Question

This is legit due today and I’m nervous that I won’t get done in time. Please help. God bless you.

Answer 1

6.

Josef receives 3$ per hour spent doing chores. So, after x hours of chores, he receives 3x dollars. This money must be added to the 10$ he would receive no matter what, so the total expression is

$m = 10+3x$

7.

We can test the options against the given patterns: in pattern 1, we have one black hexagon and 6 white hexagons. Let's see which equations fit: if we substitute b=1 and w=6 we have:

A) $6 = 6\cdot 1$ - ok

B) $6 = 3\cdot 1 +2$ - wrong

C) $6 = 2\cdot 1 +4$ - ok

D) $6 = 6\cdot 1 + 2$ - wrong

E) $6 = 2\cdot 1 + 3$ - wrong

So, the only feasible answers are A or C, because all the other functions don't fit even the first pattern. Let's test the two survivors for pattern 2: we have two black hexagons and 8 white hexagons. Plugging b=2 and w=8 into A and C we have

A) $8 = 6\cdot 2$ - wrong

C) $8 = 2\cdot 2 +4$ - ok

So, the answer is C, because it models correctly pattern 2 as well. For the sake of completeness, let's test this function against pattern 3 as well: we have 3 black and 10 white hexagons. Plugging b=3 and w=10 into C we have

C) $10 = 2\cdot 3 +4$ - ok

So, C models correctly all patterns, and thus describe the general rule.