Answer:
x=5 x=6
Step-by-step explanation:
x^2 - 8x + 30 = 3x
Subtract 3x from each side
x^2 - 8x-3x + 30 = 3x-3x
x^2 - 11x + 30 = 0
What 2 numbers multiply to 30 and add to -11
-5*-6 = 30
-5+-6 = -11
(x-5) (x-6) =0
Using the zero product property
x-5 = 0 and x-6 =0
x-5+5 =0+5 and x-6+6 =0+6
x=5 x=6
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)
That is just multiply the number of choices for each
5 colors
2 lengths of sleaves
3 colors
5*2*3=30
answer is 30
C is answer
Answer:
Part A: Option 2, A: Anna’s answer is incorrect. She correctly factored out 5x, but incorrectly identified a and b, so her answer cannot be correct.
Part B: Option 3, B: 5x(x+2)(x^2−2x+4)
Step-by-step explanation:
p(x) = 5x^4 + 40x
p(x) = 5x(x^3 + 8)
p(x) = 5x(x + 2)(x^2 - 2x + 4)
Part A: Option 2, A: Anna’s answer is incorrect. She correctly factored out 5x, but incorrectly identified a and b, so her answer cannot be correct.
Part B: Option 3, B: 5x(x+2)(x^2−2x+4)
Y2-y1 -5-(-8) 3
____ = _____ = ___ = -3/7
x2-x1 2-9 -7
