Step-by-step explanation:
Claim:
it takes n - 1 number of breaks to break the bar into n separate squares for all integers n.
Basic case -> n = 1
The bar is already completely broken into pieces.
Case -> n ≥ 2
Assuming that assertion is true for all rectangular bars with fewer than n squares. Break the bar into two pieces of size k and n - k where 1 ≤ k < n
The bar with k squares requires k − 1 breaks and the bar with n − k squares
requires n − k − 1 breaks.
So the original bar requires 1 + (k−1) + (n−k−1) breaks.
simplifying yields,
1 + k − 1 + n − k − 1
1 - 1 + n - 1
n - 1
Therefore, we proved as we claimed that it takes n - 1 breaks to break the bar into n separate squares.
Answer:
A;.........9 a.m. - Gary; 12 p.m. - Rachel; 3 p.m. - Christopher; 6 p.m. - Hannah
Step-by-step explanation:
12⁷/₁₂ - 5¹⁴/₅
12⁷/₁₂ - 7⁴/₅
12³⁵/₆₀ - 7⁴⁸/₆₀
11⁹⁵/₆₀ - 7⁴⁸/₆₀
4⁴⁷/₆₀
Answer:
y=3÷9
Step-by-step explanation:
2x-9y=11
or,2×7-9y=11
or,14-11=9y
or,3÷9=y
