skylersnoop

16 = (2y - 2) + (y + 3)

16 = 3y + 1

15 = 3y

y = 5

You can double check by plugging 5 in. BC is equal to CD, because it is a perpendicular bisector.

Both of these problems require the use of constant ratios. 

8. 

LM/QR = NK/SP

(4x+4)/48 = (7x-9)/60

(x+1)/12 = (7x-9)/60

12(7x--9) = 60(x+1)

84x - 108 = 60x + 60

24x = 168

x = 7

9.

YZ/SZ = RT/ST

(2x+2)/35 = (3x-7)/40

35(3x-7) = 40(2x+2)

105x - 245 = 80x + 80

25x = 325

x = 13

What you should do for any composite figure is divide it up into smaller parts. We can divide this figure into two parts, the semicircle at the top, and the rectangle at the bottom. 

We can find the area of the rectangle easily, it is just 8*10 = 80.

Now to find the area of the semicircle. In case you didn't know, the formula for the area of a circle is π r^2. The r in this case will be 4, because it is half of the diameter, 8. Plug this into the formula to get:

= π (4)^2

= 16π

Dont forget to divide by 2, because it is a semicircle. 

= 8π

Now, we add the rectangle and the semicircle's area together to get 80 + 8π.

If you want it in decimal form, it is 105.1327412

The way that I remember how logarithms work is to move the base of the log so that is it "under" the number on the right.

So in this case it becomes:

81 = b ^ (2/3)

81^(3/2) = b

I think you can find b now. Hope this helped!

To solve this problem, we need to find the maximum of the graph. In this case, the maximum is also the vertex of the graph. So, we just need to find the vertex of the equation. In case you didn't know, the formula for finding the x-coordinate of the vertex is   -b/2a in the form ax^2 + bx + c. 

Plugging in the values(b = 51, a = -1), we get:

x = -(51)/2(-1)

x = -51/-2

x = 51/2 or 25.5

Now, we have the x-coordinate of our vertex(maximum). All we need to do now is plug 51/2 back into the original equation.

y = -(51/2)^2 + 51(51/2) - 201

y = -(650.25) + 1300.5 - 201

y = -650.25 + 1300.5 - 201

y = 449.25

Now, we know the coordinates of the maximum. It is: (25.5, 449.25).

Convert to cash.

tldr: The company must sell their widgets for 25.50 dollars, which leads to a maximum profit of 449.25 dollars. 

To start this problem out, we will find the x and y-intercepts of 2x + 3y = 6. The x-intercept is found when y is 0. So, we plug zero into the equation to get:

2x + 3(0) = 6

2x = 6

x = 3

So now we know that the coordinates of the x-intercept is 3. (this point is b)

The y-intercept is found when x = 0. So, we do the same thing as before, except x = 0.

2(0) + 3y = 6

3y = 6

y = 2

So now we know that the coordinates of the y-intercept is 2. (this point is a)

This is as far as I will go, as the rest of the problem seems a little too complicated and confusing for my 2 little brain cells. Hope this helped though!

The first polygon will have side length will be set to 2x. So, the perimeter of the polygon is 76x. (because 38 * 2x = 76x)

The second polygon will have side length will be set to x, because the second polygon has half the side length of the first polygon. Also, the number of sides that the polygon has will be set to y. So, the perimeter will be xy.

The perimeters of both polygons are equal, so we can set 76x = xy.

Divide both sides by x to get:

76 = y

There are 76 sides in the second polygon. 

The coordinates of the given points are (-10, 5), and (-5, 6). (you can use the other two points as well). To get from the first coordinate to the second coordinate, you rise by 1 and go over by 5. The formula for slope is rise over run, so the slope of the graph is 1/5. 

Now, we plug that into the slope-intercept equation, to get y = 1/5 x + b.

All that is left to do is plug in any value into our equation to find b. I will choose the point (5, 8).

We get:

8 = 1/5 (5) + b

8 = 1 + b

7 = b

Our complete equation is 1/5 x + 7.