 in longer. What is
Find the area of a regular octagon with the apothem equal to \(18 \mathrm{~cm}\) and a side length equal to \(13 \mathrm{~cm}\) (Figure 10.117). i la 18 cm side = 13 cm Figure 10.117
Carpeting comes in units of square yards. Your living room measures \(21 \mathrm{ft}\) wide by \(24 \mathrm{ft}\) long. How much carpeting do you buy?
Find the area of a circle with diameter of \(16 \mathrm{~cm}\).
You decide to order a pizza to share with your friend for dinner. The price for an 8 -inch diameter pizza is \(\$ 7.99\). The price for 16 -inch diameter pizza is \(\$ 13.99\). Which one do you think is the better value?
You want to purchase a tinted film, sold by the square foot, for the window in Figure 10.119. (This problem should look familiar as we saw it earlier when calculating circumference.) The bottom part of the window is a rectangle, and the top part is a semicircle. Find the area and calculate the
The patio in your backyard measures \(20 \mathrm{ft}\) by \(10 \mathrm{ft}\) (Figure 10.120). On one-half of the patio, you have a 4 -foot diameter table with six chairs taking up an area of approximately \(36 \mathrm{sq}\) feet. On the other half of the patio, you want to install a hot tub
A sod farmer wants to fertilize a rectangular plot of land \(150 \mathrm{ft}\) by \(240 \mathrm{ft}\). A bag of fertilizer covers \(5,000 \mathrm{ft}^{2}\) and costs \(\$ 200\). How much will it cost to fertilize the entire plot of land?
Find the surface area and volume of the rectangular prism that has a width of \(10 \mathrm{~cm}\), a length of \(5 \mathrm{~cm}\), and a height of 3 \(\mathrm{cm}\) (Figure 10.128). w= 10 cm Figure 10.128 h = 3 cm 1=5cm
Find the surface area of the triangular prism (Figure 10.130). /= 8.49 in h = 6 in 1 = 8.49 in /= 12 in Figure 10.130 W = 10 in
Find the surface area and the volume of the right triangular prism with an equilateral triangle as the base and height (Figure 10.131). h = 10.39 cm h = 10 cm 1= 12 cm Figure 10.131
Katherine and Romano built a greenhouse made of glass with a metal roof (Figure 10.132). In order to determine the heating and cooling requirements, the surface area must be known. Calculate the total surface area of the greenhouse. 11.5 ft 12.1 ft 22 ft Figure 10.132 95 ft 6.5 ft
Given the cylinder in Figure 10.133, which has a radius of 5 inches and a height of 12 inches, find the surface area and the volume. r = 5 in 12 in Figure 10.133 Right Cylinder
A can of apple pie filling has a radius of \(4 \mathrm{~cm}\) and a height of \(10 \mathrm{~cm}\). How many cans are needed to fill a pie pan (Figure 10.134) measuring \(22 \mathrm{~cm}\) in diameter and \(3 \mathrm{~cm}\) deep? 22 cm Figure 10.134 3 cm
Suppose you have 150 meters of fencing that you plan to use for the enclosure of a corral on a ranch. What shape would give the greatest possible area?
Suppose you want to design a crate built out of wood in the shape of a rectangular prism (Figure 10.136). It must have a volume of 3 cubic meters. The cost of wood is \(\$ 15\) per square meter. What dimensions give the most economical design while providing the necessary volume? 1.44 m 1.44 m 1.44
Find the length of the missing side of the triangle (Figure 10.139). 6 14 b Figure 10.139
You live on the corner of First Street and Maple Avenue, and work at Star Enterprises on Tenth Street and Elm Drive (Figure 10.141). You want to calculate how far you walk to work every day and how it compares to the actual distance (as the crow flies). Each block measures \(200 \mathrm{ft}\) by
The city has specific building codes for wheelchair ramps. Every vertical rise of 1 in requires that the horizontal length be 12 inches. You are constructing a ramp at your business. The plan is to make the ramp 130 inches in horizontal length and the slanted distance will measure approximately
Find the measures of the missing lengths of the triangle (Figure 10.145). a 10 b Figure 10.145 30
A city worker leans a 40 -foot ladder up against a building at a \(30^{\circ}\) angle to the ground (Figure 10.146). How far up the building does the ladder reach? 40 ft 30 Figure 10.146
Find the measures of the unknown sides in the triangle (Figure 10.148). 3 a 45 C 45% Figure 10.148
Find the lengths of the missing sides for the triangle (Figure 10.151). 55 6 x Figure 10.151
Solve for the lengths of a right triangle in which \(\theta=30^{\circ}\) and \(r=6\) (Figure 10.152). y 6 30 b Figure 10.152 x
A small plane takes off from an airport at an angle of \(31.3^{\circ}\) to the ground. About two-thirds of a mile ( \(3,520 \mathrm{ft}\) ) from the airport is an 1,100-ft peak in the flight path of the plane (Figure 10.153). If the plane continues that angle of ascent, find its altitude when it is
Suppose you have two known sides, but do not know the measure of any angles except for the right angle (Figure 10.154). Find the measure of the unknown angles and the third side. 8 6 Figure 10.154 4
A guy wire of length 110 meters runs from the top of an antenna to the ground (Figure 10.155). If the angle of elevation of an observer to the top of the antenna is \(43^{\circ}\), how high is the antenna? 110 m 43 Figure 10.155
You are sitting on the grass flying a kite on a 50 -foot string (Figure 10.156). The angle of elevation is \(60^{\circ}\). How high above the ground is the kite? 50 ft 60 Figure 10.156
Identify the polygons.
Identify the polygons.
Identify the polygons.
Find the perimeter of a regular hexagon with side length equal to \(12 \mathrm{~cm}\).
A regular quadrilateral has a perimeter equal to \(72 \mathrm{in}\). Find the length of each side.
The perimeter of an equilateral triangle is \(72 \mathrm{~cm}\). Find the length of each side.
Find the dimensions of a rectangular region with perimeter of \(34 \mathrm{~m}\), where the shorter side is 13 less than twice the longer side. Let \(x=\) the longer side. Then, the shorter side is \((2 x-13)\).
Find the perimeter of the figure shown. W 10 m 4 m 130 X N 50% y
Find the perimeter of a fenced-in area where the length is \(22 \mathrm{~m}\), and the width is \(1 / 2\) of the length plus 3 .
You have \(140 \mathrm{ft}\) of fencing to enclose a rectangular region that borders a river. You do not have to fence in the side that borders the river. The width is equal to \(2 a\), and the length is equal to six times the width less 10 . Find the dimensions of the region to be fenced. 20 6a -
What is the measure of each interior angle of a regular hexagon?
What is the sum of the interior angles of a triangle?
Use algebra to find the measure of each angle of the quadrilateral shown. A (2x-15) D (6x+5) (5x) B (2x+10)>C
Find the missing sides and angles of the parallelogram shown. 10 m W 4 m Z 50 y 130 X
Find the sum of the interior and exterior angles of the regular pentagon shown.

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