Prove the divisibility of the following numbers: 51^7−51^6 by 25

Step-by-step explanation:

51^7 - 51^6  =                            => as 51^7 = 51^6 * 51

51^6*51 - 51^6 =                      => factor 51^6 form each terms

51^6(51 - 1)      =                       => as 51 -1 - 50

51^6* 50          =                      => as 50 - 2 * 25

51^6 ( 25*2)

so the original expression is divisible by 25

Step-by-step explanation:

51^6(51-1)

51^6(50)

odd number × even number = even number

50 Is divisible by 25

from the figure we get,

the x axis shows   the months and,

the y-axis shows the number of satisfied customer.

each line or each cell in upward direction (y-axis) shows 500.

the appropriate scale for the y - axis is: -

a = 2000 customers

b = 4000 customers

c = 6000 customers

d = 8000 customers

e = 10000 customers

f = 12000 customers

g = 14000 customers

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)