Please help me this question

(b) or (d)

Step-by-step explanation:

stidents who play basketball = 4y^2 + y - 8 - (2y + 16) = 4y^2 - y - 24

This is a question on forming and solving equations and expressions. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)

 Choice (b) 4y^2 - y - 24;  top right corner

Work Shown:

T = total number of students in the class

T = 4y^2 + y - 8

F = number of students who play football

F = 2y+16

B = number of students who play basketball

B = unknown for now

Since a student either plays football or basketball, but not both, this means

T = F+B

which rearranges to

B = T-F

Plug in the given expressions and simplify

B = T-F

B = (4y^2+y-8) - (2y+16)

B = 4y^2+y-8 - 2y - 16

B = 4y^2 + (y-2y) + (-8-16)

B = 4y^2 - y - 24

We can write equations, using x and y as the length and width:

xy=40
2x+2y=26

Divide the second equation by two to get:
xy=40
x+y=13

Thus, x=13-y.

We now have (13-x)x=40, so

and 

Factoring, we get:
(x-5)(x-8)=0

So, x can be either 5 or 8 (and y will be the other option).  Thus, the length and width are 8 and 5.