Final answer:
The expression that represents the radius of the circle given the equation A = π(x^2 - 22x + 121) is r = x - 11.
Step-by-step explanation:
To determine the expression for the radius of the circle given the equation of its area, A = π(x^2 - 22x + 121), we need to compare this to the standard formula for the area of a circle, which is A = πr^2, where r represents the radius. In the given equation, the part within the parentheses, x^2 - 22x + 121, can be factored into (x - 11)^2, since 121 is the square of 11 and -22 is twice the product of 11 and x. Therefore, the expression in parentheses represents the square of the radius. Thus, the radius r is given by the square root of this expression, resulting in r = x - 11.