X square= 121 can anyone solve it

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

Westkost [7]

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:

L = k × M

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 k² to get each other corresponding quantity from their similar figures' quantities.

So area of first figure = k² × area of second figure

Similarly,

Volume of first figure = k³ × volume of second figure.

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:

So area of pre-image = k² × area of dilated image

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

4 0

2 years ago

Read 2 more answers

What linear equation is represented by the table? 1

rewona [7]

Answer:

Y=4x-2

Step-by-step explanation:

You have to try it (x,y) (2,6)

y=4x-2

6=4(2)-2

6=8-2

8 0

2 years ago

50 points!!!!! Please!!!!! Sandra and Jenny spend a certain amount of money from their money box each month to buy plants. The t

nekit [7.7K]

Answer:

A) Function 2 shows a greater rate of change because Jenny spends $6 each month and Sandra spends $5 each month.

Step-by-step explanation:

The y-intercept for Sandra is 55 and the slope is -5. While Jenny's y-intercept is 50 and slope is -6.

6 is a greater number therefore causing Jenny's slope to decrease faster causing her to have less money at a much faster rate. (rate of change=slope) Jeny's slope is decreasing at a faster rate of change because she is spending more money everyday than Sandra is.

Hope this helps! Have a great day! :)

4 0

3 years ago

A paper store sells wrapping paper rolls and bags. In the spring, they order a ratio of 3:7 in wrapping paper bags in the spring

Maru [420]

If it can be assumed that the total number paper and bags is the same for both orders, then:

#bags ordered in the spring=7*(150/3)=350, so the total of both is 150+350=500. A 5:5 ratio means that the wrapping paper and bags were bout in equal quantities. That means 500/2=250 for each.

6 0

3 years ago

Ge A flower bed has the shape of a rectangle 24 feet long and 9 feet wide. What is its area in square yards? Be sure to include

Nonamiya [84]

Answer:

area = 24 yd²

Step-by-step explanation:

convert the dimensions into yards using the conversion

1 yard = 3 feet

24 feet = $\frac{24}{3}$ = 8 yards

9 feet = $\frac{9}{3}$ = 3 yards

area = length × width = 8 × 3 = 24 yd²

5 0

2 years ago