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.

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

7\( \sqrt{112} \) + 7\( \sqrt{7} \)
7\( \sqrt{16 \times 7} \) + 7\( \sqrt{7} \)
7\( \sqrt{4^2 \times 7} \) + 7\( \sqrt{7} \)
(7)(4)\( \sqrt{7} \) + 7\( \sqrt{7} \)
28\( \sqrt{7} \) + 7\( \sqrt{7} \)

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

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-9c² + 1c²
(-9 + 1)c²
-8c²

The equation for this sequence is:

a_n = a_n-1 + 2

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 + 2
a₆ = 9 + 2
a₆ = 11

Diane scored 83% on the test meaning she earned 83% of the possible points on the test. There were 160 possible points on the test so she earned 160 x 0.83 = 132 points. Each question is worth 4 points so she got \( \frac{132}{4} \) = 33 questions right.