Mathematician

-1000 = 5t(6.73 - t)

First we distribute 5t using the distributitive property:

-1000 = 5t(6.73) + 5t(t)

So we have:

-1000 = 33.65t + 5t

We can then add together the two t's:

-1000 = 38.65t

Now we divide both sides by 38.65 to fully isolate t:

-1000/38.65 = 38.65t/38.65

$${\mathtt{\,-\,}}{\frac{{\mathtt{1\,000}}}{{\mathtt{38.65}}}} = -{\mathtt{25.873\: \!221\: \!216\: \!041\: \!397\: \!2}}$$=t

Yes anon! 10 in base 4.

But in base 10, our counting system, it's 4.

I meant something like this:

      $${\mathtt{0}}$$ $${\mathtt{25}}$$     

$${\mathtt{5}}$$$${\sqrt{{\mathtt{125}}}}$$

    - $${\mathtt{10}}$$ |

       __ ↓

         $${\mathtt{25}}$$

       - $${\mathtt{25}}$$

         ___

          $${\mathtt{0}}$$ $${\mathtt{0}}$$

For explanation of long division, not calculation.

Melody how do you do the long division bracket with Math Formula or LaTeX Formula?

First let me test the rule:

$${\mathtt{\,-\,}}{\mathtt{0.25}}{\mathtt{\,\times\,}}\left(-{\mathtt{4}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{5}} = {\mathtt{6}}$$

$${\mathtt{\,-\,}}{\mathtt{0.25}}{\mathtt{\,\times\,}}\left({\mathtt{4}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{5}} = {\mathtt{4}}$$

$${\mathtt{\,-\,}}{\mathtt{0.25}}{\mathtt{\,\times\,}}\left({\mathtt{8}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{5}} = {\mathtt{3}}$$

$${\mathtt{\,-\,}}{\mathtt{0.25}}{\mathtt{\,\times\,}}\left(-{\mathtt{4}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{5}} = {\mathtt{6}}$$

It looks like Melody is accurate.

If geno3141 is correct, wouldn't it simplify further to y  =  (-1/4)x + 11?

No, not 21.

10

+9

__

19

Or:

1, 2, 3, 4, 5, 6, 7, 8, 9

O O O O O O O O O

+

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

O O O O O O O O O O

=

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19

O O O O O O O O O O  O  O  O  O  O  O  O  O  O

If you think geno's answer is correct, you can "thumbs up" him (top right corner of his comment.)

Thank you, just the word "rate" was confusing.