The graph shows the solution to which system of inequalities?

21 ≤ x2 + (y + 6)2 and 84 ≤ (x + 8)2 + y2
21 ≤ x2 + (y + 6)2 and 84 ≥ (x + 8)2 + y2
21 ≥ x2 + (y + 6)2 and 84 ≤ (x + 8)2 + y2
21 ≥ x2 + (y + 6)2 and 84 ≥ (x + 8)2 + y2

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xKelvin xKelvin · Answer 1 · 2022-03-20T00:31:42+01:00

Answer:

D

Step-by-step explanation:

The shaded area is the intersection of the two inner areas of the two circles.

Because the area is inside both circles, the two inequalities must be less than or equal to the equation of the circles.

(If the inequalities are greater than or equal to the equation of the circles, the shaded areas will lie outside the circle.)

Hence, choice D is the correct choice.

It may assist to rewrite the inequalities such that it becomes apparent the equations are indeed less than or equal to the constant:

[tex]\displaystyle x^2 + (y+6)^2 \leq 21 \text{ and } (x+8)^2 + y^2 \leq 84[/tex]