<span>Given:
AB = x + 16
BC = 4x + 11
AC= 77
We can safely assume that,
AB + BC = AC
x + 16 + 4x + 11 = 77
5x + 27 = 77
5x = 77 - 27
5x = 50
x = </span>

x = 10
Hence,
AB = x + 16 = 10 + 16 = 26
Hence, proved.
You have a lot of questions here, I can help you with a few of them.
When you simplify the polynomials, you put together all of the terms that have the same degree. That means the variables have the same exponents. The number of terms are the items separated by plus and minus signs.
Here are the answers for the first three:
1)

2)

3)
Answer:9 nickels and 19 dimes.
Step-by-step explanation:
Let
be the number of nickels Kay has.
Let
be the number of dimes Kay has.
Value of
nickel is $
Value of
nickels is $
Value of
dime is $
Value of
nickels is $
Given that Kay has a total of
coins.
So,
...(i)
Given that Kay has a total value of $
So,
...(ii)
Using (i) and (ii),


EQUATION: 5x = 2x - 9
Add 9 to both sides
NEW EQUATION: 5x + 9 = 2x
Subtact 5x from both sides:
NEW EQUATION: 9 = -3x
Divide -x on bith sides
NEW EQUATION: -3 = x, or x=-3