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Since, it is given that angle A is a right angle and angle B is a right angle.
We have to prove that
Now, we have to complete the given statement.
It is given that and
are right angles. This means that
and
because of the definition of the right angles. By the substitution property of equality
.
Using a system of equations, it is found that <u>since the solution of the system does not involve decimal numbers</u>, it is possible to arrange the books in this way.
For the system, we consider that:
- x is the number of books on the first shelf.
- y is the number of books on the second shelf.
- z is the number of books on the third shelf.
In total, there are 152 books, hence:
The first shelf has 7 fewer books than the second shelf, hence:
Also, it has 11 more books than the third shelf, hence:
Then:
Then, replacing in the first equation:
The number of books in each shelf has to be countable, that is, cannot be decimal.
- Then, <u>since the solution of the system does not involve decimal numbers</u>, it is possible to arrange the books in this way.
To learn more about system of equations, you can take a look at brainly.com/question/14183076