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3 years ago

11

Fill in the integers -10, -8, -7, -6, -5, -4, -3, -2 and 0 into a magic square so that every row, column, and diagonal has a sum

of -15.

1 answer:

ioda3 years ago

6 0

-2 -10 -3

-7 0 -8

-6 -5 -4

That's the square, it was a fun puzzle :)

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Explanation:

In the graph:

The given locations are:

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,

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,

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We determine both Owen's and David's distance from the school using the distance formula.

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

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$\begin{gathered} AC=\sqrt[]{(3-11)^2+(18-3)^2} \\ =\sqrt[]{(-8)^2+(15)^2} \\ =\sqrt[]{64+225} \\ =\sqrt[]{289} \\ AC=17\text{ miles} \end{gathered}$

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$\begin{gathered} BC=\sqrt[]{(3-15)^2+(18-13)^2} \\ =\sqrt[]{(-12)^2+(5)^2} \\ =\sqrt[]{144+25} \\ =\sqrt[]{169} \\ BC=13\text{ miles} \end{gathered}$

We see from the calculations that David lives closer to the school, and by 4 miles.

The graph below is attached for further understanding:

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