If the tiger has consumed 45 pounds of food in 5 days that's \( \frac{45}{5} \) = 9 pounds of food per day. The tiger needs to consume 99 - 45 = 54 more pounds of food to reach 99 pounds total. At 9 pounds of food per day that's \( \frac{54}{9} \) = 6 more days.

The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.

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

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

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:

9x⁷ x 6x³
(9 x 6)x^{(7 + 3)}
54x¹⁰