Point o is the center of the circle. what is the value of x?

66°

Step-by-step explanation:

Since segments MN and MP are tangent to the circle, then

The sum of the measures of all interior angles of the quadrilateral is equal to 360°, so

The value of x = 66°

Step-by-step explanation:

From the figure we can see that,

PM and MN are the tangent from the point M to the circle with center O

m<PON = 114°

To find the value of x

From the figure we can write,

m<PON + m<PMN = 180°

114 + x = 180

x = 180 - 114 = 66°

Therefore the value of x = 66°

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

answer: 12

step-by-step explanation:

because yes