Well I'm still trying to solve the first question so I'll tell you the other answers
the answer for the second question is :

and for the third question :
Answer:
80=x+y
Step-by-step explanation:
The maximum amount of glasses is 80; the solution cannot be more than 80; the number of glasses of lemonade and of iced tea cannot be more than 80 total.
Answer:
option 1) 50
Step-by-step explanation:
Let m and w denote the men and women respectively.
From the question, if the groom invited w number of women, then bride invited 2w number of women.
Also, if the bride invited m number of men,then the groom invited 2m.
Hence we can write the following maths equation:
w+2m=105.........1
2w+m=135.........2
We multiply eqn(1) by 2 to get eqn(3)
This implies that,
2w+4m=210.......3
We then subtract eqn (2) from eqn(3) to obtain;
3m=75
we divide through by 3


Substituting the value of m into eqn (1)
to find the value for w

subtracting 50 from both sides.



So we can say the :
bride invited 25 men and 110 women,
groom invited 50 men and 55 women.
Step-by-step explanation:

The binomial theorem states that for some a,b∈R and some k ∈Z+ ,
(a+b)k=∑n=0k(kn)ak−nbn.
The binomial series allows us to use the binomial theorem for instances when k is not a positive integer. The binomial series applies to a given function f(x)=(1+x)k for any k∈R with the condition that |x|<1 . It is stated as follows:
(1+x)k=∑n=0∞(kn)xn .
Note that the binomial theorem produces a finite sum and the binomial series produces an infinite sum.
I've graphed it for you below.