The length of the hypotenuse will be equal to H=122.25 when value of x=14.
<h3>What is pythagorean theorem?</h3>Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal the square of the sum of the other two sides.
It is given that:
Value of x=14
The perpendicular is =6x+5=6x14+5=89
The base is =6x=84
So by using the Pythagorean theorem:-
Hence the value of hypotenuse will be H=122.25
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Answer:
Step-by-step explanation:
If you plot the directrix and the focus, you can see that the focus is to the left of the directrix. Since a parabola ALWAYS wraps itself around the focus, our parabola opens sideways, to the left to be specific. The formula for the parabola that opens to the left is
We will solve this for x at the end. The negative is out front because it opens to the left. If it opened to the right, it would be positive.
The vertex of a parabola is exactly halfway between the focus and the directrix, so our vertex coordinates h and k are (3, 6). P is defined as the distance between the vertex and the directrix, or the vertex and the focus. Since the vertex is directly between both the directrix and the focus, each distance is the same. P = 1. Filling in what we have now:
which simplifies to
Now we will solve it for x.
and
so
