If the tiger has consumed 30 pounds of food in 6 days that's \( \frac{30}{6} \) = 5 pounds of food per day. The tiger needs to consume 45 - 30 = 15 more pounds of food to reach 45 pounds total. At 5 pounds of food per day that's \( \frac{15}{5} \) = 3 more days.

The equation for this sequence is:

a_n = a_n-1 + 3(n - 1)

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 + 3(6 - 1)
a₆ = 31 + 3(5)
a₆ = 46

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

\( \frac{7y^8}{4y^3} \)
\( \frac{7}{4} \) y^{(8 - 3)}
1\(\frac{3}{4}\)y⁵

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 share.

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

\( \frac{4 x 4}{2 x 4} \) + \( \frac{9 x 1}{8 x 1} \)

\( \frac{16}{8} \) + \( \frac{9}{8} \)

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

\( \frac{16 + 9}{8} \) = \( \frac{25}{8} \) = 3\(\frac{1}{8}\)

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.