Ruben bought 6 new books for his collection. this increased his collection by 12%. how many books did he have before his purchases?

 The required number of books that Ruben had before purchases is 50.

Step-by-step explanation:  Given that Ruben bought 6 new books for his collection that increased his collection by 12%.

We are to find the number of books that Ruben had before purchases.

Let x denotes the number of books that Ruben had before purchases.

Then, according to the given information, we have

Thus, the required number of books that Ruben had before purchases is 50.

the circumference of a circle is, 10.676 cm.

step-by-step explanation:

the formula for circumference of a circle is given by:

where

c is the circumference of a circle and

d is the diameter of a circle.

given: diameter(d) = 3.4 cm and use

substitute these values in [1] we get;

cm

therefore, the circumference of a circle is, 10.676 cm