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Elenna [48]
3 years ago
5

Prove the following statement.

Mathematics
1 answer:
gayaneshka [121]3 years ago
6 0

Answer:

You can prove this statement as follows:

Step-by-step explanation:

An odd integer is a number of the form 2k+1 where k\in \mathbb{Z}. Consider the following cases.

Case 1. If k is even we have: (2k+1)^{2}=(2(2s)+1)^{2}=(4s+1)^{2}=16s^2+8s+1=8(2s^2+s)+1.

If we denote by m=2s^2+2 we have that (2k+1)^{2}=8m+1.

Case 2. if k is odd we have: (2k+1)^{2}=(2(2s+1)+1)^{2}=(4s+3)^{2}=16s^2+24s+9=16s^{2}+24s+8+1=8(2s^{2}+3s+1)+1.

If we denote by m=2s^{2}+24s+1 we have that (2k+1)^{2}=8m+1

This result says that the remainder when we divide the square of any odd integer by 8 is 1.

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Karolina [17]

Hello There!

<u><em>n - d = 0</em></u>

<u><em>5n+10d = 90</em></u>

<u><em>----------------------</em></u>

<u><em>n-d = 0</em></u>

<u><em>n+2d = 18</em></u>

<u><em>-------------------</em></u>

<u><em>Subtract and solve for "d":</em></u>

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If Jerry initially releases 10 videos a week and creates an additional 3 each week, he will create a total of 3w+10 videos, where w is the number of weeks. If Martin initially releases 15 videos a week and creates an additional 2 each week, he will create a total of 2w+10 videos, since w is maintained. Therefore, the inequality \fbox{$3w+10>2w+15$} can be used to find who creates more videos, where w is the number of weeks.

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