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irakobra [83]
2 years ago
12

A trapezoidal prism undergoes a dilation. The surface area of the pre-image is 35 m². The surface area of the image is 315 m². T

he height of the pre-image is 5. 8 m. What is the height of the image? Enter your answer as a decimal in the box. M.
Mathematics
2 answers:
UkoKoshka [18]2 years ago
5 0

17.4 m - I took the test on k-12 and I got it wrong because I thought it was 52.2m. I reviewed the test and the correct answer said "17.4m"
Westkost [7]2 years ago
4 0

The original object is called pre-image, and its dilated version is called image. The height of the image for the considered case is 17.4 m

<h3>How does dilation affect length, area, and volume of an object?</h3>

Suppose a figure (pre image) is dilated (dilated image) by scale factor of k.

So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:

<u><em>L = k × M</em></u>

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by <u><em>k²</em></u><em> </em>to get each other corresponding quantity from their similar figures' quantities.

<u><em>So </em></u><u><em>area </em></u><u><em>of </em></u><u><em>first figure </em></u><u><em>= k² × area of second figure</em></u>

Similarly,

<u><em>Volume </em></u><u><em>of first figure = k³ × volume of second figure.</em></u>

It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.

For this case, we're given that;

  • Surface area of pre-image = 35 m²
  • Surface area of dilated image = 315 m²
  • Height of pre-image = 5.8 m
  • Height of dilated image.

Let the scale fator of dilation be k.

Then:

<u><em>So area of pre-image = k² × area of dilated image</em></u>

Thus, we get:

35 = k^2 \times 315\\\\k = \sqrt{\dfrac{35}{315}} = 1/3

(took positive root as scaling is done by non-negative factors as only magnitude matters mostly)

Thus, we get:

Height of pre-image = (1/3) × Height of dilated image (say h)

5.8 = (1/3) \times h\\h = 3 \times 5.8 = 17.4 \rm \: m

Thus, the original object is called pre-image, and its dilated version is called image. The height of the image for the considered case is 17.4 m

Learn more about dilation here:

brainly.com/question/3266920

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Lesechka [4]

Answer:

55.5

Step-by-step explanation:

6 0
3 years ago
A cross-country team had a total of 10 practices last week, with each practice being in the morning or the afternoon. During eac
GalinKa [24]

x= morning

y = afternoon

 x + y = 10

x=10-y

5x + 6y =57

5(10-y) +6y =57

50-5y +6y =57

y=7

x=10-7 =3

 check 3*5 = 15, 7*6 = 42, 42 + 15 = 57


3 morning practices

3 0
3 years ago
ℓ=gT24π2 what is g equal to
V125BC [204]

If a=48Tg\pi then g=\frac{a}{48T\pi}.

Hope this helps.

4 0
3 years ago
A mistake was made in mixing the lemonade—<br> PLEASE HELP!!
beks73 [17]

Answer:

Part A:

4 + x = y

0.5*4 + 1*x = 0.7*y

x = 8/3\ quarts\ of\ 100\%\ solution

y = 20/3\ quarts\ of\ 70\%\ solution

Part B:

x + y = 10

2x + 3y = 23

x = 7 and y = 3

Step-by-step explanation:

Part A:

The inicial concentration of the lemonade is 50%, and the volume is 4 quarts, and we will add x quarts of a lemonade with a concentration of 100%, so the total volume will be y, and the concentration will be 0.7, so we have that:

4 + x = y

0.5*4 + 1*x = 0.7*y

Using the value of y from the first equation in the second one, we have:

2 + x = 0.7*(4 + x)

2 + x = 2.8 + 0.7x

0.3x = 0.8

x = 8/3\ quarts

y = 4 + 8/3 = 20/3\ quarts

Part B:

If he shoots a total of ten targets, we can write the equation:

x + y = 10

Each stationary target is 2 points, and each moving target is 3 points, so if the total points is 23, we have:

2x + 3y = 23

If we subtract the second equation by two times the first one, we have:

2x + 3y - 2*(x + y) = 23 - 2*10

2x + 3y - 2x - 2y = 23 - 20

y = 3

x + 3 = 10 ⇒ x = 7

4 0
3 years ago
What is the measure of the indicated angle 103° ?
Elina [12.6K]

Answer:

77 degrees.

Step-by-step explanation:

180-103=77

4 0
3 years ago
Read 2 more answers
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