Henry needs to give an informal proof of the formula for the circumference of a circle. • He first constructs a Circle, with center o, and Labels as a point on the Circle P.
• He draws a Radius from 0 to P.
• He then uses point P as the center to construct a new circle.
• He draws two line segments, each formed by joining point o with the points of intersection of the two circles.
Which of these is a plausible next step in Henry's proof process?
A.
Construct another circle with a doubled radius.
B.
C.
Construct a rectangle that circumscribes the original circle.
Construct an octagon that circumscribes the original circle.
Construct a hexagon inscribed in the original circle.
D.

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