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mathematics
contemporary mathematics
Contemporary Mathematics 1st Edition OpenStax - Solutions
\(m \measuredangle A=30^{\circ}, m \measuredangle B=120^{\circ}, m \measuredangle C=30^{\circ}\)Classify the triangle with the listed angle measurements as acute, right, or obtuse.
\(m \measuredangle A=85^{\circ}, m \measuredangle B=50^{\circ}, m \measuredangle C=45^{\circ}\)Classify the triangle with the listed angle measurements as acute, right, or obtuse.
Find the missing angles in the given figure. 74 z b 28 C
What are the measurements of each angle in the given figure? A (4x+7) (23x) (7x+3) B
Find the angle measurements in the given figure. (7x+11) (4x+2) B
Find the angle measurements in the given figure. (x-2) (7x-14) (x-2)
Determine which congruence theorem is used to show that the two triangles are congruent.
Determine which congruence theorem is used to show that the two triangles are congruent.
Determine which congruence theorem is used to show that the two triangles are congruent. B A C D
Are these triangles similar? If so, what is the common proportion or the scaling factor? 2 0.6 1.2
Are the images in the given figure similar? If so, what is the common proportion or the scaling factor? 1 4 1.5 15 6
In the figure shown, given \(\overline{B E}\) is parallel to \(\overline{C D}\), find \(x\) and \(y\). 3 B 4 E 2 C X D
Find \(a\) and \(t\) in the given figure. A 10 16 B R 20 14 t 12 S
In the given figure, find the proportions and solve for \(a\) and \(b\). a 25 b 8 6 10
In the given figure, find the proportions and solve for \(r\). 21 12 14
A triangular plot of land has a perimeter of \(2,400 \mathrm{ft}\). The longest side is \(200 \mathrm{ft}\) less than twice the shortest side. The middle side is \(200 \mathrm{ft}\) less than the longest side. Find the lengths of the three sides.
The Orange Tree Hotel in Charleston, North Carolina has a fountain in the shape of a cylinder with a circular foundation. The circumference of the foundation is 6 times the radius increased by \(12.88 \mathrm{ft}\). Find the radius of the circular foundation. (Use 3.14 as an approximation for
\(m \measuredangle=32^{\circ}\)Classify the angles in the following exercises as acute, obtuse, right, or straight.
\(m \measuredangle=120^{\circ}\)Classify the angles in the following exercises as acute, obtuse, right, or straight.
\(m \measuredangle=180^{\circ}\)Classify the angles in the following exercises as acute, obtuse, right, or straight.
\(m \measuredangle=90^{\circ}\)Classify the angles in the following exercises as acute, obtuse, right, or straight.
\(m \measuredangle=110^{\circ}\)Classify the angles in the following exercises as acute, obtuse, right, or straight.
\(m \measuredangle=45^{\circ}\)Classify the angles in the following exercises as acute, obtuse, right, or straight.
Use the given figure to solve for the angle measurements. 39x-2 5x+4
Use the given figure to solve for the angle measurements. 3x + 2 3x+7 2x + 3
Give the measure of the supplement to \(89^{\circ}\).
Find the measure of angle 1 and state the reason for your solution.Use the given figure for the following exercises. Let angle 2 measure \(35^{\circ}\). 3 5. 6 4 2 7 8 12
Find the measure of angle 3 and state the reason for your solution.Use the given figure for the following exercises. Let angle 2 measure \(35^{\circ}\). 3 5. 6 4 2 7 8 12
Find the measure of angle 4 and state the reason for your solution.Use the given figure for the following exercises. Let angle 2 measure \(35^{\circ}\). 3 5. 6 4 2 7 8 12
Find the measure of angle 5 and state the reason for your solution.Use the given figure for the following exercises. Let angle 2 measure \(35^{\circ}\). 3 5. 6 4 2 7 8 12
Find the measure of angle 6 and state the reason and state the reason for your solution.Use the given figure for the following exercises. Let angle 2 measure \(35^{\circ}\). 3 5. 6 4 2 7 8 12
Find the measure of angle 7 and state the reason for your solution.Use the given figure for the following exercises. Let angle 2 measure \(35^{\circ}\). 3 5. 6 4 2 7 8 12
Find the measure of angle 8 and state the reason for your solution.Use the given figure for the following exercises. Let angle 2 measure \(35^{\circ}\). 3 5. 6 4 2 7 8 12
Use the given figure to solve for the angle measurements. 5x 129 2x-21
Find the measure of angle 3 and explain the reason for your solution.Use the given figure for the following exercises. 8 3. 50
Find the measure of angle 8 and explain the reason for your solution.Use the given figure for the following exercises. 8 3. 50
amount of juice in a carton Determine the base unit of the metric system described: liter, gram, or meter.
weight of a puppy Determine the base unit of the metric system described: liter, gram, or meter.
height of a wall Determine the base unit of the metric system described: liter, gram, or meter.
hectogram or centigram Choose the smaller of the two units.
decameter or kilometer Choose the smaller of the two units.
milliliter or deciliter Choose the smaller of the two units.
Convert \(236 \mathrm{~cm}\) to meters (m).
Convert \(137.5 \mathrm{mg}\) to grams ( \(\mathrm{g})\).
You purchase \(15 \mathrm{~kg}\) of birdseed. You divide the birdseed into 10 bags. How many grams of birdseed are in each bag?
A track is \(650 \mathrm{~m}\) long. If you run 8 laps around the track, how many kilometers did you run?
bedroom floor\(12 \mathrm{~km}^{2}\)\(12 \mathrm{~m}^{2}\)\(12 \mathrm{~cm}^{2}\)\(12 \mathrm{~mm}^{2}\)Determine the most reasonable value for each area.
nature preserve\(800 \mathrm{~km}^{2}\)\(800 \mathrm{~m}^{2}\)\(800 \mathrm{~cm}^{2}\)\(800 \mathrm{~mm}^{2}\)Determine the most reasonable value for each area.
desk surface\(0.125 \mathrm{~km}^{2}\)\(0.125 \mathrm{~m}^{2}\)\(0.125 \mathrm{~cm}^{2}\)\(0.125 \mathrm{~mm}^{2}\)Determine the most reasonable value for each area.
\(650,000 \mathrm{~cm}^{2}=\) __________ \(\mathrm{m}^{2}\)Convert the given area to the units shown.
\(17 \mathrm{~m}^{2}=\) ___________ \(\mathrm{cm}^{2}\)Convert the given area to the units shown.
\(759 \mathrm{~cm}^{2}=\) ____________ mm2.Convert the given area to the units shown.
A laptop is \(30 \mathrm{~cm}\) by \(20 \mathrm{~cm}\). A sticker on the laptop cover measures \(15 \mathrm{~mm}\) by \(15 \mathrm{~mm}\). How many square centimeters of the laptop cover is still visible?
A dining room wall is \(2.75 \mathrm{~m}\) by \(2.25 \mathrm{~m}\). A window on the wall is \(0.75 \mathrm{~m}\) by \(1.5 \mathrm{~m}\). How many square meters is the surface of the wall?
A floor is \(6 \mathrm{~m}\) by \(4 \mathrm{~m}\). A rug on the floor measures \(200 \mathrm{~cm}\) by \(100 \mathrm{~cm}\). How much of the floor, in \(\mathrm{m}^{2}\), is not covered by the rug?
A ceiling is \(4 \mathrm{~m}\) by \(2.5 \mathrm{~m}\). A skylight in the ceiling measures \(75 \mathrm{~cm}\) by \(80 \mathrm{~cm}\). How much of the ceiling, in \(\mathrm{m}^{2}\), would need to be painted if you decide to change the color of the ceiling?
aquarium\(65,750 \mathrm{~km}^{3}\)\(65,750 \mathrm{~m}^{3}\)\(65,750 \mathrm{~cm}^{3}\)\(65,750 \mathrm{~mm}^{3}\)Determine the most reasonable value for each volume.
carton of soup\(94,000 \mathrm{~L}\)\(94 \mathrm{~L}\)\(940,000 \mathrm{~mL}\)\(940 \mathrm{~mL}\)Determine the most reasonable value for each volume.
gift box\(6,250 \mathrm{~km}^{3}\)\(6,250 \mathrm{~m}^{3}\)\(6,250 \mathrm{~cm}^{3}\)\(6,250 \mathrm{~mm}^{3}\)Determine the most reasonable value for each volume.
\(59,837 \mathrm{~mm}^{3}=\) ____________ \(\mathrm{cm}^{3}\)Convert the given volume to the units shown.
\(12.5 \mathrm{dm}^{3}=\) ______________ \(\mathrm{mL}\)Convert the given volume to the units shown.
\(368 \mathrm{~cm}^{3}=\) ______________ mm3.Convert the given volume to the units shown.
A box has dimensions of \(15 \mathrm{~cm} \times 10 \mathrm{~cm} \times 25 \mathrm{~cm}\). The box currently holds \(1,750 \mathrm{~cm}^{3}\) of black beans. How many cubic centimeters of black beans are needed to completely fill the box?
The dimensions of a small storage unit are \(3 \mathrm{~m} \times 3 \mathrm{~m} \times 3 \mathrm{~m}\). What is the volume of a medium storage area with dimensions twice the size of the small unit?
How much liquid, in liters, can a container with dimensions of \(35 \mathrm{~cm} \times 15 \mathrm{~cm} \times 20 \mathrm{~cm}\) hold?
A box is \(20 \mathrm{~cm}\) long and \(15 \mathrm{~cm}\) wide. The volume of the box is \(2,100 \mathrm{~cm}^{3}\). What is the height of the box?
What is the most reasonable estimate for the weight of a small stack of coins?\(120 \mathrm{mg}\)\(12 \mathrm{~g}\)\(1.2 \mathrm{~kg}\)\(0.12 \mathrm{mt}\)
\(7,900 \mathrm{~g}=\) ____________ \(\mathrm{kg}\)Convert the given weight to the units shown.
\(81 \mathrm{~g}=\) _____________ \(\mathrm{mg}\)Convert the given weight to the units shown.
\(0.12 \mathrm{~kg}=\) _____________ g.Convert the given weight to the units shown.
four \(450 \mathrm{mg}\) tablets ___________ \(g\)Determine the total weight in the units shown.
six \(45 \mathrm{~g}\) candy bars _______________ \(\mathrm{kg}\)Determine the total weight in the units shown.
seven \(1.5 \mathrm{~g}\) buttons ___________ \(\mathrm{mg}\)Determine the total weight in the units shown.
A box of chocolate weighs \(2.75 \mathrm{~kg}\). If you share the candy bar equally with 5 friends, how many grams of chocolate does each person get?
You purchase 15 tomatoes that weigh 100 grams each. If tomatoes cost \(\$ 1.18\) per kilogram, how much did you pay?
A value-size package of ground chicken costs \(\$ 23.00\). The package weighs \(2.5 \mathrm{~kg}\). What is the cost per gram of the chicken?
\(365^{\circ} \mathrm{F}=\) __________ \({ }^{\circ} \mathrm{C}\)Convert the temperatures to the nearest degree.
\(42^{\circ} \mathrm{C}=\) ____________ \({ }^{\circ} \mathrm{F}\)Convert the temperatures to the nearest degree.
\(575^{\circ} \mathrm{F}=\) _______________ \({ }^{\circ} \mathrm{C}\)Convert the temperatures to the nearest degree.
\(135^{\circ} \mathrm{C}=\) _____________ \({ }^{\circ} \mathrm{F}\)Convert the temperatures to the nearest degree.
\(-20^{\circ} \mathrm{F}=\) ______________ \({ }^{\circ} \mathrm{C}\)Convert the temperatures to the nearest degree.
\(73^{\circ} \mathrm{C}=\) ______________ °F.Convert the temperatures to the nearest degree.
The temperature of a welder's torch increases \(1,112^{\circ} \mathrm{F}\) every 3 minutes. About how many minutes does it take for the torch to increase \(1,200^{\circ} \mathrm{C}\) ?
A substance is heated to \(302^{\circ} \mathrm{F}\). As the substance cools the temperature drops \(4^{\circ} \mathrm{C}\) every 3 minutes. How many minutes until the temperature of the water reaches \(130^{\circ} \mathrm{C}\) ?
On November 1 the temperature was \(40^{\circ} \mathrm{F}\). On December 1 the temperature was \(7{ }^{\circ} \mathrm{C}\). Which day was cooler?
The instructions to cook lasagna say to set the oven at \(475^{\circ} \mathrm{F}\). To the nearest degree, what is the temperature in degrees Celsius?
A student consumed 10 cans of their favorite soda last week. If each can contained \(39 \mathrm{~g}\) of sugar, how many milligrams of sugar did they consume?
An athlete ran a total distance of \(154 \mathrm{~km}\) in one month while training for a \(5 \mathrm{~K}\) fun run. How many meters did they run?
A doctor recommends their patient drinks 5 liters of water on days of vigorous exercise. If the patient drinks 3,400 \(\mathrm{mL}\), how much more do they need to drink?
A garden walkway has the dimensions shown. How many square meters of brick are needed to cover the walkway? \(10 \mathrm{~m}\) 10 m 8 m T 3 m 7 m 10 m 3 m
A studio apartment has a length of \(1,200 \mathrm{~cm}\) and a width that one half of the length. What is the area of the apartment in meters?
A living room is \(7 \mathrm{~m}\) long and \(8 \mathrm{~m}\) wide. Carpet costs \(\$ 9.50\) per square meter. How much will it cost to carpet the room?
Arif mixed two cartons of orange juice that each contain \(600 \mathrm{cL}\), two bottles of cranberry juice that each contain \(1,250 \mathrm{~mL}\), and one 2 -liter bottle of soda water to make punch for a party. How much punch, in liters, did Arif make?
A fish tank has the dimensions \(40 \mathrm{~cm} \times 20 \mathrm{~cm} \times 25 \mathrm{~cm}\). What is the capacity of the fish tank in liters?
A recipe for chili makes \(5.4 \mathrm{~L}\) of chili. If a restaurant serves chili in \(300 \mathrm{~mL}\) bowls, how many bowls of chili can they serve?
If a person weighs \(76 \mathrm{~kg}\) but loses 3 kilograms, how much does the person weigh in grams?
A car weighs approximately 2 metric tons (mt). If a used car dealer has \(222,000 \mathrm{~kg}\) of cars in their lot, how many cars are in the lot?
A restaurant has \(126 \mathrm{~kg}\) of rice. If each serving contains \(125 \mathrm{~g}\), how many servings will they make?
A boiling pan of water is \(212^{\circ} \mathrm{F}\). As the water cools the temperature drops \(12^{\circ} \mathrm{C}\) every 3 minutes. How many minutes until the temperature of the water reaches \(28^{\circ} \mathrm{C}\) ?
On May 1 the temperature was \(75^{\circ} \mathrm{F}\). On June 1 the temperature was \(28^{\circ} \mathrm{C}\). Which day was warmer?
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