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Ksenya-84 [330]
3 years ago
10

Find the sum of the measures of the interior angles of the polygon. 15-gon A. 2340° B. 2520° C. 2160° D. 1170°

Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
8 0

Answer:

2340

Step-by-step explanation:

Formulae for sum of interior angles is 180(n-2)

Whereby n=number of sides

180(15 - 2) \\ 180(13) \\  = 2340degrees

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Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Select two options.
Elanso [62]

Answer:

2 and 5

Step-by-step explanation:

The slope-intercept form of a line is y=mx-b where m is slope and b is y-intercept.

The point-slope form of a line is y-y1=m(x-x1) where m is the slope and (x1,y1) is a point on the line.

The standard form a line is ax+by=c.

So anyways parallel lines have the same slope.

So if we are looking for a line parallel to 3x-4y=7 then we need to know the slope of this line so we can find the slope of our parallel line.

3x-4y=7

Goal: Put into slope-intercept form

3x-4y=7

Subtract 3x on both sides:

  -4y=-3x+7

Divide both sides by -4:

   y=\frac{-3}{-4}x+\frac{7}{-4}

Simplify:

   y=\frac{3}{4}x+\frac{-7}{4}

So the slope of this line is 3/4.  So our line that is parallel to this one will have this same slope.

So we know our line should be in the form of y=\frac{3}{4}x+b.

To find b we will use the point that is suppose to be on our new line here which is (x,y)=(-4,-2).

So plugging this in to solve for b now:

-2=\frac{3}{4}(-4)+b

-2=-3+b

3-2=b

b=1

so the equation of our line in slope-intercept form is y=\frac{3}{4}x+1

So that isn't option 1 because the slope is different.  That was the only option that was in slope-intercept form.

The standard form of a line is ax+by=c and we have 2 options that look like that.

So let's rearrange the line that we just found into that form.

y=\frac{3}{4}x+1

Clear the fractions because we only want integer coefficients by multiplying both sides by 4.

This gives us:

4y=3x+4

Subtract 3x on both sides:

-3x+4y=4

I don't see this option either.

Multiply both sides by -1:

3x-4y=-4

I do see this as a option. So far the only option that works is 2.

Let's look at point slope form now.

We had the point that our line went through was (x1,y1)=(-4,-2) and the slope,m, was 3/4 (we found this earlier).

y-y1=m(x-x1)

Plug in like so:

y-(-2)=3/4(x-(-4))

y+2=3/4 (x+4)

So option 5 looks good too.

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