Use Figure 1 to answer the question.
What is another name for plane Z?
(1 point)
Responses
plane ZXL
plane ZXL
plane XTV
plane XTV
plane SLT
plane SLT
plane XSL
plane XSL
Use Figure 1 to answer the question.
Plane STL and plane Z would intersect at _____.
(1 point)
Responses
line TV
Image with alt text: line TV
line XL
Image with alt text: line XL
plane STV
Image with alt text: plane STV
plane SLV
Image with alt text: plane SLV
Which of the following angles, when placed in standard position, does not land in quadrant III?
(1 point)
Responses
181°
181°
–179°
–179°
145°
145°
–97°
The correct answer is 145°.
Find the area of the shaded region.
A square is shown with circle upper O inscribed inside of the square. A side is labeled 8. The area of the square outside of the circle is shaded.
(1 point)
Responses
64 – 16symbol pi square units
64 – 16 Image with alt text: symbol pi square units
64 – 64symbol pi square units
64 – 64 Image with alt text: symbol pi square units
64 – 18symbol pi square units
64 – 18 Image with alt text: symbol pi square units
64 square units
64 square units
The correct answer is 64 – 16π square units.
f the measures of two complementary angles are 7x and 11x, then find x.
(1 point)
Responses
x = 5
x = 5
x = 10
x = 10
x = 22.5
x = 22.5
x = 12
To find x, we need to set up an equation based on the fact that two angles are complementary:
7x + 11x = 90
Combining like terms:
18x = 90
Dividing both sides by 18:
x = 5
The correct answer is x = 5.
Find a point E on ModifyingAbove C D with bar such that the ratio of ModifyingAbove C E with bar to ModifyingAbove C D with bar is one-fourth.
A number line measures from negative 10 to 10. C is located at negative 9. D is located at 7.
(1 point)
Responses
negative 7
Image with alt text: negative 7
negative 5
Image with alt text: negative 5
negative 3
Image with alt text: negative 3
negative 1
Image with alt text: negative 1
To find point E, we can use the given information that the ratio of line segment CE to line segment CD is one-fourth. CD measures from -9 to 7, which is a distance of 16 units.
Since the ratio of CE to CD is 1/4, we divide 16 by 4 to find the length of CE:
16/4 = 4
Starting from point C at -9, we move 4 units to the right to locate point E.
Therefore, point E is located at -5.
The correct answer is negative 5.
What is the perimeter of a rectangle with width 10 inches and length 13 inches?
To find the perimeter of a rectangle, you add up all the sides. In this case, we have a rectangle with a width of 10 inches and a length of 13 inches.
The formula for the perimeter of a rectangle is:
Perimeter = 2 × (Length + Width)
Substituting the given values:
Perimeter = 2 × (13 + 10)
Perimeter = 2 × 23
Perimeter = 46
Therefore, the perimeter of the rectangle is 46 inches.
What is the area of a triangle with base 19 inches and height 11 inches?
To find the area of a triangle, you can use the formula:
Area = (base × height) / 2
Substituting the given values:
Area = (19 inches × 11 inches) / 2
Area = (209 inches^2) / 2
Area = 104.5 inches^2
Therefore, the area of the triangle is 104.5 square inches.
What is the area of a circle with a radius of 15 inches, to the nearest tenth? Use 3.14 for pi.
To find the area of a circle, you can use the formula:
Area = pi × radius^2
Given that the radius is 15 inches and pi is approximated as 3.14, we can calculate the area as follows:
Area = 3.14 × (15 inches)^2
Area = 3.14 × 225 square inches
Area ≈ 706.5 square inches
Rounded to the nearest tenth, the area of the circle is approximately 706.5 square inches.
How is naming a line segment different from naming a line?
Naming a line segment and naming a line differ in terms of the information conveyed.
When naming a line segment, you typically use two distinct points on the line segment and write them in the order they appear on the line segment. For example, if we have points A and B on a line segment, we would name the line segment as AB.
On the other hand, when naming a line, you usually choose any two points on the line and write them in any order with a line symbol above. For instance, if we have points P and Q on a line, we would name the line as line PQ or PQ with a line symbol above it.
In summary, naming a line segment focuses on the specific segment between two points, while naming a line encompasses the entire line extending infinitely in both directions.
How is constructing a perpendicular bisector similar to constructing an angle bisector? How is it different?
Constructing a perpendicular bisector and constructing an angle bisector are similar in that they both involve dividing a segment or an angle into two equal parts.
A perpendicular bisector is constructed by drawing a line that intersects the given segment at a 90-degree angle, creating two equal segments. This perpendicular bisector divides the original segment into two congruent segments.
An angle bisector, on the other hand, is constructed by drawing a line that divides the given angle into two equal angles. This angle bisector divides the original angle into two congruent angles.
Both constructions involve dividing a figure into two equal parts, but the main difference lies in what is being divided. The perpendicular bisector divides a segment, while the angle bisector divides an angle.
Describe a process you would use to create the perpendicular bisector to a segment AB using only an unmarked straightedge and an unmarked compass.
To create the perpendicular bisector of segment AB using only an unmarked straightedge and an unmarked compass, you can follow the following steps:
1. Place the compass at point A and draw an arc that intersects segment AB on both sides. Label these points of intersection as C and D.
2. Without adjusting the compass width, place the compass at point B and draw another arc that intersects segment AB. Label this point of intersection as E.
3. With the compass width still unchanged, place the compass at point C and draw an arc above segment AB.
4. Without adjusting the compass width, place the compass at point D and draw another arc above segment AB, intersecting the arc from step 3.
5. Use the straightedge to draw a line connecting the point where the two arcs intersect (F) with the midpoint of segment AB (M). This line will be the perpendicular bisector of segment AB.
6. You can verify that the line is the perpendicular bisector by measuring the distance between points A and M, as well as between points B and M. If the measurements are equal, it confirms that the line is indeed the perpendicular bisector.
By following these steps and using just an unmarked straightedge and compass, you can construct the perpendicular bisector of segment AB.
Find the distance between points M(6,16)
and Z(−1,14)
to the nearest tenth.
To find the distance between two points in a coordinate plane, you can use the distance formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Given the coordinates of point M as (6, 16) and point Z as (-1, 14), we can substitute these values into the distance formula:
Distance = √[(-1 - 6)² + (14 - 16)²]
Distance = √[(-7)² + (-2)²]
Distance = √[49 + 4]
Distance = √53
Distance ≈ 7.28
Rounded to the nearest tenth, the distance between points M(6,16) and Z(-1,14) is approximately 7.3.
The midpoint of UV
is (5,−11)
. The coordinates of one endpoint are U(3,5)
. Find the coordinates of endpoint V.
To find the coordinates of endpoint V, we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint is the average of the coordinates of the endpoints:
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Given that the midpoint is (5, -11) and the coordinates of endpoint U are (3, 5), we can substitute these values into the midpoint formula:
(5, -11) = ((3 + x₂)/2, (5 + y₂)/2)
Simplifying the equation, we have:
5 = (3 + x₂)/2 and -11 = (5 + y₂)/2
Solving for x₂:
10 = 3 + x₂
x₂ = 7
Solving for y₂:
-22 = 5 + y₂
y₂ = -27
Therefore, the coordinates of endpoint V are (7, -27).
GI−→ bisects ∠DGH so that m ∠DGI is x−3 and m ∠IGH is 2x −13.
Find The value of x
To find the value of x, we can use the fact that the angle bisector of an angle divides it into two congruent angles.
Given that m∠DGI is x-3 and m∠IGH is 2x-13, we can set these two expressions equal to each other:
x-3 = 2x-13
Simplifying the equation, we have:
x - 2x = -13 + 3
-x = -10
Multiplying both sides by -1, we get:
x = 10
Therefore, the value of x is 10.
∠1 and ∠2
are supplementary angles. m∠1 is 4y+7, and m∠2 is 9y+4
. Find m∠2
.
If ∠1 and ∠2 are supplementary angles, their measures sum up to 180 degrees.
Given that m∠1 is 4y + 7 and m∠2 is 9y + 4, we can set up an equation:
m∠1 + m∠2 = 180
(4y + 7) + (9y + 4) = 180
Combining like terms:
13y + 11 = 180
Subtracting 11 from both sides:
13y = 169
Dividing both sides by 13:
y = 13
Now that we have the value of y, we can substitute it back into the expression for m∠2:
m∠2 = 9y + 4 = 9(13) + 4 = 117 + 4 = 121
Therefore, m∠2 is 121 degrees.