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 40% the radius (and, consequently, the total area) increases by \( \frac{40\text{%}}{2} \) = 20%

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

2 + (4 + 2) ÷ 2 x 4 - 5²
P: 2 + (6) ÷ 2 x 4 - 5²
E: 2 + 6 ÷ 2 x 4 - 25
MD: 2 + \( \frac{6}{2} \) x 4 - 25
MD: 2 + \( \frac{24}{2} \) - 25
AS: \( \frac{4}{2} \) + \( \frac{24}{2} \) - 25
AS: \( \frac{28}{2} \) - 25
AS: \( \frac{28 - 50}{2} \)
\( \frac{-22}{2} \)
-11

To multiply terms with radicals, multiply the coefficients and radicands separately:

7\( \sqrt{8} \) x 5\( \sqrt{2} \)
(7 x 5)\( \sqrt{8 \times 2} \)
35\( \sqrt{16} \)

Now we need to simplify the radical:

35\( \sqrt{16} \)
35\( \sqrt{4^2} \)
(35)(4)
140

The factors of a number are all positive integers that divide evenly into the number. The factors of 28 are 1, 2, 4, 7, 14, 28.