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I FIGURED IT OUT. Turns out I misread the question; it's basically just asking for me to plug in 2 for the tangent equation so that I have multiple points to write a coherent equation with down the line. :|

Hint:    x = 28 / (3 + 5 + 6) 

The remainder theorem tells us that:

If a polynomial f(x) is divided by (x-a), then the remainder is f(a).

So for this problem, the polynomial is divided by (x-1), (x+1), and (x+2) and the remainders are given.

Therefore, we can conclude that

f(1) = 13

f(-1) = 3

f(-2) = -12

You can now plug in those x values and y values to solve for a, b, and c.

\(x^4+ax^3+bx+c\\ 1^4+a(1)^3+b(1)+c=13\implies a+b+c=12\\ (-1)^4+a(-1)^3+b(-1)+c=3\implies -a-b+c=2\\ (-2)^4+a(-2)^3+b(-2)+c=-12\implies -8a-2b+c=-28\)

We now have a system of three equations.

Now to find a, b, and c.

We can first add the first two equations together

\(a+b+c=12\\ -a-b+c=2\\ ==========\\ 2c=14\\ c=7 \)

We can then multiply the 2nd equation by -2 and add it with the 3rd equation

\(\underset{\downarrow}{-2(-a-b+c)=-2(2)}\\ 2a+2b-2c=-4\\ -8a-2b+c=-28\\ ============\\ -6a-c=-32\\ -6a-7=-32\\ -6a=-25\\ a=\frac{25}{6} \)

Now, we can plug in a and c into any other equation to find b.

\(a+b+c=12\\ \frac{25}{6}+b+7=12\\ \frac{25}{6}+b=5\\ b=\frac{5}{6}\)

TL;DR

a = 25/6, b = 5/6, c = 7

can you elaborated on that more?

Using the tangent line, f(2) = 1/2.

XU = 4        UV = 6        VY = 8

~~~~~~~~~~~~~~~~~~~~~~~

XV * VY = GV * VH = 80

~~~~~~~~~~~~~~~~~~~~~~~

XU * UY = EU * UF = 56

~~~~~~~~~~~~~~~~~~~~~~~

XY = 18 units  

Each tick marks 60 units.

Samantha traveled two ticks to the right.

2 * 60 units = 120 units

Ryu traveled 8 ticks to the left.

(Negative values represent the distance traveled west, in this case to the left.)

-8 * 60 units = -480 units

Now there are two ways you can find the distance between them.

1) You can subtract their positions.

120 - (-480) = 120 + 480 = 600 units

2) Draw a picture.

As you can see from drawing the picture, the distance between them can be found by doing 480 + 120 = 600 units

There are 33 values of n that work.

 N=2*4; R=0.055/4;PV=5000; FV=PV*(1 + R)^N; print"FV =$",FV

FV =$5,577.21 =~$5,577

Thank you! Is there any faster way to do this?

There are 36 ways to color the diagonals.

There are 5 functions that work.

Not sure if this is what you wanted:

12345 , 12354 , 12435 , 12453 , 12534 , 12543 , 13245 , 13254 , 13425 , 13452 , 13524 , 13542 , 14235 , 14253 , 14325 , 14352 , 14523 , 14532 , 15234 , 15243 , 15324 , 15342 , 15423 , 15432 , 21345 , 21354 , 21435 , 21453 , 21534 , 21543 , 23145 , 23154 , 23415 , 23451 , 23514 , 23541 , 24135 , 24153 , 24315 , 24351 , 24513 , 24531 , 25134 , 25143 , 25314 , 25341 , 25413 , 25431 , 31245 , 31254 [This is the 50th integer in the list]

Thanks!!!!

I got 11=20+-9 and it was incorrect

The Question is:

Y=AX     Make X the subject

Divide both sides by A

X = Y / A      Now, X is the subject!.

Listfor(n, 1, 50, n % 5 == 2)

2  7  12  17  22  27  32  37  42  47 >>Total = 10 Blue Tiles.

Therefore, probability is: 10 / 50 = 1 / 5

1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1  4  1  2  1 >> These are the GCD's of [4T_n, n-1] for the first 100 triangular numbers. As you can see, 4 is the greatest GCD.

That's cheating :)