The diameter of a circle has endpoints P(–7, –10) and Q(3, 2).

Step-by-step explanation:

Since we are given the endpoints of the circle, the midpoint between the two endpoints will be the center of the circle. The formula for determining midpoint of a line is

Midpoint = 1/2(x1 + x2), 1/2(y1 + y2)

= 1/2(- 7 + 3), 1/2(- 10 + 2)

= (- 2, - 4)

The radius of the circle is the distance from the center to the endpoint. To determine the radius of the circle, we would apply The formula for determining the distance between two points on a straight line is expressed as

Distance = √(x2 - x1)² + (y2 - y1)²

Therefore,

Radius = √(- 2 - - 7)² + (- 4 - - 10)²

Radius = √5² + 6² = √61

A circle is the set of all points in a plane equidistant from a fixed point called the origin or center.

The center of the circle is (- 6, - 8)

The formula for determining the equation of a circle us expressed as

(x - h)² + (y - k)² = r²

Where

r represents the radius of the circle

h and k represents the x and y coordinates of the center of the circle. Comparing with the given points,

h = - 2 and k = - 4

Radius, r = √61

Substituting into the formula, it becomes

(x - h)² + (y - k)² = r²

(x - - 2)² + (y - - 4)² = √61²

(x + 2)² + (y + 4)² = 61

that is the sum

step-by-step explanation:

there are no other answers without knowing the variables values

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be