Which equation describes a circle with center (4,−7) and radius 9? A (x−4)2+(y+7)2=81 B (x+4)2+(y−7)2=81 C (x−4)2+(y+7)2=9 D (x+4)2+(y−7)2=9

A. (x - 4)² + (y + 7)² = 81

Step-by-step explanation:

The general equation for a circle is given by the formula;

x² + y² + 2hx + 2ky + c = 0  equation 1.

Where the center is C(-h, -k)

Also, the standard form of the equation of a circle is;

(x - h)² + (y - k)² = r²  equation 2.

Where;

Given the following data;

h = 4

k = -7

r = 9

Substituting into eqn 2, we have;

(x - 4)² + (y - {-7})² = 9²

Simplifying further, we have;

(x - 4)² + (y + 7)² = 81

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.