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3 years ago

Find the slope of the line passing through the points (7, 8) and (-7, 1). Show your work.

Mathematics

1 answer:

anygoal [31]3 years ago

4 0

Answer:

The slope is $\frac{1}{2}$

Step-by-step explanation:

∵ The rule of the slope passing through 2 points is:

m = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∵ The points are (7 , 8) and (-7 , 1)

∴ m = $\frac{1-8}{-7-7}=\frac{-7}{-14}=\frac{1}{2}$

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3 years ago

What are the coordinates of the center and the

Misha Larkins [42]

Answer: The coordinate of the center is (4,-3)

radius = 8

Step-by-step explanation:

Given ;

$x^{2} +y^{2}=8x-6y+39$

re - arranging , we have

$x^{2} +y^{2}-8x+6y-39=0$

comparing with the general equation

$x^{2} +y^{2}+2gx+2fy+c=0$

This means that

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also

$2fy=6y$

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The coordinate of the center is (-g,-f)

Therefore;

the coordinate of the center = (4,-3)

the formula for calculating r is given by:

$r = \sqrt{g^{2}+f^{2}-c}$

$r = \sqrt{16+9+39}$

$r=\sqrt{64}$

$r=8$

METHOD 2

$x^{2} +y^{2}-8x+6y-39=0$

using completing the square method , we have

$x^{2} -8x+y^{2}+6y-39=0$

completing the square , we have

$(x-4)^{2}+(y+3)^{2} = 39 +4^{2}+3^{2}$

$(x-4)^{2}+(y+3)^{2}=64$

comparing with the general equation

$(x-a)^{2}+(y-b)^{2}=r^{2}$

where a and b are the coordinate of the center , that is

the coordinate of the center is ( 4 , -3)

$r^{2}=64$

$r=8$

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Hnece, you have:

The shoreline is reduced by 0.5 foot every 10 years

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1 year ago

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Answer:

Step-by-step explanation:

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