Let's put this in terms of a system of equations. Let's call the numbers x and y, with x being the larger integer and y the smaller one. Since they are consecutive odd integers, we know that:
x = y + 2
The constraint is:
xy= 3(x+y) + 71 Simplify
xy = 3x + 3y + 71 Plug in (y+2) for x:
(y + 2) y = 3(y + 2) + 3y + 71 Simplify
y² + 2y = 3y + 6 + 3y + 71 Subtract 6y from both sides, add 71+6
y² -4y = 77
y² - 4y - 77 = 0
Factor:
(y - 11) (y+7) = 0
y = 11 or y=-7
When y = 11, x = 13, since x = y+2
Plug in to make sure:
xy = 3(x+y) + 71
11*13 = 3 (11 + 13) + 71
143 = 3 (24) + 71
143 = 72 + 71
143 = 143
Our values work!
Answer: 11, 13
All real numbers are solutions, let me know if you need an explanation luv
1a= (2x+5)+3x+15
1b= (2(4)+5)+3(4)+15=40
2a= (3x+5)•(4x-3)
2b= (3(2)+5)•(4(2)-3)=55
2c= 2(x) or 2(2)
How I got 2c is the perimeter of the rectangle LMNP subtract from (2(2)+9)+(2(2)+9)=26 which in return means you subtract 30 from 26 and get 4 which is 2(2) or 2x
Combine like terms
-6x^2+2y + -1 +2x^2 + -5y +3
( -6x^2+2x^2)+(2y-5y)+(-1+3)
= -4x^2+3y+2
Answer : C
I hope that's help !
