Question

review the graph. which system of inequalities is shown in the graph? 36 > (x + 3)^2+(y - 2)^2 and 16 > (x - 4)^2+y^2 36 > (x - 2)^2+(y + 3)^2 and 16 > (x - 4)^2+y^2 36 < (x + 3)^2+(y - 2)^2 and 16 > (x - 4)^2+y^2 36 < (x - 2)^2+(y + 3)^2 and 16 > (x - 4)^2+y^2

Explanation:

Step1: Recall circle - inequality form

The equation of a circle with center \((h,k)\) and radius \(r\) is \((x - h)^2+(y - k)^2=r^2\). The inequality \((x - h)^2+(y - k)^2<r^2\) represents the interior of the circle, and \((x - h)^2+(y - k)^2>r^2\) represents the exterior of the circle.

Step2: Identify the first circle

The first circle has a center at \((- 3,2)\) and a radius \(r_1 = 6\) (since \(r_1^2=36\)). The shaded - region is inside this circle, so the inequality is \(36>(x + 3)^2+(y - 2)^2\).

Step3: Identify the second circle

The second circle has a center at \((4,0)\) and a radius \(r_2 = 4\) (since \(r_2^2 = 16\)). The shaded - region is inside this circle, so the inequality is \(16>(x - 4)^2+y^2\).

Answer:

\(36>(x + 3)^2+(y - 2)^2\) and \(16>(x - 4)^2+y^2\)