Which of the following demonstrates how the first 21 (on the left side of the triangle) is calculated using the combination pattern?
1
(
1
1
1
2
1
1
3
3
1
1
4
6
4
1
1 5 10 10 5 1
16 15 20 15 6 1
1 7 21 35 35 21 7 1
OA
71
- 21
(7-2)121
o
B.
2162
211
- 21
(21-2)121
-~-
---
-C)
-(1)-
Ос.
216
211
(21-7)171
-21
D
71
- 21
(7-7)17!

option: d is the correct answer.

d) none of the above.

step-by-step explanation:

clearly from the figure attached to the question we could see that there is no shape given. hence without any shape given in the figure and after rotation we can't obtained a square pyramid.

since, to obtain a image we need a proper figure of the pre-image so that it can be transformed.

hence, the correct answer is:

d) none of the above.

step-by-step explanation:

1 + (6 / x - 1)

step-by-step explanation:

divide using polynomial division.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt