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mathematics
holt mcdougal larson geometry
Holt McDougal Larson Geometry 1st Edition Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff - Solutions
You are designing a wall hanging that is in the shape of a rhombus. The area of the wall hanging is 432 square inches and the length of one diagonal is 36 inches. Find the length of the other diagonal.
Find the angle measures of an isosceles triangle if the measure of a base angle is 4 times the measure of the vertex angle.
Sails A and B are right triangles. The lengths of the legs of Sail A are 65 feet and 35 feet. The lengths of the legs of Sail B are 29.5 feet and 10.5 feet. Find the area of each sail to the nearest square foot. About how many times as great is the area of Sail A as the area of Sail B? A B
You can use the area formula for a parallelogram to justify the area formula for a triangle. Start with two congruent triangles with base b and height h. Place and label them as shown. Explain how you know that XYZW is a parallelogram and that Area of ΔXYW = 1/2bh. X #1 b W Z T h T
You have enough silver to make a pendant with an area of 4 square centimeters. The pendant will be an equilateral triangle. Let s be the side length of the triangle.a. Find the height h of the triangle in terms of s. Then write a formula for the area of the triangle in terms of s. b. Find the side
You are earning money by painting a shed. You plan to paint two sides of the shed today. Each of the two sides has the dimensions shown at the right. You can paint 200 square feet per hour, and you charge $20 per hour. About how much will you get paid for painting those two sides of the shed?
The pattern below shows how to make an envelope to fit a card that is 17 centimeters by 14 centimeters. What are the dimensions of the rectangle you need to start with? What is the area of the paper that is actually used in the envelope? of the paper that is cut off? 17 cm 14 cm card fits here: 3
What is the area of the parallelogram shown at the right? 2 ft 3 in. 4 ft 2 in.
In ▱ABCD, base AD is 15 and AB is 8. What are the height and area of ▱ABCD if m∠DAB is 20°? if m∠DAB is 50°?
Find the length of the midsegment MN of the trapezoid. M 18 8 N
Find the area of a right triangle with side lengths 12 centimeters, 35 centimeters, and 37 centimeters. Then find the length of the altitude drawn to the hypotenuse.
Find the length of the midsegment MN of the trapezoid. M 13 27 N
Find the area of a triangle with side lengths 5 feet, 5 feet, and 8 feet. Then find the lengths of all three altitudes of the triangle.
Find the length of the midsegment MN of the trapezoid. 46 M N 29
You can mow 10 square yards of grass in one minute. How long does it take you to mow a triangular plot with height 25 yards and base 24 yards? How long does it take you to mow a rectangular plot with base 24 yards and height 36 yards?
You are making a tabletop in the shape of a parallelogram to replace an old 24 inch by 15 inch rectangular one. You want the areas of the tabletops to be equal. The base of the parallelogram is 20 inches. What should the height be?
Graph the points and connect them to form a polygon. Find the area of the polygon. E(-2,-2), F(5, 1), G(3,-2)
The base of a parallelogram is 7 feet and the height is 3 feet. Explain why the perimeter cannot be determined from the given information. Is there a least possible perimeter for the parallelogram? Is there a greatest possible perimeter? Explain.
Find the area of the shaded polygon. 17 ft 5 ft 8 ft
Find the area of the shaded polygon. 9 cm 18 cm 13 cm 11 cm
Find the area of the shaded polygon. 10 m 40 m 26 m 20 m
Find the area of the shaded polygon. -16 m- 11 m 10 m
Find the area of the shaded polygon. 8 in. -T 5 in. ㅗ
Find the area of the shaded polygon. 15 in. 19 in. 25 in.
Describe and correct the error in finding the area of the parallelogram. A = bh = = (6) (5) = 30 5 4 6
Graph the points and connect them to form a polygon. Find the area of the polygon. A(3, 3), B(10, 3), C(8, -3), D(1, -3)
The lengths of the hypotenuse and one leg of a right triangle are given. Find the perimeter and area of the triangle. Hypotenuse: 85 m; leg: 84 m
The lengths of the hypotenuse and one leg of a right triangle are given. Find the perimeter and area of the triangle. Hypotenuse: 29 cm; leg: 20 cm
Describe and correct the error in finding the area of the parallelogram. A = bh = (7)(4) = 28 4 4 3 x
The lengths of the hypotenuse and one leg of a right triangle are given. Find the perimeter and area of the triangle. Hypotenuse: 34 ft; leg: 16 ft
The lengths of the hypotenuse and one leg of a right triangle are given. Find the perimeter and area of the triangle. Hypotenuse: 15 in.; leg: 12 in.
A polygon has an area of 80 square meters and a height of 10 meters. Make scale drawings of three different triangles and three different parallelograms that match this description. Label the base and the height.
The area of a parallelogram is 507 square centimeters, and its height is three times its base. Find the base and the height.
The area of a triangle is 4 square feet. The height of the triangle is half its base. Find the base and the height.
Show two different ways to calculate the area of parallelogram ABCD. Compare your results. A 16 20 E B 8 D 10 C
Find the area of the polygon. 9 15
Find the area of the polygon. 30 18
Find the area of the polygon. 14 12
Find the area of the polygon. 4 7
Find the area of the polygon. 13 10
Find the area of the polygon. -15
Find the radius r of ⊙C. 20 28 C
Find the radius r of ⊙C. C 21 15
Find the circumference of the circle with given radius r or diameter d. Use π = 3.14. d = 48 yd
Find the radius r of ⊙C. C 15 9
Find the perimeter of the figure. (p. 433) 57 m 40 m
Find the circumference of the circle with given radius r or diameter d. Use π = 3.14. d = 160 in.
Find the circumference of the circle with given radius r or diameter d. Use π = 3.14. r = 7 cm
What are the two formulas you have learned for the area of a rectangle? Explain why these formulas give the same results.
Either pair of parallel sides of a parallelogram can be called its _?_, and the perpendicular distance between these sides is called the_?_.
Copy and complete the proof that opposite angles of an inscribed quadrilateral are supplementary. E D C F G
Use the given equations to determine whether the line is a tangent, secant, secant that contains a diameter, or none of these. Circle: (x-4)² + (y - 3)² = 9 Line: y=-3x + 6
Determine whether the given equation defines a circle. If the equation defines a circle, rewrite the equation in standard form. 2 x² - 2x + 5+ y² = 81
In the diagram at right, A and D are points of tangency on ⊙C. Explain how you know that BC bisects ∠ABD. в A D C
Classify the dilation and find its scale factor. C 12 -16- P' P
A block and tackle system composed of two pulleys and a rope is shown at the right. The distance between the centers of the pulleys is 113 centimeters and the pulleys each have a radius of 15 centimeters. What percent of the circumference of the bottom pulley is not touching the rope? 4
Use the given equations to determine whether the line is a tangent, secant, secant that contains a diameter, or none of these. Circle: (x + 2)² + (y-2)² = 16 Line: y = 2x - 4
Classify the dilation and find its scale factor. P' P -15- 9 C
Find the indicated measure. AC and BE are diameters. mAB
Use the given equations to determine whether the line is a tangent, secant, secant that contains a diameter, or none of these. Circle: (x - 5)2 + (y + 1)² = 4 Line: y = x x-3
Make and prove a conjecture about chord lengths.a. Sketch a circle with two noncongruent chords. Is the longer chord or the shorter chord closer to the center of the circle? Repeat this experiment several times. b. Form a conjecture related to your experiment in part (a). c. Use the
In the diagram at the right, AB = AC = 12, BC= 8, and all three segments are tangent to ⊙P. What is the radius of ⊙P? B E D P F A
Q and R are points on a circle. P is a point outside the circle. PQ and PR are tangents to the circle. Prove that QR is not a diameter.
Use the given equations to determine whether the line is a tangent, secant, secant that contains a diameter, or none of these. Circle: (x + 3)² + (y - 6)² = 25 Line: y = 4 x+ +2
Find the indicated measure. AC and BE are diameters. mCD
Use the quadratic formula to solve the equation. Round decimal answers to the nearest hundredth. x² + 7x+6=0
A car is designed so that the rear wheel is only partially visible below the body of the car, as shown. The bottom panel is parallel to the ground. Prove that the point where the tire touches the ground bisects AB. В
Use the quadratic formula to solve the equation. Round decimal answers to the nearest hundredth. x² - x - 12 = 0
On modern bicycles, rear wheels usually have tangential spokes. Occasionally, front wheels have radial spokes. Use the definitions of tangent and radius to determine if the wheel shown has tangential spokes or radial spokes.
On modern bicycles, rear wheels usually have tangential spokes. Occasionally, front wheels have radial spokes. Use the definitions of tangent and radius to determine if the wheel shown has tangential spokes or radial spokes.
Find the indicated measure. AC and BE are diameters. mBCA
Four tangent circles are centered on the x-axis. The radius of ⊙A is twice the radius of ⊙O. The radius of ⊙B is three times the radius of ⊙O. The radius of ⊙C is four times the radius of ⊙O. All circles have integer radii and the point (63, 16) is on ⊙C. What is the equation of ⊙A?
For any point outside of a circle, is there ever only one tangent to the circle that passes through the point? Are there ever more than two such tangents? Explain your reasoning.
Find the indicated measure. AC and BE are diameters. mCBD
A city's commuter system has three zones covering the regions described. Zone 1 covers people living within three miles of the city center. Zone 2 covers those between three and seven miles from the center, and Zone 3 covers those over seven miles from the center.a. Graph this situation with the
Find the indicated measure. AC and BE are diameters. mCDA
GPS satellites orbit about 11,000 miles above Earth. The mean radius of Earth is about 3959 miles. Because GPS signals cannot travel through Earth, a satellite can transmit signals only as far as points A and C from point B, as shown. Find BA and BC to the nearest mile. A C D 3959 mi 11,000 mi B
Use the quadratic formula to solve the equation. Round decimal answers to the nearest hundredth. x² + 16 = 8x
Quadrilateral JKLM is a parallelogram. Graph ▱JKLM. Decide whether it is best described as a rectangle, a rhombus, or a square. J(-3, 5), K(2, 5), L(2, -1), M(-3,-1)
Quadrilateral JKLM is a parallelogram. Graph ▱JKLM. Decide whether it is best described as a rectangle, a rhombus, or a square. J(-5, 2), K(1, 1), L(2, -5), M(-4,-4)
Write an indirect proof that if a line is perpendicular to a radius at its endpoint, the line is a tangent. GIVEN ► mLQP PROVE ► Line m is tangent to OQ.
The diameter of a CD is about 4.8 inches. The diameter of the hole in the center is about 0.6 inches. You place a CD on the coordinate plane with center at (0, 0). Write the equations for the outside edge of the disc and the edge of the hole in the center. 4.8 in. 0.6 in.
Find the indicated measure. AC and BE are diameters. mBAE
To maximize thrust on a NASA space shuttle, engineers drill an 11-point star out of the solid fuel that fills each booster. They begin by drilling a hole with radius 2 feet, and they would like each side of the star to be 1.5 feet. Is this possible if the fuel cannot have angles greater than 45 at
Use the quadratic formula to solve the equation. Round decimal answers to the nearest hundredth. x² + 6x = 10
Use the quadratic formula to solve the equation. Round decimal answers to the nearest hundredth. 5x + 9 = 2x²
Determine whether AB is a diameter of the circle. Explain. A C 8 6 B 10 D
Use the quadratic formula to solve the equation. Round decimal answers to the nearest hundredth. 4x2 + 3x - 11 = 0
Determine whether AB is a diameter of the circle. Explain. R A 6 B 1 S
Find the approximate length of the hypotenuse. Round your answer to the nearest tenth. 55 X 60
Find the approximate length of the hypotenuse. Round your answer to the nearest tenth. X 82 38
Telecommunication towers can be used to transmit cellular phone calls. Towers have a range of about 3 km. A graph with units measured in kilometers shows towers at points (0, 0), (0, 5), and (6, 3).a. Draw the graph and locate the towers. Are there any areas that may receive calls from more than
Determine whether AB is a diameter of the circle. Explain. D A 3.2 4 4 5 B C
Find the approximate length of the hypotenuse. Round your answer to the nearest tenth. 26 X 16
Sketch the image of A(3, -4) after the described glide reflection. Translation: Reflection: in the y-axis (x, y) → (x, y2)
Find the perimeter of the figure. (p. 49) ++ 22 in. -9 in.
Find the perimeter of the figure. (p. 49) -18 ft
Sketch the image of A(3, -4) after the described glide reflection. Translation: Reflection: in y = 4x (x, y) → (x + 1, y + 4)
D is in the interior of ∠ABC. If m∠ABD = 25° and m∠ABC = 70°, find m∠DBC.
A triangle has sides of lengths 8 and 13. Use an inequality to describe the possible length of the third side. What if two sides have lengths 4 and 11?
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