2 years ago

10. Sevi wants to save to buy a guitar. The guitar costs $900. Sevi has $150 3 points

Mathematics

1 answer:

levacccp [35]2 years ago

8 0

Answer

Step-by-step explanation:

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Le's round this to
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Prove the following statement.

gayaneshka [121]

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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: $(2k+1)^{2}=(2(2s+1)+1)^{2}=(4s+3)^{2}=16s^2+24s+9=16s^{2}+24s+8+1=8(2s^{2}+3s+1)+1$ .

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

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