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Alex17521 [72]
3 years ago
15

Find an equation of the line through the given point and perpendicular to the given line

Mathematics
1 answer:
s344n2d4d5 [400]3 years ago
4 0

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

For two lines to be perpendicular, the slope of one line is the negative reciprocal of the other line. The equation of the given line is

y = 2x - 2

Comparing with the slope intercept form,

Slope, m = 2

This means that the slope of the line that is perpendicular to it is -1/2

The given points are (-3, 5)

To determine c,

We will substitute m = -1/2, y = 5 and x = - 3 into the equation, y = mx + c

It becomes

5 = -1/2 × - 3 + c

5 = - 3/2 + c

c = 5 + 3/2

c = 13/2

The equation becomes

y = -x/2 + 13/2

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The figure is mad up of two shapes? A semicircle and a rectangle
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the length of a rectangle is 5 less than twice the width.if the perimeter of the rectangle is 146,find the area of the rectangle
raketka [301]

Answer:

The area of the rectangle is 1222 units²

Step-by-step explanation:

The formula of the perimeter of a rectangle is P = 2(L + W), where L is its length and W is its width

The formula of the area of a rectangle is A = L × W

∵ The length of a rectangle is 5 less than twice the width

- Assume that the width of the rectangle is x units and multiply

   x by 2 and subtract 5 from the product to find its length

∴ W = x

∴ L = 2x - 5

- Use the formula of the perimeter above to find its perimeter

∵ P = 2(2x - 5 + x)

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- Multiply the bracket by 2

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- Equate the two expression of P

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- Divide both sides by 6

∴ x = 26

Substitute the value of x in W and L expressions

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∴ L = 47 units

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∴ A = 1222 units²

∴ The area of the rectangle is 1222 units²

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