Answer:
Step-by-step explanation:
Domain:
![\dfrac{x^2+9y^2}{x-3y}+\dfrac{6xy}{3y-x}=\dfrac{x^2+9y^2}{x-3y}+\dfrac{6xy}{-(x-3y)}\\\\=\dfrac{x^2+9y^2}{x-3y}-\dfrac{6xy}{x-3y}=\dfrac{x^2+9y^2-6xy}{x-3y}\\\\=\dfrac{x^2-2(x)(3y)+(3y)^2}{3y-x}=\dfrac{(x-3y)^2}{3y-x}\\\\=\dfrac{\bigg[-1(3y-x)\bigg]^2}{3y-x}=\dfrac{(-1)^2(3y-x)^2}{3y-x}\\\\=\dfrac{1(x-3y)(x-3y)}{x-3y}=x-3y](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E2%2B9y%5E2%7D%7Bx-3y%7D%2B%5Cdfrac%7B6xy%7D%7B3y-x%7D%3D%5Cdfrac%7Bx%5E2%2B9y%5E2%7D%7Bx-3y%7D%2B%5Cdfrac%7B6xy%7D%7B-%28x-3y%29%7D%5C%5C%5C%5C%3D%5Cdfrac%7Bx%5E2%2B9y%5E2%7D%7Bx-3y%7D-%5Cdfrac%7B6xy%7D%7Bx-3y%7D%3D%5Cdfrac%7Bx%5E2%2B9y%5E2-6xy%7D%7Bx-3y%7D%5C%5C%5C%5C%3D%5Cdfrac%7Bx%5E2-2%28x%29%283y%29%2B%283y%29%5E2%7D%7B3y-x%7D%3D%5Cdfrac%7B%28x-3y%29%5E2%7D%7B3y-x%7D%5C%5C%5C%5C%3D%5Cdfrac%7B%5Cbigg%5B-1%283y-x%29%5Cbigg%5D%5E2%7D%7B3y-x%7D%3D%5Cdfrac%7B%28-1%29%5E2%283y-x%29%5E2%7D%7B3y-x%7D%5C%5C%5C%5C%3D%5Cdfrac%7B1%28x-3y%29%28x-3y%29%7D%7Bx-3y%7D%3Dx-3y)
Used:
The distributive property: a(b + c) = ab + ac
(a - b)² = a² - 2ab + b²
If the polygons are similar, then we can set up a similarity ratio using sides AB and EF and any other 2 sides where both side lengths are given. That appears to be true for sides BC and FG. Our similarity ratio would be this then, going from the bigger polygon stuff on top and the smaller polygon stuff on bottom:
.
If we cross multiply we have 8y = 36 and divide both sides by 8 to get that y = 4.5. There you go!
Answer: F(x, y) = 40x + 25y
Step-by-step explanation:
Given the following :
x = number of leather wallets
y = number of canvas wallets
PROFIT on canvas wallet = $25
PROFIT on leather wallet = $40
Function that calculates the total profit on both wallets:
Profit on each wallet type is the product of the profit per wallet and the number of wallet.
The total profit generated on each wallet type is given by :
F(x) = 40x - - - - (1) leather wallet
F(y) = 25y - - - - (2) canvas wallet
Adding (1) and (2) to get total profit on both wallets:
F(x, y) = 40x + 25y
length=8 units
Step-by-step explanation:
- LET,
- A=16 units
- L=a units
- B=a-6 units
- L*B=A
- Replacing value of L with 'a'. and B with 'a-6',
- a(a-6)=16
- a*a-a*6=16
- a^2-6a=16
- a^2-6a-16=0
- a^2-8a+2a-16=0
- a(a-8)+2(a-8)=0
- (a-8)(a+2)=0
- Either,. a-8=0
- first value a=8
- Or,. a+2=0
- second value a=-2(Rejected due to negative)
- therefore, a=L=8
- Length=8 units
