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3 years ago

Solve. 7x+2y=2, x-2y=14

Mathematics

2 answers:

balu736 [363]3 years ago

8 0

Isolate the X in the second equation

x=2y+14

Substitute that in for the x in the fist equation

7(2y+14) + 2y = 2

Distribute the 7

14y+14+2y=2

Combine like terms

16y+14=2

Isolate the 16y

16y=-12

Isolate y by dividing the whole equation by 16

y=-12/16

Simplify

y=-3/4

That is your y. To find x, plug y into one of the equations. I'm plugging it into the version of the second equation after we isolated x.

x=2(-3/4)+14

Distribute the 2

x=(-1.5)+14

Simplify

x=12.5

nikitadnepr [17]3 years ago

6 0

I have the answer and process on the attachment.

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3 years ago

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3 years ago

What is 8^1/2 in simplest form

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3 years ago

OBC is a sector of a circle with centre o and radius 9cm work out the area of the shaded region as a percentage of the area of s

NARA [144]

Answer:

83.7 %

Step-by-step explanation:

To get the area of the shaded region, we will following these steps.

Step one: Get the area of the sector of the circle.

The area of the sector of the circle can be obtained using the formula:

$Area = \frac{\theta}{360}\times \pi r^{2}$

Theta will be 60 degrees because triangle OAD is an equilateral triangle

Hence, $Area = \frac{60}{360}\times \pi \times 9^{2}= 42.42cm^{2}$

Step Two: Get the area of the equilateral triangle

The area of the equilateral triangle can be got using the formula

$Area = \frac{1}{2} Base \times Height$

The height of the triangle can be got by drawing an imaginary line bisecting the triangle into two parts and applying the Pythagoras' theorem to any of the resulting right-angled triangles formed.

This will be $height =\sqrt{4^{2}-2^{2}} =3.46cm$

Thus $Area = \frac{1}{2}\times 4\times 3.46=6.93cm^{2}$

Step Three: Subtract the area of the triangle from the area of the sector

Area of the shaded portion = $42.42cm^{2}-6.93cm^{2}=35.49cm^{2}$

Step Four: Divide the area of the shaded portion by the area of the entire shape and multiply the result by 100:

Expressing the ratio of the two areas as a percentage, we have

$\frac{35.49}{42.42} \times 100\approx 83.7 %$ %

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3 years ago