Question

Please help meee asap!​

Answer 1

1.

Original square side: s

Area = s^2

Modified square:

Length = 1.3s

Width = 0.82s

Area = 1.3s * 0.82s = 1.066s^2

(1.066 - 1)/1 * 100% = 6.6%

The area increases by 6.6%

2.

`(1)/(x) + (1)/(y) = (2)/(15)`

`(y)/(xy) + (x)/(xy) = (2)/(15)`

`(x + y)/(xy) = (2)/(15)`

`x + y = (2xy)/(15)`

`(7y + 5xy + 7x)/(y + x + 2xy) =`

`= (7x + 7y + 5xy)/(x + y + 2xy)`

`= (7(x + y) + 5xy)/(x + y + 2xy)`

`= (7((2xy)/(15)) + 5xy)/((2xy)/(15) + 2xy)`

`= (15)/(15) * (7((2xy)/(15)) + 5xy)/((2xy)/(15) + 2xy)`

`=  (14xy + 75xy)/(2xy + 30xy)`

`=  (89xy)/(32xy)`

`=  (89)/(32)`

3.

`(x - 3)/(x^3 + 3x) = (A)/(x) + (Bx + C)/(x^2 + 3)`

`= (A(x^2 + 3))/(x(x^2 + 3)) + ((Bx + C)x)/((x^2 + 3)x)`

`= (Ax^2 + 3A)/(x(x^2 + 3)) + (Bx^2 + Cx)/((x^2 + 3)x)`

`= (Ax^2 + 3A + Bx^2 + Cx)/(x(x^2 + 3))`

`(x - 3)/(x^3 + 3x) =((A + B)x^2 + Cx + 3A)/(x(x^2 + 3))`

`A + B = 0`

`C = 1`

`3A = -3`

`A = -1`

`-1 + B = 0`

`B = 1`

`A + B + C = -1 + 1 + 1 = 1`