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Len [333]
3 years ago
6

Ayesha has a theory about two digit numbers that have a larger tens digit than ones digit. she says that reversing the digits an

d subtracting the reversed number from the original number will always generate a number that is a multiple of 9. Is Ayesha right ? If so why do you think this works ? If not ,why not ?
would the same patterns work for three -digit numbers in which the hundreds digit is larger than the tens digit and the tens digit is larger than the ones digit.
Mathematics
2 answers:
Nataliya [291]3 years ago
7 0

Answer:

Ayesha says that reversing the digits and subtracting the reversed number from the original number will always generate a number that is a multiple of 9.

Lets take a number 63

Now reverse of this is 36. Subtracting 63-36 we get 27, which is a multiple of 9.

Lets take 76. The reverse is 67 and the difference is 76-67=9, which is a multiple of 9.

So, yes Ayesha's theory is correct.

This theory works because-

Lets say the original number is 10x+y and the reverse is 10y+x

So, the difference will be

10x+y-(10y+x)

=9x-9y=9(x-y)

This shows why the resulting number is a multiple of 9.

Yes, this works for three digits as well.

Example:

762-267=495 (multiple of 9)

321-123=198 (multiple of 9)

stira [4]3 years ago
6 0
<span>Ayesha's right.  There's a good trick for knowing if a number is a multiple of nine called "casting out nines."  We just add up the digits, then add up the digits of the sum, and so on.  If the result is nine the original number is a multiple of nine.  We can stop early if we recognize if a number along the way is or isn't a multiple of nine.  The same trick works with multiples of three; we have one if we end with 3, 6 or 9.

So </span>1284673 <span>has a sum of digits 31 whose sum of digits is 4, so this isn't a multiple of nine.  It will give a remainder of 4 when divided by 9; let's check.

</span>1284673 = 142741 \times 9 + 4 \quad\checkmark<span>

</span>Let's focus on remainders when we divide by nine. The digit summing works because 1 and 10 have the same remainder when divided by nine, namely 1.  So we see multiplying by 10 doesn't change the remainder.  So 100 \times a + 10 \times b + c has the same remainder as a+b+c.

When Ayesha reverses the digits she doesn't change the sum of the digits, so she doesn't change the remainder.  Since the two numbers have the same remainder, when we subtract them we'll get a number whose remainder is the difference, namely zero. That's why her method works.
<span>
It doesn't matter if the digits are larger or smaller or how many there are. We might want the first number bigger than the second so we get a positive difference, but even that doesn't matter; a negative difference will still be a multiple of nine. Let's pick a random number, reverse its digits, subtract, and check it's a multiple of nine:

</span>813219543092195 - 591290345912318 =  221929197179877 = 9 \times 24658799686653 \quad \checkmark

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NISA [10]
We are given 2 points with there coordinates easy to calculate:

the upper one A(1,15) & the lower one B(6,10). Moreover the equation of this linear function is y = mx + b

1st) calculate m= (10-15) / (6-1)  [FOMULA m=(y₂ - y₁) / (x₂ - x₁)]

m= -5/5 ==> m= - 1==> y=-x + b. To calculate b, replace x & y by any of the 2 points A, B. Say A(1,15)

15 = - (1) + b ==> b= 16 & final equation y = -x +16


3 0
3 years ago
Read 2 more answers
(3x²+3x+5)+(7x²-9x=8)=10x²-12x=13
Brilliant_brown [7]

The value of x is equal to -5/6

To solve this question, we have to add two polynomials together. The polynomials are;

  • 3x^2+3x+5
  • 7x^2-9x=8
<h3>Addition of Polynomials</h3>

This involves adding of two or more different polynomials together. The polynomials adding together are or must be of the same degree. i.e x^2 must add to another coefficient of x^2 and x^3 adds to another coefficient of x^3 and so on.

In this given question, let's add the polynomials together.

(3x^2+3x+5) + (7x^2-9x = 8\)\\3x^2 + 7x^2 + 3x-9x+5-8 =10x^2-6x-3

Now, let's equate this with the last polynomial given

10x^2-6x-3=10x^2-12x-13\\10x^2-10x^2-6x+12x-3+13\\0+12x+10\\12x=-10

Let's solve for x

12x=-10\\x=-\frac{10}{12}\\x = -\frac{5}{6}

The value of x is equal to -5/6

Learn more on addition of polynomials here;

brainly.com/question/4142886

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Monica made a drawing of her patio using the scale 1 inch equals 4 feet. The length of the patio in her drawing was 11 inches. W
kow [346]

1 inch = 4 feet

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<h3>Answer: 44 feet</h3>
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If your dinner bill was $80 and you left a 15% tip. How much money did you leave as a tip? What is your total bill cost?
nadya68 [22]

Answer: 92 dollars because 15% divided into 80 is 12 and add 80 to 12 and its 92

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3 years ago
PLZ HELP!!!!!! (WILL GIVE BRAINLIEST!!!!)
nasty-shy [4]
I think you times all of the inchs together. 5x3x2=30.

I dont know if i am right tho. Hope this help ya.
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