Determine the longest distance inside a rectangular prism with dimensions of 8 ft x 3 ft by 9 ft
1 answer:
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<em>Question:</em>
<em>Abraham has visited at least 50 countries; he plans to visit five new countries per year (Y) for the next several years. Which inequality and solution shows the amount of years they will take for Abraham to meet his goal.</em>
Answer:
Step-by-step explanation:
Given
------ at least
Required
Represent as an inequality
"at least" means
So the countries he has visited can be represented as thus;
If
1 year = 5 countries
y years would be 5y countries
So, in y years; he'd have visited
To determine the value of y.
We have that
<em>in the world</em>
<em>Substitute 195 for Countries</em>
<em>Collect Like Terms</em>
<em>Divide through by 5</em>
<em>Reorder</em>
This means that; he'll visit all countries in at most 29 years' time
I'm not sure if this is the easiest way of doing this, but it surely work.
Let the base of the triangle be AB, and let CH be the height. Just for reference, we have
Moreover, let CH=y and BC=z
Now, AHC, CHB and ABC are all right triangles. If we write the pythagorean theorem for each of them, we have the following system
If we solve the first two equations for y squared, we have
And we can deduce
So that the third equation becomes
(we can't accept the negative root because negative lengths make no sense)