Patrick has 1 1/2 quarts of blue paint and 3 3/5 quarts of red paint. he mixes 2/3 of the blue paint and 5/6 of the red paint to
1 answer:
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First of all, we can observe that
So the expression becomes
This means that the expression is defined for every
Now, since the denominator is always positive (when it exists), the fraction can only be positive if the denominator is also positive: we must ask
Since we can't accept 3 as an answer, the actual solution set is
The solution of the system of equation is the intersection point of the two quadratic equations, so we need to equate both equations, that is,
So, by moving the term -3x^3+20 to the left hand side, we have
Then, in order to solve this equation, we can apply the quadratic formula
In our case, a=5, b=-3 and c=-30. So we get
which gives
By substituting these points into one of the functions, we have
and
Then, by rounding these numbers to the nearest tenth, we have the following points:
Therefore, the answer is the last option