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 45% the radius (and, consequently, the total area) increases by \( \frac{45\text{%}}{2} \) = 22\(\frac{1}{2}\)%

The factors of a number are all positive integers that divide evenly into the number. The factors of 64 are 1, 2, 4, 8, 16, 32, 64.

If the tiger has consumed 33 pounds of food in 3 days that's \( \frac{33}{3} \) = 11 pounds of food per day. The tiger needs to consume 110 - 33 = 77 more pounds of food to reach 110 pounds total. At 11 pounds of food per day that's \( \frac{77}{11} \) = 7 more days.

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

4\( \sqrt{45} \) + 8\( \sqrt{5} \)
4\( \sqrt{9 \times 5} \) + 8\( \sqrt{5} \)
4\( \sqrt{3^2 \times 5} \) + 8\( \sqrt{5} \)
(4)(3)\( \sqrt{5} \) + 8\( \sqrt{5} \)
12\( \sqrt{5} \) + 8\( \sqrt{5} \)

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

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:

-5z⁷ x 9z³
(-5 x 9)z^{(7 + 3)}
-45z¹⁰