Cubing both sides of an equation is a reversible process. Detailed explanation: Squaring both sides isn't reversible because squaring a negative number produces a positive result, thus making it impossible to retrieve the original negative base, as square roots of negative numbers do not exist within real numbers. In contrast, cubic powers allow for reversibility; the cubic root of a negative number remains negative. For example, if we cube both sides and wish to revert to the original equation, we can do so using the cubic root on each side. Hence, cubing both sides is reversible.
Answer with explanation: Given that Circle 1 has a center at (−4, −7) and a radius of 12 cm, while Circle 2's center is at (3, 4) with a radius of 15 cm. Two circles are similar if one can be transformed and scaled to fit over the other, creating identical circles. The circles qualify as similar because the transformation rule (x,y) → (x+7,y+11) can be applied to Circle 1, followed by dilation using a scale factor of 5/4. Since Circle 1's center is at (-4,-7), we translate it to (3,4) through (-4+7,-7+11). With Circle 1 having a radius of 12 and Circle 2 having 15 cm, we denote the scale factor as k.
