The factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80] and the factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40]. They share 8 factors [1, 2, 4, 5, 8, 10, 20, 40] making 40 the greatest factor 80 and 40 have in common.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{3 x 5}{9 x 5} \) - \( \frac{4 x 3}{15 x 3} \)

\( \frac{15}{45} \) - \( \frac{12}{45} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{15 - 12}{45} \) = \( \frac{3}{45} \) = \(\frac{1}{15}\)

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 equation for this sequence is:

a_n = a_n-1 + 7

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 7
a₆ = 29 + 7
a₆ = 36

First, solve for \( \left|y - 1\right| \):

\( \left|y - 1\right| \) - 9 = 3
\( \left|y - 1\right| \) = 3 + 9
\( \left|y - 1\right| \) = 12

The value inside the absolute value brackets can be either positive or negative so (y - 1) must equal + 12 or -12 for \( \left|y - 1\right| \) to equal 12:

So, y = -11 or y = 13.