5 thoughts on “Algebra

  1. When you reverse the digits in a certain two-digit number you decrease it’s value by 45. What is the number if the sum of its digits is 13?

    • Thanks for writing! I would set it up this way: let x be the tens digit and y be the ones digit. Then you have (10y + x) – (10x + y) = 45 (see how the original number is 10x + y ?- put in some numbers to see this), and x + y = 13. Solving these 2 equations gives you x = 4 and y = 9. So the number is 49. Let’s check: 94 – 49 = 45 and 4 + 9 = 13. But it doesn’t really matter if you move the graph to the right 6 before or after doing the y transformations – you’ll get the same result. Does this make sense? Lisa

  2. Hello LisaWithWW
    Could you suggest a way to put these calculations into computer form? With this arithmetic I was able to reduce the original root to a lesser form (?). That is, given the nth root of the square of a^m I could determine m for any a. Is it worth it. I don’t understand why it works.
    ^4sqrt(a^7) = (0) (-4)+ 7=7 =3.36359
    a(^4sqrt(a^3)= (1)(-4)+7=3 =3.36359
    a^3(^4sqrt(a^-4) = (3)(-4)+7= -5 = 3.36359
    a^5(^4sqrt(a^-13)= ((5)(-4)+7= -13 =3.36359
    I just put in a few examples but it works for any combination.
    Thanks in advance

  3. Hello Lisa
    Sorry I made a mistake in the 3rd example:
    Should be a^3 (^4 sqrt a^(-5)) that is (3)(-4) +7 =-5 = 3.36359

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