Firebolt

P is going to meet A and B at their midpoint, which is (27/2, 3/2). 2x - 4y = 27 - 3*2 = 21. 

A - 470 Y, 480 O
B - 350 Y, 200 O

So let's say after transferring the M&M's, box B has b yellow ones. That means box B also has 4b orange ones (because 0.8 = 4 times of 0.2). Meanwhile, box A will have a yellow M&M's and 2a/3 orange ones.  

We have 820 yellow ones total and 680 orange ones total. 

a + b = 820 
2/3*a + 4b = 680 

We can multiply the first equation by 4 to get 4a + 4b = 3280. Now subtract the second equation from this, and we find that 10/3*a = 2600. So a = 780. 

So box A now has 780 yellow ones and 520 orange ones. 

Subtracting, we find that 310 yellow M&M's and 40 orange M&M's were moved. 

First you can subtract the parts Mr. Rand cut off which is $18 - 1\frac{15}{16} - 3\frac{1}{8} - 4\frac{1}{2} = 8\frac{7}{16}$ pounds left because 16 ounces make up a pound. After dividing it by $\frac{9}{16}$ we get $\frac{135}{16} \div \frac{9}{16} = \frac{135}{16} \times \frac{16}{9} = 15$ patties. Dividing 15 by 3 we get 5 packs of 3 patties for $3.12, so $3.12 \times 5 = \boxed{\$15.60}$

Area = pi*r^2

254.34 = pi*r^2

254.34 = 3.14*r^2

81 = r^2

r = 9

So, the diameter = 2r, so the diameter = 18.

You can split this into smaller parts and calculate the area, or use the Shoelace Theorem. Since I can't demonstrate splitting the shape here, I can use the shoelace theorem. 

Either way will give you 87/2 .

(3 + 5^2 -8)4

I'm assuming you mean $(3 + 5^2 -8)^4$, but I'll solve it both ways.

$(3 + 5^2 -8)^4 = (3+25-8)^4 = 20^4 = 160,000$

Or, if you meant $4(3 + 5^2 -8)$, then $4(3 + 5^2 -8) = 4(3 + 25 -8) = 4(20) = 80$

I hope this helped. :)

By the way, I found a helpful link - this might be helpful. It uses the same method I used but it explains it better than I did.

https://math.stackexchange.com/questions/1873138/distribution-of-4-distinct-balls-into-5-identical-boxes-without-any-restrictions#:~:text=There%20are%202%20ways%20to,6%C3%972%3D12%20cases.

Assuming order matters:

There are 5 cases, {4}, {3,1}, {2, 2}, {2, 1, 1}, and {1, 1, 1, 1}.

{4} - 4! which is 24

{3, 1} - 4 x 3! - 24 (4 ways to pick the single one and 3! ways to rearrange the others)

{2, 2} - 6 x 2 = 12 (6 ways to choose the pairs, and two ways to order the pairs)

{2, 1, 1} - 12 (6 ways to choose the pair and two ways to order it)

{1, 1, 1, 1} - 1 (just one way to order it)

24+24+12+12+1 = 73.

I hope this helped.

Yeah, same . . . I can't give thumbs-ups, the latex box isn't working, and it's very glitchy when you're trying to post a new question or answer. I hope they fix this bug soon.

If $x^2$ is less than 500, then X is at most 22 and at least -22. There are 6 numbers: -21, -14, -7, 7, 14, 21.

I hope this helped.

Angle WVT is equal to 14x+7 minus 7x+11, so 3x+4 = 7x-4

3x+4=7x-4

4x=8

x=2

Plugging x=2 back into Angle WVT, then Angle WVT equals 10 degrees.

5+30 is 35, and half of 35 is 17.5. So 2x+10 = 17.5, 2x = 7.5, so x = 15/4

However, if there is a typo and it says 5x+30, then:

2(2x+10) = 5x+30

4x+20 = 5x+30

0 = x+10

x = -10

I hope this helped.

https://web2.0calc.com/questions/find-the-number-of-ordered-pairs-a-b-of-real-numbers

I already found the answer, thanks!

Using the Pythagorean Theorem, CD = 2.4. We notice that $\bigtriangleup$ABC is similar to $\bigtriangleup$ACD (this is a 3-4-5 right triangle). Since AC is the shorter side, it is 3, BC is 4, and AB is 5, so the area of a 3-4-5 triangle is 3x4/2 which is 6.

We can check if BD is 3.2.

$2.4/x = 3/4$ so BD = 3.2. 

So all of our work adds up; the area of $\bigtriangleup$ABC is 6.

I think the answer should be 6.

In every three consecutive integers, one of them must be a multiple of three. And there must be at least one multiple of two as well. So 3 x 2 = 6.

I hope this helped.

Thanks, all of you, it really helped.

And the answer is 16.

If you graph these coordinates, you will find it is a 5 x 6 rectangle. Thus the area is 30.