Final answer:
The ratio of the areas of two circles with a scale factor of 2x/5y is 4x^2/25y^2, which is the scale factor squared.
Step-by-step explanation:
When comparing the areas of two similar shapes, such as circles, the ratio of their areas is the square of the scale factor. If the scale factor between two circles is 2x/5y, to find the ratio of their areas, we'll need to square that scale factor.
The ratio of the areas of the two circles would be:
(2x/5y)2 = (2x)2/(5y)2 = 4x2/25y2
This means that the area of the larger circle is 4x2/25y2 times the area of the smaller circle.