Answer:
6/9
Step-by-step explanation:
Answer:

Step-by-step explanation:
Given
Points: (1, 9) and (9, 3)
Ratio = 2/3
Required
Determine the coordinate of the center
Represent the ratio as ratio

The new coordinate can be calculated using

Where



Substitute these values in the equation above



Hence;
<em>The coordinates of the new center is </em>
<em></em>

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:
23
Step-by-step explanation:
23 + 24 + 25 = 72