Answer: 24.49 or 24.5 if rounded.
Step-by-step explanation: We have to use the pythagorean theorem of course...
a² + b² = c²
15² + 20² = c²
225 + 400 = c²
600 = c²

c = 24.49 (If we round to the nearest tenth then the answer is 24.5)
Answer: 
Center = (2, 3) radius = 
<u>Step-by-step explanation:</u>
When both the x² and y² values are equal and positive, the shape is a circle. Complete the square to put the equation in format:
(x-h)² + (y-k)² = r² where
- (h, k) is the vertex
- r is the radius
1) Group the x's and y's together and move the number to the right side
4x² - 16x + 4y² - 24y = -51
2) Factor out the 4 from the x² and y²
4(x² - 4x ) + 4(y² - 6y ) = -51
3) Complete the square (divide the x and y value by 2 and square it)
![4[x^2-4x+\bigg(\dfrac{-4}{2}\bigg)^2]+4[y^2-6y+\bigg(\dfrac{-6}{2}\bigg)^2]=-51+4\bigg(\dfrac{-4}{2}\bigg)^2+4\bigg(\dfrac{-6}{2}\bigg)^2](https://tex.z-dn.net/?f=4%5Bx%5E2-4x%2B%5Cbigg%28%5Cdfrac%7B-4%7D%7B2%7D%5Cbigg%29%5E2%5D%2B4%5By%5E2-6y%2B%5Cbigg%28%5Cdfrac%7B-6%7D%7B2%7D%5Cbigg%29%5E2%5D%3D-51%2B4%5Cbigg%28%5Cdfrac%7B-4%7D%7B2%7D%5Cbigg%29%5E2%2B4%5Cbigg%28%5Cdfrac%7B-6%7D%7B2%7D%5Cbigg%29%5E2)
= 4(x - 2)² + 4(y - 3)² = -51 + 4(-2)² + 4(-3)²
= 4(x - 2)² + 4(y - 3)² = -51 + 4(4) + 4(9)
= 4(x - 2)² + 4(y - 3)² = -51 + 16 + 36
= 4(x - 2)² + 4(y - 3)² = 1
4) Divide both sides by 4

- (h, k) = (2, 3)

12c=22
6c=11
c=1 5/6
20c=33
c= 1 13/20
5/6 is about .83
13/20 is .65
12 chocolate bars for $22 is about $1.83 each
20 chocolate bars for $33 is $1.65 each
The 20 chocolate bars for $33 dollars has a better unit rate and is a better buy.
Answer:
No solution
Step-by-step explanation:
Substitution is done by substituting one equation into another. To begin solve one equation for a variable.
Substitute y=-4x+3 into -4x-y=-2.
-4x -(-4x + 3) = -2
-4x + 4x - 3 = -2
-3=-2
This is a false statement and there is no variable present anymore. This means the equations have no solution.