There may be more brilliant solution than the following, but here are my thoughts.
We make use of Euclid's algorithm to help us out.
Consider finding the hcf of A=2^(n+x)-1 and B=2^(n)-1.
If we repeated subtract B from A until the difference C is less than B (smaller number), the hcf between A and B is the same as the hcf between B and C.
For example, we would subtract 2^x times B from A, or
C=A-2^xB=2^(n+x)-2^x(2^n-1)=2^(n+x)-2^(n+x)+2^n-1=2^n-1
By the Euclidean algorithm,
hcf(A,B)=hcf(B,C)=hcf(2^n-1,2^x-1)
If n is a multiple of x, then by repetition, we will end up with
hcf(A,B)=hcf(2^x-1,2^x-1)=2^x-1
For the given example, n=100, x=20, so
HCF(2^120-1, 2^100-1)=2^(120-100)-1=2^20-1=1048575
(since n=6x, a multiple of x).
Answer:
8
Step-by-step explanation:
If j represents Jack's age, we have ...
2j +5 = 21
2j = 16 . . . . . . subtract 5
j = 8 . . . . . . . . divide by 2
Jack is 8 years old.
I would say the 15.5 ounce box .
24 (1/3 + 1/8) ->
24/3 + 24/8 ->
8 + 3 = 11
Distribute the 24 to the numerator in each fraction. Simply the fraction (this part is easy because 24 is divisible by both 3 and 8). Then, once you have simplified the numbers, add them.
Answer:
72 inches
Step-by-step explanation:
The total in ratio would be 3 + 4 + 5 = 12
The largest side is the ratio of "5". Now we can setup a proportionality and solve for other sides:
Let smallest side (3) be x and 2nd largest be (4) y. SO,
18 is the smallest side.
Also
2nd largest side is 24
We know largest side is 30
Thus perimeter (sum of 3 sides) = 18 + 24 + 30 = 72 inches
