The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

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 75% the radius (and, consequently, the total area) increases by \( \frac{75\text{%}}{2} \) = 37\(\frac{1}{2}\)%

To divide fractions, invert the second fraction and then multiply:

\( \frac{2}{6} \) ÷ \( \frac{2}{8} \) = \( \frac{2}{6} \) x \( \frac{8}{2} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{6} \) x \( \frac{8}{2} \) = \( \frac{2 x 8}{6 x 2} \) = \( \frac{16}{12} \) = 1\(\frac{1}{3}\)

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 $400
i = 0.07 x $400
i = $28

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

2\( \sqrt{12} \) + 9\( \sqrt{3} \)
2\( \sqrt{4 \times 3} \) + 9\( \sqrt{3} \)
2\( \sqrt{2^2 \times 3} \) + 9\( \sqrt{3} \)
(2)(2)\( \sqrt{3} \) + 9\( \sqrt{3} \)
4\( \sqrt{3} \) + 9\( \sqrt{3} \)

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