If the tiger has consumed 120 pounds of food in 10 days that's \( \frac{120}{10} \) = 12 pounds of food per day. The tiger needs to consume 168 - 120 = 48 more pounds of food to reach 168 pounds total. At 12 pounds of food per day that's \( \frac{48}{12} \) = 4 more days.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.

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

\( \frac{6 x 3}{3 x 3} \) - \( \frac{4 x 1}{9 x 1} \)

\( \frac{18}{9} \) - \( \frac{4}{9} \)

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

\( \frac{18 - 4}{9} \) = \( \frac{14}{9} \) = 1\(\frac{5}{9}\)

The equation for this sequence is:

a_n = a_n-1 + 3

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
a₆ = 13 + 3
a₆ = 16

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $100
i = 0.02 x $100

No payments were made so the total amount due is the original amount + the accumulated interest:

First, solve for \( \left|z - 2\right| \):

\( \left|z - 2\right| \) + 6 = 3
\( \left|z - 2\right| \) = 3 - 6
\( \left|z - 2\right| \) = -3

The value inside the absolute value brackets can be either positive or negative so (z - 2) must equal - 3 or --3 for \( \left|z - 2\right| \) to equal -3:

So, z = 5 or z = -1.