proyaop

Using order of operations "PEMDAS":

We must first do 1 x 8 / 69, this order doesnt matter. 

8/69 cannot be simplified, and 1 x 8 / 69 = 8 / 69.

1 + 8 / 69 = 69/69 + 8 / 69.

That equals to 77/69. This cannot be simplified.

Your answer is 77/69 or approximately 1.116.

AB = BC = CD by the definition of square ( I didn't forget DA ). 

Thus we can use distance formula to calculate length AB, which has length sqrt(34) units, and slope -5/3. Thus CD should also have slope -5/3, and length sqrt(34) units. 

Point D should be on line y = -5x/3 - 4. DA has equation y = 3x/5 + 2.8 (perpendicular).

Thus we can solve for the x coodinate of D, which is obtained by using transitive property:

Point D has coordinates (-3,1)

x = -3

y = 1

u could also use desmos lol 

Can you show a diagram or where the "shaded region" is? I would like a visual please.

Today we can set as day 'n'.

Each week, his vocab doubles, so on the next week the day would be 'n + 7', and his vocab would be 2(30).

For 'x' weeks, the day would be n + 7x. The vocabulary corresponding to that would be 30 * 2x.

You can do the job of writing the function rule.

:D hope it helps

The suplement is "180 - that angle" degrees. Its complement is "90 - that angle" degrees. If "that angle" is "x" degrees, then our equation is: \(180 - x = 6(90 - x)\) Simplifying, we can get:

\(180 - x = 540 - 6x\)

\(5x = 360\)

\(x = 72\)

The measure of an angle who's supplement is 6x its complement is 72 degrees.

Thanks for the initial step Melody.

So for the first line I got 1.2499999744.

Then subtracting from the first line with the second line I got very close guess. Instead of subtracting everything else. I got to 0.6250015744, and I knew rounding to the nearest hundredth would get me 0.63 or 0.62. 

With your strategy, I got 0.62 as the nearest hundredth.

Wow! Thanks melody..

no wonder why i couldnt guess and check, they were all the same!

The answer was 6...

Using synthetic division it says that 1-x^5 / 1-x = 1 + x + x^2 + x^3 + x^4, I don't get this "synthetic division" could someone explain to me how it really works. 

No problem, just remember the fact that whenever you encounter a hard system of equations problem, either use substitution or try factoring the shenanigans before brute forcing the question with guess and check.

Work smart not hard... :D yw

Jurie, even if you didn't get the Tn shenanigans, you could still have looked for a pattern in the equations.

Example:

For T1, you notice that it is 2/5, and for T2, the denominator increases by 2.

The right side of the equation has a number that has a denominator that multiples the left side of the equation's denominator to get the very end term.

2/5 = 1/3 + 1/15.

The 5 * 3 = 15.

This pattern will continue forever. 

You could also generalize this with a variable just like how Alan and melody described it.

The best idea to work with these is to get more practice.