The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

6y⁷ x 6y⁶
(6 x 6)y^{(7 + 6)}
36y¹³

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 60% the radius (and, consequently, the total area) increases by \( \frac{60\text{%}}{2} \) = 30%

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $1,000
i = 0.09 x $1,000
i = $90

To add these radicals together their radicands must be the same:

3\( \sqrt{125} \) + 2\( \sqrt{5} \)
3\( \sqrt{25 \times 5} \) + 2\( \sqrt{5} \)
3\( \sqrt{5^2 \times 5} \) + 2\( \sqrt{5} \)
(3)(5)\( \sqrt{5} \) + 2\( \sqrt{5} \)
15\( \sqrt{5} \) + 2\( \sqrt{5} \)

Now that the radicands are identical, you can add them together: