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pogonyaev
3 years ago
12

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

o the pre-image? Check all that apply.
A) The corresponding sides of the triangles are congruent.
B) The corresponding angles of the triangles are congruent.
C) The corresponding sides of the image are 5 times as long as those of the pre-image.
D) The image is a reduction of the pre-image.
E) Neither the dilation nor the rotation change the shape of the triangle.
F) The rotation reduces the size of the triangle.
Mathematics
2 answers:
DerKrebs [107]3 years ago
4 0

Answers:

<em>B.The corresponding angles of the triangles are congruent </em>

<em>D.The image is a reduction of the pre-image </em>

<em>E. Neither the dilation nor the rotation change the shape of the triangle</em>

yan [13]3 years ago
3 0
<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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Step-by-step explanation:

Here, the parking cost of 1 night at the airport  = $24.99

Now, here the total number of nights the car is parked at airport = s

R = The total cost of parking s nights

Now, The cost for parking s nights  = s x ( Cost of parking 1 night)

= s x ($24.99) = 24.99 s

Also the cost for parking s nights    = r

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Hence, equation  which can be used to find r, the cost in dollars to park s nights is  r = 24.99 s

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2 years ago
Two boats sail away from a buoy making a 90 degree angle. The first boat is 165 meters away and is traveling at 25 m/s. The seco
NikAS [45]

Answer:


Step-by-step explanation:

lets say in the shown triangle x=165

so speed \frac{dx}{dt} =25

and  \frac{dy}{dt} =35


Also since distance = speed* time

time = pi minutes = pi/60 seconds

y = \frac{35\pi \pi }{60}

y = \frac{7\pi }{12}


Now using the pythagorean :

x^2+y^2=z^2\\so \\165^2+(\frac{7\pi }{12} )^2 =z^2

<u>derivate the equation so  we get :</u>

x\frac{dx}{dt} +y\frac{dy}{dt} =z\frac{dz}{dt} \\165*25+35*\frac{7\pi }{12}=\sqrt{165^2+(\frac{7\pi }{12})^2} *\frac{dz}{dt}


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5 0
3 years ago
There are 4,200 adults in Lakeview. Three-eighths of the adults in Lakeview do not have children. How many adults in Lakeview ha
Inessa [10]

To answer this, you first have to find 3/8 of 4200 by multiplying those two numbers.

\frac{4200}{1} *\frac{3}{8}


First, multiply the numerators.

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Next, multiply the denominators.

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You end up with \frac{12600}{8}.

This fraction can be simplified to 1575.

All that's left is to subtract that number from 4200.

4200-1575=2625


The final answer is 2625 adults in Lakeview have children.


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3 years ago
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pashok25 [27]

Answer:

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We know a^b^c = a^(b*c)

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Since the bases are the same, the exponents are the same

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Nana76 [90]

Answer:

4

Step-by-step explanation:

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So, the number 10,000 which is the square of 100 has 4 zeros.

Hope this helped!

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