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3 years ago

Parallelogram DEFG, DH = x + 3, HF = 3y, GH = 2x – 5, and HE = 5y + 2. Find the values of x and y.

Mathematics

1 answer:

12345 [234]3 years ago

5 0

Your answer is x = 36, y = 13.

We can find this by first realising that DH = HF, and GH = HE, as they are both diagonals of the parallelogram. This allows us to write the equations:

2x - 5 = 5y + 2
x + 3 = 3y

If we rearrange the equation x + 3 = 3y into x = 3y - 3, we can see that this becomes a pair of simultaneous equations that we can solve with substitution. Then we can substitute 3y - 3 into the first equation and solve for y:

2(3y - 3) - 5 = 5y + 2
6y - 6 - 5 = 5y + 2
6y - 11 = 5y + 2
- 5y
y - 11 = 2
+ 11
y = 13

Now because we know that x = 3y - 3, we can substitute 13 into this equation:

x = 3(13) - 3
x = 39 - 3
x = 36

I hope this helps!

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notsponge [240]

Answer:

D. 28.54

Step-by-step explanation:

To find the area of the shaded region, find the area of the circle and divide it in 4. This will the area of the portion with the triangle.

Now, find the area of the triangle and subtract the two. The resulting value will be the area of the shaded region.

Circle:

$A = \pi r^2\\A = \pi 10^2\\A = 100 \pi\\A = 314$

Divide by 4 for the area of the section with the triangle.

314/4 = 78.5

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$A = \frac{1}{2}bh\\A = 0.5 (10 )(10)\\A=0.5(100)\\A=50$

Subtract the two, 78.5 - 50 = 28.5.

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A person invested 3,900 in an account growing at a rate allowing the money to double every 7 years. How much money would be in t

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Step-by-step explanation:

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3 years ago

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

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