A ratio of 5:7 means out of 12 books, 5 are in one category and 7 are in another. (The “category” isn’t specified in this problem.)
So here we’re STARTING with 36 books; we want to find a ratio that is equal to 5:7 and adds up to 36. Well 36 = 3(12), and so if we multiply each number in the ratio by 3 as well, we might get what we want. Doing that gives us 15:21, which adds up to 36 and is equal to 5:7. Boom, that’s the answer.
P.S. Here’s a question you can think about: why do ratios stay the same when you multiply each number by the same amount? (For example, why is 3:1 the same as 6:2?)
The three points give you three equations, which you can solve by your favorite method.
.. 0m +0n +b = 6
.. 1m +0n +b = -3
.. 0m +2n +b = 5
(m, n, b) = (-9, -1/2, 6)
so the equation of the plane can be written as
.. z = -9x -1/2y +6
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In standard form, this would be
.. 18x +y +2z = 12
Use Pythagoras theorem. (a^2 + b^2 = c^2)
300^2+300^2 = 180000
√180000 = 424.3
The answer is 424 foot.
Hope this helps.