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djverab [1.8K]
3 years ago
9

PLEASE SOLVE THE QUESTION BELOW

Mathematics
1 answer:
valkas [14]3 years ago
6 0

Answer:

There are 4 chairs in one row.

Step-by-step explanation:

Let $ x $ be the number of chairs in one row.

That is the length of one row.

Now, from the given data, three rows of length 3x can be formed with one chair left.

Or, if 15 extra chairs given, we can form 7 rows of the same length.

This means that there are $ 3x + 1 $ chairs in the first case. And since with 15 extra chairs we can form 7 rows, the equation would be

$ (3x + 1) + 15 = 7x $

Solving this for '$ x $', we get:

$ 3x + 16 = 7x $

$ \implies 4x = 16 $

$ \implies x = 4 $

Therefore, the length of each row is four.

That is, there are four chairs in one row.

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A triangle is dilated by a scale factor of 1/5 and then rotated 90 degree clockwise about the origin. Why is the image similar t
yan [13]
<u><em>Answers:</em></u>
The corresponding angles of the triangles are congruent
The image is a reduction of the pre-image
Neither the dilation nor the rotation change the shape of the triangle

<u><em>Explanation:</em></u>
<u>For shapes to be similar:</u>
1- there should be a ratio between the sides
2- angles in first shape should be congruent to angles in second shape

Now, a scale factor of 0.2 means that the sides of the image are 0.2 of the length of the original shape. However, angles are not changes

<u>Let's check the choices:</u>
<u>1- </u><span><u>The corresponding sides of the triangles are congruent:</u>
This option is incorrect as dilation changes the lengths of the sides

<u>2- </u></span><span><u>The corresponding angles of the triangles are congruent:</u>
This option is correct as neither dilation nor rotation alters the measures of the angles

<u>3- </u></span><span><u>The corresponding sides of the image are 5 times as long as those of the pre-image:</u>
This option is incorrect as the sides of the image are only 0.2 times as long as those of the pre-image

<u>4- </u></span><span><u>The image is a reduction of the pre-image:</u>
This option is correct as the sides of the image are 0.2 times those of the pre-image which means that the shape is reduced

<u>5- </u></span><span><u>Neither the dilation nor the rotation change the shape of the triangle:</u>
This option is correct as both dilation and rotation are rigid transformations that do not alter the shape of the triangle (a triangle remains a triangle only with different side lengths)

<u>6- </u></span><u>The rotation reduces the size of the triangle:</u>
This option is incorrect as rotation does not alter the size of the shape. It only changes its position

Hope this helps :)

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Gekata [30.6K]

Answer:

b

Step-by-step explanation:

The median of a triangle is a line that from the vertex touches the middle lets eliminate options

a=ab starts at a vertex but doensn't touch a the middle of a line X

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<u>SO THE CORRECT ANSWER IS B</u>

<em>-hope this helps :)</em>

8 0
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