Multiple Choice
Which of the following best describes a political cartoon?
(1 point)
Responses
It uses humor and exaggeration to express a particular point of view.
It uses humor and exaggeration to express a particular point of view.
It offers a well-reasoned list of pros and cons about a controversial subject.
It offers a well-reasoned list of pros and cons about a controversial subject.
It makes fun of politicians and their families.
It makes fun of politicians and their families.
It avoids controversial topics and offers light-hearted humor instead.
It uses humor and exaggeration to express a particular point of view.
Multiple Choice
Which of the following statements about the women’s suffrage movement is most accurate?
(1 point)
Responses
Women received the vote with little effort or opposition.
Women received the vote with little effort or opposition.
Suffragists’ main strategy was the use of political cartoons.
Suffragists’ main strategy was the use of political cartoons.
The women’s suffrage movement occurred in isolation from other social reforms.
The women’s suffrage movement occurred in isolation from other social reforms.
Many different strategies were used over several decades to accomplish women’s suffrage.
Many different strategies were used over several decades to accomplish women’s suffrage.
Which of the following is NOT a cause of mental or emotional illness?
(1 point)
Responses
physical factors
physical factors
heredity
heredity
values
values
early experiences
values
True or False:
Mood disorders and personality disorders often make it difficult for a person to get along with others.
(1 point)
Responses
true
true
false
true
True or False:
Mental or emotional problems may cause physical problems.
(1 point)
Responses
true
true
false
true
Use the image to answer the question.
An illustration shows a cone that rests flat on the circular base. The visible circumference of the base and sides are in solid lines. The circumference of the base at the back that is not visible is indicated by a dashed line. Parts are labeled. A large point is marked in the center of the base. A solid line passes through this point and extends from one edge of the base to the other to indicate the diameter of the base. The line is labeled d equals 10 centimeters. The right side of the cone extending from where the diameter meets the edge of the base up to the point of the cone shows a slant height of 13 centimeters. A dotted line extends from the interior of the vertex of the cone down to the point marked in the center of the base. A right angle is indicated where the dotted height line meets the diameter line in the center of the base.
Find the length of the height of the cone.
(1 point)
cm
Skip to navigation
page 14 of 15
Unfortunately, as an AI text-based model, I am unable to view or analyze images. Please provide the necessary information or description to answer the question.
From 13 cm to d = 10 cm
To find the length of the height of the cone, we can use the Pythagorean theorem.
The slant height (s) is given as 13 cm and the diameter (d) is given as 10 cm.
Using the Pythagorean theorem, we have:
(s^2) = (h^2) + (r^2)
Where r is the radius of the base and h is the height of the cone.
The radius (r) is half the diameter, so r = (d/2) = (10/2) = 5 cm.
Plugging in the given values, we have:
(13^2) = (h^2) + (5^2)
169 = (h^2) + 25
Subtracting 25 from both sides of the equation:
144 = (h^2)
Taking the square root of both sides:
h = √144
h = 12 cm
Therefore, the length of the height of the cone is 12 cm.
Use the image to answer the question.
An illustration shows a three dimensional rectangular prism with labeled parts. The top, front and right sides are visible. The bottom, left, and rear sides are not visible, but their positions are indicated by dashed lines. The vertical edge joining the front and left sides is labeled h. A right angle is indicated where that edge meets the front base edge. The front base edge is labeled l. A right angle is indicated where that edge meets the right base edge. The right base edge is labeled w. Two dotted lines extend from the vertex at the back right side of the prism through the interior. The first dotted line extends up to the vertex at the front left side and is labeled d. The second dotted line extends diagonally across the base to the vertex at the front left side where the perpendicular height line meets the base edge and is labeled x.
Given l=30 in. , w=20 in. , h=18 in. , and x=36.1 in. , find the length of d . Round the answer to the nearest tenth.
(1 point)
in.
Skip to navigation
page 14 of 15
use point H to Pont W to Point X
To find the length of d in the given rectangular prism, we can use the Pythagorean theorem.
From point H to point W to point X forms a right triangle. We have the values l, w, and x for the lengths of the sides.
Using the Pythagorean theorem, we have:
(l^2) + (w^2) = (d^2)
Plugging in the given values, we have:
(30^2) + (20^2) = (d^2)
900 + 400 = (d^2)
1300 = (d^2)
Taking the square root of both sides to solve for d:
d = √1300
d ≈ 36.06 inches
Rounding to the nearest tenth, the length of d is approximately 36.1 inches.
Use the image to answer the question.
An illustration shows a square pyramid with labeled parts. The left, front, and right faces of the pyramid and base are visible. The back face is not visible, but its position is indicated by a dashed line. The back base edge is not visible, but its position is indicated by a dashed line. The left base edge is labeled a. The back left lateral edge is labeled e. A dotted line extends from the interior of the vertex straight down to the center of the base and is labeled h. A right angle is indicated where the dotted height line meets the base. Another dotted line extends from the center of the base where the height line meets to the center of the right base edge and is labeled r. A dotted line extends from the right base edge straight up the center of the right face of the prism and meets the height line at the vertex. The dotted slant height line is labeled s.
For the square pyramid, the lateral edge length, e , is 25 in., and the slant height, s , is 24 in. Find the height of the pyramid, h . Round the answer to the nearest whole number. Hint: Before finding the length of h , you will first need to find the length of r
.
(1 point)
The height of the square pyramid is
in.
Skip to navigation
page 14 of 15
use Point H to Point R to Point 8
To find the length of h in the given square pyramid, we need to first find the length of r.
From point H to point R to point 8 forms a right triangle. We have the values h, r, and s for the lengths of the sides.
Using the Pythagorean theorem, we have:
(r^2) + (h^2) = (s^2)
Plugging in the given values, we have:
(r^2) + (h^2) = (24^2)
(r^2) + (h^2) = 576
We also know that the length of e is given as 25 inches, and e is the hypotenuse of the triangle formed by r, h, and e.
Using the Pythagorean theorem again, we have:
(r^2) + (h^2) = (e^2)
(r^2) + (h^2) = (25^2)
(r^2) + (h^2) = 625
Since we have two equations with the same variables (r^2 + h^2 = 576 and r^2 + h^2 = 625), we can subtract one from the other to eliminate the variable r:
(r^2 + h^2) - (r^2 + h^2) = 625 - 576
0 = 49
This equation is not possible, as it leads to an inconsistency. Therefore, there may be an error in the given values or problem setup.
Please double-check the values and information provided to clarify the problem setup.
Use the image to answer the question.
A square pyramid is shown. Its height is shown with a dotted line labeled 321 feet. Its slant height is shown with a dotted line labeled 436.5 feet. The variable l is shown along one of the edges of the square base.
The Pyramid is an arena in Memphis, Tennessee. Its height is 321 ft., and its slant height is 436.5 ft. Find the length of the edge of the square base. Round the answer to the nearest tenth.
(1 point)
ft.
Skip to navigation
page 14 of 15
To find the length of the edge of the square base of the given pyramid, we can use the Pythagorean theorem.
The height of the pyramid (h) is given as 321 ft, and the slant height (s) is given as 436.5 ft.
Using the Pythagorean theorem, we have:
(l^2) = (s^2) - (h^2)
Plugging in the given values, we have:
(l^2) = (436.5^2) - (321^2)
(l^2) = 190545.25 - 103041
(l^2) = 87404.25
Taking the square root of both sides to solve for l:
l = √87404.25
l ≈ 295.4 ft
Rounding to the nearest tenth, the length of the edge of the square base is approximately 295.4 ft.
A juice can is in the shape of a cylinder. It has a height of 122 mm and a diameter of 52 mm. What is the longest straw that can fit completely inside the juice can diagonally? Round the answer to the nearest tenth. (1 point)
mm
To find the longest straw that can fit completely inside the juice can diagonally, we need to find the length of the diagonal of the cylinder.
The height of the cylinder (h) is given as 122 mm, and the diameter (d) is given as 52 mm. Since the diameter is twice the radius, we can find the radius (r) by dividing the diameter by 2:
r = d/2 = 52/2 = 26 mm
The diagonal of the cylinder can be found by forming a right triangle inside the cylinder using the height, radius, and the diagonal as the hypotenuse.
Using the Pythagorean theorem, we have:
(diagonal)^2 = (height)^2 + (radius)^2
(diagonal)^2 = 122^2 + 26^2
(diagonal)^2 = 14884 + 676
(diagonal)^2 = 15560
Taking the square root of both sides to solve for the diagonal:
diagonal ≈ √15560
diagonal ≈ 124.8 mm
Rounding to the nearest tenth, the longest straw that can fit completely inside the juice can diagonally is approximately 124.8 mm.
The Pythagorean Theorem in Three Dimensions Quick Check
1 of 51 of 5 Items
Question
Use the image to answer the question.
An illustration shows a square pyramid with labeled parts. The left, front and right faces of the pyramid and base are visible. The back face is not visible. The back base edge is not visible but its position is indicated by a dashed line. The front base edge shows a length of 40 feet. A dotted line extends from the interior of the vertex straight down to the center of the base and is labeled h. A right angle is indicated where the dotted height line meets the base. Another dotted line extends from the center of the base where the height line meets to the center of the right base edge. A dotted line extends from the right base edge straight up the center of the right face of the prism and meets the height line at the vertex. This dotted line shows a slant height of 25 feet.
Apply the Pythagorean Theorem to determine the height of the square pyramid, h. Round the answer to the nearest tenth.
(1 point)
Responses
47.2 ft.
47.2 ft.
32.0 ft.
32.0 ft.
31.2 ft.
31.2 ft.
15.0 ft.
15.0 ft.
Skip to navigation
page 15 of 15
To determine the height of the square pyramid (h) using the Pythagorean theorem, we can use the given values of the slant height (s) and the side length of the base (l).
In the image, the slant height is given as 25 feet and the base length is given as 40 feet.
Using the Pythagorean theorem, we have:
(h^2) = (s^2) - ((l/2)^2)
Plugging in the given values, we have:
(h^2) = (25^2) - ((40/2)^2)
(h^2) = 625 - (20^2)
(h^2) = 625 - 400
(h^2) = 225
Taking the square root of both sides to solve for h:
h ≈ √225
h ≈ 15 feet
Rounding to the nearest tenth, the height of the square pyramid is approximately 15 feet.
The Pythagorean Theorem in Three Dimensions Quick Check
2 of 52 of 5 Items
Question
Use the image to answer the question.
An illustration of a rectangular prism is shown with labeled parts. The left and back base edges are not visible but their positions are indicated by a dashed line. The 6 vertices are labeled A B C D E F and G. The base edge A B is labeled length. Base edge B C is labeled width. The perpendicular C D is labeled height. A dotted line crosses the rectangular base through the center to show diagonal B H. A dashed line extends up from the base indicating the left rear perpendicular E H. A dotted line crosses from the back top left vertex E to the front bottom right vertex B to show diagonal B E. This dotted line is labeled diagonal.
The length of the prism is 32 cm, the width is 24 cm, the height is 44 cm, and the length of the diagonal of the base, segment BH, is 40 cm. Find the length of the diagonal of the rectangular prism, segment BE. Round the answer to the nearest tenth.
(1 point)
Responses
46.6 cm
46.6 cm
51.2 cm
51.2 cm
54.4 cm
54.4 cm
59.5 cm
59.5 cm
Skip to navigation
page 15 of 15
To find the length of the diagonal of the rectangular prism (segment BE) using the given values, we can use the Pythagorean theorem.
The length of the prism is given as 32 cm, the width is given as 24 cm, the height is given as 44 cm, and the length of the diagonal of the base (segment BH) is given as 40 cm.
Using the Pythagorean theorem, we have:
(diagonal)^2 = (length)^2 + (width)^2 + (height)^2
Plugging in the given values, we have:
(diagonal)^2 = (32^2) + (24^2) + (44^2)
(diagonal)^2 = 1024 + 576 + 1936
(diagonal)^2 = 3536 + 1936
(diagonal)^2 = 5472
Taking the square root of both sides to solve for the diagonal:
diagonal ≈ √5472
diagonal ≈ 73.99 cm
Rounding to the nearest tenth, the length of the diagonal of the rectangular prism (segment BE) is approximately 74.0 cm.
The Pythagorean Theorem in Three Dimensions Quick Check
3 of 53 of 5 Items
Question
Use the image to answer the question.
A drawing shows a circle showing diameter below a sector of a circle showing slant height. A double-headed arrow crossing the center of the circle is labeled as d equals diameter. A dotted double-headed arrow is drawn from the top point of the sector of the circle to a point along the curved edge. The arrow is labeled as lower L equals slant height.
Chem Tech makes paper cones used to filter liquids in lab experiments. To make the paper cones, the company starts with the net of the shape, where the slant height is needed. The company wants the height of the cones to be 6 cm. If they make the diameter 13 cm, what must the slant height be? Use the Pythagorean Theorem and round the answer to the nearest tenth.
(1 point)
Responses
2.5 cm
2.5 cm
14.3 cm
14.3 cm
8.8 cm
8.8 cm
11.5 cm
11.5 cm
Skip to navigation
To find the slant height of the paper cone, we can use the Pythagorean theorem.
The height of the cone (h) is given as 6 cm, and the diameter (d) is given as 13 cm.
First, we need to calculate the radius (r) of the cone. The radius is half the diameter, so r = d/2 = 13/2 = 6.5 cm.
Next, we can apply the Pythagorean theorem to find the slant height (l) of the cone.
Using the formula:
(l^2) = (r^2) + (h^2)
Plugging in the given values, we have:
(l^2) = (6.5^2) + (6^2)
(l^2) = 42.25 + 36
(l^2) = 78.25
Taking the square root of both sides to solve for l:
l ≈ √78.25
l ≈ 8.8 cm
Rounding
The Pythagorean Theorem in Three Dimensions Quick Check
4 of 54 of 5 Items
Question
A circus tent is in the shape of a square pyramid. Each edge of the square base is 20 m and its slant height is 13.5 m. Find the height of the tent. Round the answer to the nearest tenth.(1 point)
Responses
9.1 m
9.1 m
14.8 cm
14.8 cm
24.1 cm
24.1 cm
16.8 m
16.8 m
Skip to navigation
page 15 of 15