If figure x is inscribed in figure y, which statement must be true? . a. figures x and y are congruent. b. figures x and y are polygons. c. figure x is circumscribed about figure y.. d. figure y is circumscribed about figure x.. give me the best answer.

 The correct option is

(D) Figure Y is circumscribed about figure X.

Step-by-step explanation:  Given that a figure X is inscribed in figure Y.

We are to select the statement that must be TRUE.

We know that

if a figure X is inscribed in a figure Y, then the figure X must be smaller than figure Y.

So, the figures X and Y will not be congruent to each other and thus option (A) is incorrect.

Since a circle can be inscribed in another circle and a circle is not a polygon. So, option (B) is incorrect.

If a figure lies lies inside another figure, then the outer figure is said to be circumscribed about the inner figure.

So, figure Y is circumscribed about figure X.

Therefore, option (C) is incorrect and option (D) is CORRECT.

Thus, (D) is the correct option.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for