Find the value if x=2+root3
1 answer:
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The fraction of the image in blue with respect to the <em>entire</em> hexagon is .
Initially we proceed to create auxiliar constructions , represented by red line segments, to re-define the hexagon as a sum of standard figures. According to the figure, we find two types of triangles (type-1 and type-2), and the following relationship between the two types:
(1)
Where:
- Area of a type-1 triangle.
- Area of a type-2 triangle.
The formulae for the area of the shaded region () and the <em>entire</em> hexagon (
) are, respectively:
(2)
(3)
And the fraction of the image in blue is:
The fraction of the image in blue with respect to the <em>entire</em> hexagon is .
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Answer:
C. The x-coordinate of the vertex must be 6
Step-by-step explanation:
The parabola intercepts the x-axis when y = 0.
Therefore, if the quadratic equation has the points (2, 0) and (10, 0) then the x-intercepts or "zeros" are x = 2 and x = 10.
The x-coordinate of the vertex is the midpoint of the zeros.
Therefore, the solution is option C.
<u>Additional Information</u>
The leading coefficient of a quadratic tells us if the parabola opens upwards or downwards:
- Positive leading coefficient = parabola opens upwards
- Negative leading coefficient = parabola opens downwards
We have not been given this information and so therefore cannot determine the way in which it opens.
As we do not know the way in which way the parabola opens, we cannot determine if the parabola will have a negative or positive y-intercept.
We have not been given the full quadratic equation, and so we cannot determine if the parabola is wider (or narrower) than the parent function.