Slope is 5
Y intersect is 0
Y= 5x

The rows add up to

, respectively. (Notice they're all powers of 2)
The sum of the numbers in row

is

.
The last problem can be solved with the binomial theorem, but I'll assume you don't take that for granted. You can prove this claim by induction. When

,

so the base case holds. Assume the claim holds for

, so that

Use this to show that it holds for

.



Notice that






So you can write the expansion for

as

and since

, you have

and so the claim holds for

, thus proving the claim overall that

Setting

gives

which agrees with the result obtained for part (c).
Answer:
18 Minutes
Step-by-step explanation:
Simon and sophie each do a fraction of the job per minute like this:
-Simon does
per minute (if we multiply this by 30 we have the completed job)
-Sophie does
of the job per minute (again if we multiply this by 45 we have the completed job)
We will add this two to know how much of the job they do together in a minute:

They will do
of the job per minute.
So the total time will be when they do
, we can put this in one equation like this:

where x is the total times we need to do
of the job to complete it. We solve for x:
