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guapka [62]
3 years ago
11

Joe wants to multiply a number by 15. First, he multiplies the number by 5. What number does he now need to multiply his answer

by?
Mathematics
1 answer:
pishuonlain [190]3 years ago
8 0

Answer: 3

Step-by-step explanation: its 3 because 5X3=15

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Prove that 2n^3 + 3n^2 + n is divisible by 6 for every integer n > 1 by mathematical induction. (7 marks)
notka56 [123]

Answer:

The answer is True

Step-by-step explanation:

A <em>mathematical induction</em> consists in only 2 steps:  

<u>First step</u>: Show the proposition is true for the first one valid integer number.

<u>Second step</u>: Show that if any one is true then the next one is true  

Finally, if first step and second step are true, then the complete proposition is true.

So, given 2*n^3+3*n^2+n

First step: using and replacing n=2 (the first valid integer number >1)

2*(2)^3 +3*(2)^2+2=30

\frac{30}{6} =5

As the result is an integer number, so the first step is true.

Second step: using any next number, n+1, let it replace

2*(n+1)^3+3*(n+1)^2+(n+1)\\2*(n^3+3*n^2+3*n+1)+3*(n^2+2*n+1)^2+(n+1)\\2*n^3+6*n^2+6*n+2+3*n^2+6*n+3+n+1\\(2*n^3+3*n^2+n)+(6*n^2+12*n+6)

As the First step is true, we know that

2*n^3+3*n^2+n=6*k,

So let it replace in the previous expression

6*k+6*(n^2+2*n+1)\\6*[k+(n^2+2*n+1)]

Finally

\frac{6*[k+(n^2+2*n+1)]}{6} =k+(n^2+2*n+1)

where the last expression is an integer number

So the second step is true, and the complete proposition is True

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I say it’s c it makes the most sense to me
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