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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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Setler [38]

Answer:

about $1.17 for each soda

Step-by-step explanation:

5 0
3 years ago
In a school of 2000 students, 1150 do not like puzzles. 2/5 of the students travel to school by bus. 595 of the people that do l
Vadim26 [7]

The number of students who do not like puzzles and ride the bus to school is 205

To find the answer it is necessary to do the following procedure:

To find out how many people the 2/5 traveling by bus are equivalent to, divide the total number (2000) of people by 5, and then multiply that value by 2.

  • 2000 ÷ 5 = 400
  • 400 × 2 = 800

From the above, it can be established that 800 people travel by bus to school. Now, to know how many people travel by bus and do not like puzzles, the following operation must be done.

Subtract the number of students who do like puzzles and ride the bus (595) from the total number of students who ride the bus (800)

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So the answer is 205 students ride the bus and they don't like puzzles.

Learn more at: brainly.com/question/24558946

6 0
2 years ago
A class has a ratio of boys to girls 3:4.
Nat2105 [25]

Answer:

a)F

b)A

c)F

d)F

Step-by-step explanation:

a)3+4=7 which is the total number of pupils in class

So, the fraction should be 3/7✅not 3/4❌

b) The girls in the class are 4 and the total number of pupils in class are 7. So, the fraction is correct✅.

c) The number of boys in class is 3✅ which is given in the ratio. Not 6❌

d) If you add the both numbers in the ratio, you will get the total number of pupils which is 7✅not 12❌

Hope this will help ya!

4 0
3 years ago
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pshichka [43]
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8x - Linda's distance for 8 h
8(x+8) = 8x+64  - Colleen's distance for 8 h

8x + 8x + 64 = 176 - distance between Colleen and Linda after 8 h


8x + 8x + 64 = 176 
16x +64 = 176
16x = 176 - 64
16x = 112
x= 7 mph Linda's speed
x+8
= 7+8 = 15 mph Colleen's speed
8 0
3 years ago
For what values of the variable is each rational expression undefined 2x-3/2x-1( step by step please)
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\frac{2x-3}{2x-1}\\\\Rational\ expression\ unde fined\ if\ 2x-1=0\\\\2x=1\ \ \ \ /:2\\\\x=\frac{1}{2}\leftarrow answer
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3 years ago
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