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NARA [144]
2 years ago
8

Prove or disprove: For any odd integer x, (x^2 -1) is divisible by 8.

Mathematics
2 answers:
cricket20 [7]2 years ago
8 0

Answer:

True

Step-by-step explanation:

To prove by induction, first show that the statement is true at an initial value (in this case, x = 1).

8 | (1² − 1)

8 | 0

Next, assume the statement is true at x = k.

8 | (k² − 1)

Now show that it is true at the next value of x (x = k + 2).

(k + 2)² − 1

= k² + 4k + 4 − 1

= k² − 1 + 4(k + 1)

k + 1 is an even number, so 4(k + 1) is a multiple of 8.  And since we're assuming that k² − 1 is a multiple of 8, that means the sum is also a multiple of 8.

8 | ((k + 2)² − 1)

So the statement is true.

Logically, here's another way of proving it:

x² − 1 = (x − 1) (x + 1)

Since x is an odd integer, both x − 1 and x + 1 are even numbers.  Since the difference between them is 2, one of them is a multiple of 4.  An even number times a multiple of 4 is a multiple of 8.

Angelina_Jolie [31]2 years ago
3 0

Answer:

Is the statement ∃!x∈R:(x−2 =√x+7) true or false? ... Problem 8. Let x, y, and z be natural numbers. Prove or disprove: If x+y is odd and y+z is odd, then x+z is odd.

Step-by-step explanation:

<em> </em><em>hope</em><em> </em><em>this</em><em> </em><em>helps</em><em> </em><em>you</em><em> </em>

<em> </em><em>❤</em><em> </em><em>❤</em><em> </em><em>❤</em><em> </em><em>❤</em><em> </em><em>❤</em><em> </em>

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X-4/10=7/5<br> Plz solve these
iragen [17]
(x-4)/10=7/5
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here you go, practice it once or twice. good luck
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.416 is rounded to the nearest thousandth
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The gross pay of a worker in a factory is €30800.60 per annum. If €504 is deducted from his salary month,how much does he take h
barxatty [35]

The amount of money worker will take home is €24752.6

<h3>What is gross pay?</h3>

Gross pay is the amount earned by any individual without any deductions of the taxes, and charges. It is the total amount of money earned by anyone.

Given that:-

  • The gross pay of a worker in a factory is €30800.60 per annum. If €504 is deducted from his salary month.

The amount of money he will take home will be calculated as:-

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Deductions = €504 per month = 504 x 12 = €6048 per year.

So net pay = 30800.6 - 6048 =  €24752.6

Therefore the amount of money the worker will take home is €24752.6

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1 year ago
To find the product 3/7 x 4/9 Cameron simplified 3/7 to 1/7 and then mulitiplied the fractions 1/7 and 4/9 to find the product 4
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He was not supposed to simplify. He could have multiplied straight across and got 12/63 and he would simplify that which would be 4/21 im thinking
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3 years ago
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PLEASE HELP AS SOON AS YOU CAN!!
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The Answer would be -6(3x-5).
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