Answer: the value of x is 10.5.
Step-by-step explanation:The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the coordinates [(x1 + x2)/2, (y1 + y2)/2].
In this case, the endpoints of the diameter of the circle are (6, 8) and (15, 8), so the midpoint of the diameter is [(6 + 15)/2, (8 + 8)/2] = (10.5, 8).
Since the midpoint of the diameter is the center of the circle, the coordinates of the center of the circle are (10.5, 8).
Therefore, the value of x is 10.5.
I hope this helps! Let me know if you have any further questions.