Which graph represents the inequality y> 3−x?

B

Step-by-step explanation:

The first step is to draw the line y = 3 - x to see what the line itself looks like. Is it going from left to right as in A and C is going up as you go  from right to left as in B and D? The graph on the left (below) gives you the answer. It is going up as you progress from right to left.

The next step is to answer which is it: B or D.

y has to be above the line. it is B. See the graph below on the right.

The sum of the first 47 terms of the series, 12, 16, 20, ... S₄₈ is 4,888

Step-by-step explanation:

The given series is;

12, 16, 20, ...,

Therefore, the first term of the series is, a = 12

The common difference of series is found as follows;

The difference between subsequent terms, 12 and 16 is  16 - 12 = 4

The difference between subsequent terms, 16, and 20 is  20 - 16 = 4

Therefore, the common difference, d = 4

The series is therefore an arithmetic projection, AP

The sum of the first 'n' terms of an AP, Sₙ, is given as follows;

(47/2)*(2*12+(47-1)*4)

The sum of the first 47 terms is therefore given as follows;

The sum of the first 47 terms of the series, 12, 16, 20, ... S₄₈ = 4,888