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Romashka-Z-Leto [24]
2 years ago
7

4. What is the value of a in the following equation: 6a = 54? b. 7 C. 12 d. 8 a. 9

Mathematics
1 answer:
Korolek [52]2 years ago
8 0

Answer:

9

Step-by-step explanation:

6a=54

a=54/6

a=9

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Alexander is riding his bicycle to school. After one mile he is a third of the way there. How much more does he have to ride
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Read 2 more answers
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

5 0
2 years ago
35.75÷3.64 please help help wanted
IrinaK [193]
<span>the answer is 9.82. hope this helps!

</span>
5 0
3 years ago
5x-6_&lt; -5x +16 <br> solve
Olegator [25]

Answer:

haha

Step-by-step explanation:

thanks for the points

4 0
2 years ago
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