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Yup! We're adding the 121 to each side, right?

Let's say that y=mx+b, m=slope, b=y-intercept

y=-2x+b
We can solve for b using given coordinates on the line (-2,7)
7=-6*(-2)+b
b=-5
 

Therefore, the equation would be y=-2x-5.

Hope this helped!

Here is a hint to help you out:

We know that a composite polynomial p(x) can be decomposed into two or more polynomials only if there are polynomials w(x) and c(x) for which p(x) = w(c(x)).

If we know that p(x) is nonnegative, what must w(c(x)) be?

Hope this helped!

What formula did you use for part B? I mean the part where you add 5-1? Also, I'm not sure of how to do part A.

That's true. I'm really not sure.

congrats u about 50 hearts away from reaching the top 100 leaderboard!! (:

Sleeping and eating are equally important. 

If you don't sleep enough, you're too tired and can't get through a day with a lot of homework.

If you don't eat enough.... well.... you die.

That wouldn't really make sense tho, bc how would the forum know if someone was sure or not? Just food for thought.

so here's the link to my solution for part B:

https://web2.0calc.com/questions/can-t-solve-this-blame-skyrim

I don't really know why, but the forum keeps flagging my solution to part a for moderation(even when I post it in snippets) so I'll have to wait on that. In the meantime, you could look at how I solved part B(which in my opinion is harder than part A!). Using that, try solving Part A yourself!

I guess it is to check for correct answers? People may not be sure of their answer so yea

:D :D

Congrats on the hearts!

1.  This is a textbook case of a method of counting known colloquially as "stars and bars" or "balls and urns"(I'd recommend you to search it up online). We can think of the 50 votes as 50 balls or stars laid out in a row, divided by 3 "dividers" or bars which separate the balls into 4 separate regions for each candidate, with each region being how many votes a candidate gets. With this, we can think of how many possibles "spaces" you can choose for the dividers to go in. Using stars and bars, we get the equation:

(50+4-1) c (50),  or (53c50). This gives us 53*52*51/3!

This simplifies to:

53*26*17 = 23426 totals

I don't understand how "1,1,8,5,5,5,5 -> 7!/(4!*2!) = 105" is incorperated into this question because it makes 5000. Also, you add 120 and not 210.

2. So as for Part b, it becomes a little trickier. Imagine the problem as the same as the first part, except there are 4 dividers. You might be wondering why there are four dividers, since that produces 5 "regions", but there are only 4 candidates! However, you need the 5th "region" to count for people who abstain(which is a clever trick you can use for problems like this) from voting for a candidate; you could almost think of the people who abstain as people who vote for another candidate. With this knowledge in hand, the problem becomes a lot like the first problem, and with stars and bars, we get:

(50+5-1) c (50) or (54c50). This gives us 54*53*52*51/4!, or 316251 totals

EDIT: Since this post finally got through, my answer to part A was flagged for moderation, but using stars and bars, we can find the answer to both the first and second parts. However, Part B just puts a "spin" on the stars and bars technique as I mention above

I've tried posting answers to this before but the explanations were too long so I'll post it in bits:

1.  This is a textbook case of a method of counting known colloquially as "stars and bars" or "balls and urns"(I'd recommend you to search it up online). We can think of the 50 votes as 50 balls laid out in a row, divided by 3 "dividers" which separate the balls into 4 separate regions for each candidate, with each region being how many votes a candidate gets. Using stars and bars, we get the equation:

(50+4-1) c (50),  or (53c50). This gives us 53*52*51/3!

This simplifies to:

53*26*17 = 23426 totals

Could you please post the link? Thank you so much! I really appreciate it!

Oh i think that would explain it

Did you count the posts for both answers and questions?

(x+y)^2 = 16

x^2+2xy+y^2 = 16

x^2 + y^2 = 22

2xy = -6

xy = -3

y = -3/x

(x - 3/x)^2 = 16

x^2 - 6 + 9/(x)^2 = 16

x^2 + 9 / (x)^2 = 22

Completing the square, we can get:

x^2 + 6 + 9/(x)^2 = 28

This is useful, because it asks us for x-y. Remembering our earlier substitution of y = -3/x:

x - y = x - (-3/x) = x + 3/x

(x+3/x)^2 = 28

(x+3/x) = sqrt(28)

Let's first start off with a knowledge of what "average speed" actually is. Average speed is defined as:

total distance / total time

The distance to the train station is equal to 45 * 4km, which is how far he traveled on the return trip(45 km per hour for 4 hours). That means that the distance for one trip is equal to 180 km. Since we only need total distance / total time, the total distance is equal to the distance of one trip multiplied by 2, which is 180*2 = 360. Then, total time is just 6 hours + 4 hours, which is 10 hours.

360 / (6+4) = 360 / 10 = 36 km/h

I already posted an answer on this and there are previous questions asking this. Not sure if they've gone through moderation though.

Sleep> Food

Well, none of the digits can be 0 because the product is than going to be 0. You can't have more than 2 1's either.

To get started, we turn to the factorization of 10,000. It factors out as 2^4 * 5^4. This means that the only possible combinations of numbers are:

1,2,8,5,5,5,5 -> 7!/4! = 210 ways to arrange this

2,2,4,5,5,5,5 -> 7!/(4!*2!) = 105 ways to arrange this

1,4,4,5,5,5,5 -> 7!/(4!*2!) = 105 ways to arrange this

1,1,8,5,5,5,5 -> 7!/(4!*2!) = 105 wasy to arrange this

So the number of different possible codes is 120+105+105+105 = 435 possible codes.

both are necessary i could not survive one day without doing either without wanting to die