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bogdanovich [222]
3 years ago
5

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Mathematics
1 answer:
makvit [3.9K]3 years ago
4 0
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Prove the 'rule of 9': an integer is divisible by 9 if and only if the sum of its integers is divisible by 9.
patriot [66]

Answer:

Rule of 9 : an integer is divisible by 9 if and only if the sum of its integers is divisible by 9.

Proof :

Let us consider a number x such that,

a=a_n......a_3a_2a_2

Where, a_0, a_1, a_2......,a_n are the the digits of the number x,

So, we can write,

x=a_0+a_1\times 10 + a_2\times 10^2 +a_3\times 10^3..........a_n\times 10^n

Let,

S=a_0+a_1+a_2+a_3+.......a_n

x-S=a_1(10-1)+a_2(10^2-1)+a_3(10^3-1)+.......a_n(10^n-1)

Since, a number is in the form of 10^k-1, where k is an positive integer, is always divisible by 9,

⇒ a_1(10-1), a_2(10^2-1), a_3(10^3-1),.......a_n(10^n-1) are divisible by 9.

⇒ x-S is divisible by 9,

⇒ If S is divisible by 9 ⇒ x must divisible by 9,

Or if x is divisible by 9 ⇒ S must divisible by 9.

Hence, proved...

7 0
3 years ago
Nevermind. I figured it out the problem out
devlian [24]
Which problem I don’t see any problem hear
5 0
4 years ago
If a cylinder has a surface area of 59 square inches and its radius is 2.1 inches, how tall is the cylinder in inches? Round to
Romashka [77]
Hey ok, let me work this problem out, could u give me the formal?
i cant find the notes so i need the formal.

5 0
3 years ago
What is one exterior angle in a 26-gon
AnnZ [28]

Answer:

not possible to answer on text, very sorry we cant help

3 0
3 years ago
What is an equation of the line that is perpendicular to y=−4/5x+3 and passes through the point (4, 12) ?
PilotLPTM [1.2K]
The slope of the given line is -4/5.  The line perpendicular to that line will have a slope that is the opposite reciprocal.  In other words, the perpendicular slope will be 5/4.  If it passes through (4, 12), we have an x and a y value to use in y=mx+b.  y is 12, x is 4, and we have a slope of 5/4.  Filling in accordingly: 12= \frac{5}{4}(4)+b and 12 = 5 + b.  So b = 7.  Rewriting with our new slope and b value, y= \frac{5}{4}x+7.  And there you go!
3 0
3 years ago
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