a)points d, e, and f are not in a line. to construct a circle through points d, e, and f, begin by drawing line segments and . then construct the perpendicular bisectors of and , and name the point of intersection of the perpendicular bisectors o. how do you know that point o is the center of the circle that passes through the three points

O is the center of the Circle

Step-by-step explanation:

Please see that , in order to draw a circumcircle we have to first draw the perpendicular bisectors of the sides. The point at which these perpendicular bisectors meet is called circumcenter and the it is the center of circumcircle passes through three vertices D, E and F.

This is because, When we draw the circle from these vertices, we can see that the three sides forms that three chords of the circle. And circle has a property that , the perpendicular bisectors of chords always passes through the center.  And here o is the point through which all the perpendicular bisectors of all three chords are passing through. Hence 0 is the center

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !