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charle [14.2K]
3 years ago
12

Write

ula1" title=" \frac{x(x+1)^2(x-5)}{x(x+2)(x-5)^3} " alt=" \frac{x(x+1)^2(x-5)}{x(x+2)(x-5)^3} " align="absmiddle" class="latex-formula"> in simplest forms. Show your work.
Mathematics
1 answer:
Marizza181 [45]3 years ago
5 0

\bf \cfrac{x(x+1)^2(x-5)}{x(x+2)(x-5)^3}\implies \cfrac{(x+1)^2}{(x+2)(x-5)^2}


all we can really cancel is one of the (x-5) and the "x", is all.

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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 :)

3 0
3 years ago
Read 2 more answers
Find the volume of th] cylinder. Round your answer to the nearest tenth if necessary. Use 3.14 for 1.
spayn [35]

Answer:197.8

The formula for a cylinder is 3.14*r^2*h but if you don't round to the nearest tenth the the answer is 197.82034.

Step-by-step explanation:Step one mutiply 3^2=9, Step two mutiply 3.14*

9=28.26, Step three mutiply 28.26*7=197.82.But if you round 197.82034 to the nearest tenth which is moving one decimal place to the right you'll will get 197.8.

6 0
3 years ago
The Fernandez family drove 273 miles in 5.25 hours. How far would they have driven at that rate in 4 hours?
Vaselesa [24]
The Fernandez family would have driven 208 miles in a rate of 4 hours. 
4 0
3 years ago
You and two friends plan to walk your dogs together. You want the meeting place to be the same distance from each person’s resid
AveGali [126]
If we join the points we are gonna end up with a triangle, from there by finding the centroid of the triangle we will get a point which is equidistant from all the three points given in the diagram.

Formula for Centroid:
6 0
2 years ago
Please answer it for me or show me how to do it? I will mark you branliast answer !!
klasskru [66]

Answer:

25

Step-by-step explanation:

If HI and IJ are both the same and meet at the same point, the triangles would be the same.

7 0
4 years ago
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