shad0w

Method: Start by checking the different values, until you hit a pattern!

I'll just show it to you, the pattern repeats every four

i^1 = i

i^2 = -1

i^3 = -i    because (-1*i)

i^4 = 1 because (-1*-1)

And after this it repeats as x * 1 = x

for the negatives,

i^-1 = -i

i^-2 = -1

i^-3 = i

i^-4 = 1

this repeats for the same reason.

I could let you finish the problem from here but this is webcalc you're here for the answers :)

Diff values:
1: i + -i = 0

2: -1 + -1 = -2

3: -i + i = 0 (again)

4: 1 + 1 = 2 (my favorite expression of all time :D )

the total answers aare 0 -2 and 2, so your answer is : 3

just multiply it out, 4*(x+3)*2 or 8(x+3) is 8x + 24, and then plus 5 so the final answer is 8x + 29

edit: Accidentally wrote (x+2) isntead of (x+3) which screwed up the answer

You didn't specify if each girl/boy is uinique, or not, so I will do the nonunique verison, and you can just use factorials to finish it off.

Since all 5 girls have to stand together, just count them as 1 girl, so 1 girl and 5 boys, and the girl cannot be at one end. Its pretty easy to just brute force it

BGBBBBB

BBGBBBB

BBBGBBB

BBBBGBB

BBBBBGB

so 5 different ways they can stand if the individual boys and girls do not matter, however if they do, you can order the boys 6! ways, and the girls 5! ways, so 6!5! or 86400 times 5 or 432000.

It seems like alot, but if you didnt care about the way either sat, that would be 11! or 39916800 ways.

rearranging the second equation, you get x = 2 + y, so we can substitute this into the first equation.

Its actually more useful to rearrange the second one into - y = 2 - x, or y = x - 2, so we dont have to use FOIL

Plugging this into the first equation, its x - 2 = 4 - x^2, adding 2 to both sides, x = 6 - x^2. At this point, we can just kinda bash it out, (bad strategy but in competition its easier to do this than actually go through each problem but hopefully somone else explains going the full route), but testing values, 2, is immediatly the answer. 2 = 6 - 4 which is true, so x = 2. Just looking at the other two answers, -4 doesnt work, but -3 does, -3 = 6 - 9, so the answer is D.

Again, this is a more competition style way to quickly observe the answer instead of hashing the full thing out, and instead just bashing it.