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3 years ago

Which lines are parallel if m 3 = m 6?Justify your answer.

Mathematics

2 answers:

andrew-mc [135]3 years ago

5 0

This is an example

Opposite angles formed by two intersecting lines are equal, so angle 1 is the same as angle 4. That means angle 1 = angle 5 as well.

When a line intersects two parallel lines, the corresponding angles are equal. That is, if r and s are parallel, then the angles formed when l intersects r are the same s the angles formed when l intersects s. Angle 1 = Angle 5, Angle 2 = Angle 6, and so forth. Since we know angle 1 = angle 5, so from that you can see that r and s are parallel

Brums [2.3K]3 years ago

4 0

Answer:

$r \parallel s$ by the Converse of the Alternate Interiors Angles Theorem.

Step-by-step explanation:

Remember that two lines are parallel if their angle of direction is the same.

So, in this case we know that $m\angle 3 = m\angle 6$ , where $\angle 3$ is the direction of $r$ and $\angle 6$ is the direction of $s$ .

Therefore, $r \parallel s$ by the Converse of the Alternate Interior Angles Theorem, which states that if two lines are cut by a transversal and the alternate interior angles are congruent, then those lines are parallel.

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What is the longest line segment that can be drawn in a right rectangular prism that is 15 cm long,

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3 years ago

What is the diameter of the following circle <br>

Margaret [11]

Answer:

d = 140 in

Step-by-step explanation:

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3 years ago

find the width of the rectangular prism if the volume is 165,000 the length is 100 mm and the height is 55

scoundrel [369]

Answer:

30 mm

Step-by-step explanation:

The volume of a rectangular prism is the product of its three dimensions. To find the missing dimension, divide the volume by the product of the two that are given:

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3 0

3 years ago

Find the percentage of students that scored higher than 95.5. Round your answer to the nearest percent.

My name is Ann [436]

Answer:

$\% Change = \frac{9}{64} *100 = 14.0625\% \approx 14\%$

So then we have approximately 14% of the values higher than 95.5

Step-by-step explanation:

For this case we assume that the info is given on the figure attached.

From this figure we have the following frequencies for each class

Class Frequency

___________________________

70.5-75.5 13

75.5-80.5 7

80.5-85.5 6

85.5-90.5 10

90.5-95.5 19

95.5-100.5 9

____________________________

Total 64

So we have a total of 64 values and we want to find the percentage of students that scored higher than 95.5 so we can use the formula of relative change and we got:

$\% Change = \frac{9}{64} *100 = 14.0625\% \approx 14\%$

So then we have approximately 14% of the values higher than 95.5

6 0

4 years ago

Clayton needs to reflect the triangle below across the line y = x. On a coordinate plane, triangle A B C has points (5.5, 7), (6

Ksju [112]

Answer:

Clayton could use the relationship (x,y) - (y,x) to find the points of the image.

C’ will remain in the same location as C because it is on the line of reflection.

The image and the pre-image will be congruent triangles.

The image and pre-image will not have the same orientation because reflections flip figures

Step-by-step explanation:

Clayton needs to reflect the triangle below across the line y=x

Which statements about the reflection are true? Check all that apply.

Clayton could use the relationship (x,y) - (y,x) to find the points of the image.Clayton could negate both the x and y values in the points to find the points of the image.C’ will remain in the same location as C because it is on the line of reflection.C’ will move because all points move in a reflection.The image and the pre-image will be congruent triangles.The image and pre-image will not have the same orientation because reflections flip figures.

Solution:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, dilation and translation.

Reflection is the flipping of a figure over a line. If a point A(x, y) is reflected over the line y=x, the new location is A'(y, x).

If the triangle ABC with vertices A(5.5, 7), B(6, 2), C(4, 4) is reflected over the line y=x, the new location would be A'(7, 5.5), B'(2, 6) and C'(4, 4).

A. Clayton could use the relationship (x,y) - (y,x) to find the points of the image. Reflection across the line y = x is the swapping of the x and y coordinates. Option A is correct

B. Clayton could negate both the x and y values in the points to find the points of the image. Option B is wrong

C. C’ will remain in the same location as C because it is on the line of reflection. C is on the line of reflection, hence it remains the same. Option C is correct.

D. C’ will move because all points move in a reflection.

Option D is wrong.

E. The image and the pre-image will be congruent triangles.

Option E is correct. Reflection preserves the shape and length of an object.

F. The image and pre-image will not have the same orientation because reflections flip figures. Option F is correct

8 0

3 years ago

Read 2 more answers

Which lines are parallel if m 3 = m 6?Justify your answer.​

Which lines are parallel if m 3 = m 6?Justify your answer.