Assume a is not divisible by 10. (otherwise the problem is trivial).
<span>Define R(m) to be the remainder of a^m when divided by 10. </span>
<span>R can take on one of 9 possible values, namely, 1,2,...,9. </span>
<span>Now, consider R(1),R(2),......R(10). At least 2 of them must have the sames value (by the Pigeonhole Principle), say R(i) = R(j) ( j>i ) </span>
<span>Then, a^j - a^i is divisible by 10.</span>
Answer:
13.25
Step-by-step explanation:
|x + 11| = 8
x + 11 = 8
<u> -11 -11</u>
x = -3
|3x - 2| = 16
3x + 2 = 16
<u> -2 -2</u>
<u>3x</u> = <u>14</u>
3 3
x = 4 2/3
Answer:
I can't seem to get the correct answer . I set it up as x (2x-7)=64, 2x^2-7x-64=0, (2x )(x ). And that's where I am stuck. Please help!
Step-by-step explanation:
the length of a rectangle is 7 inches less than twice its width. if the perimeter of the rectangle is 64 inches, find the dimensions of the rectangle.
Answer:
3/4
Step-by-step explanation:
First find the number that are not seniors
80 -20 = 60
60 are not seniors
The ratio of not seniors to total
60/80
Divide top and bottom by 20
3/4