(Hard) A composite number n is called a Carmichael number bn−1 ≡ 1 (mod n) for every number b such ... Base case: When n = 2 the formula a + c ≡ b + d (mod m) was already given. ... The sequence goes 1, 3, 7, 15, 31,... guess that it is equal to 2n+1 − 1. ... Prove (now using induction on n) that fm|fmn for all n ≥ 1.


if we were to place <5, 12> in standard position, so it'd be originating from 0,0, then the rise is 12 and the run is 5.
so any other vector that has a negative reciprocal slope to it, will then be perpendicular or "orthogonal" to it.
so... for example a parallel to <-12, 5> is say hmmm < -144, 60>, if you simplify that fraction, you'd end up with <-12, 5>, since all we did was multiply both coordinates by 12.
or using a unit vector for those above, then
Answer:
The graph of the parent function f(x) = |x| is dashed and the graph of the transformed function g(x) = |x| + k is solid. Use the slider to change the value of k. How does changing the value of k affect the graph? Positive values of k shift the graph . Negative values of k shift the graph .
I think Its 66 cm. Hope This Helped! Good Luck...