First, solve for \( \left|y + 9\right| \):

\( \left|y + 9\right| \) + 5 = 2
\( \left|y + 9\right| \) = 2 - 5
\( \left|y + 9\right| \) = -3

The value inside the absolute value brackets can be either positive or negative so (y + 9) must equal - 3 or --3 for \( \left|y + 9\right| \) to equal -3:

So, y = -6 or y = -12.

If the tiger has consumed 135 pounds of food in 9 days that's \( \frac{135}{9} \) = 15 pounds of food per day. The tiger needs to consume 195 - 135 = 60 more pounds of food to reach 195 pounds total. At 15 pounds of food per day that's \( \frac{60}{15} \) = 4 more days.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{2!}{3!} \)
\( \frac{2 \times 1}{3 \times 2 \times 1} \)
\( \frac{1}{3} \)
\( \frac{1}{3} \)

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.