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2 answers:
Answer:
C
Step-by-step explanation:
Median of triangle: It is a line segment joining a vertex to the midpoint of the opposite side.
Consider ΔABC, point F id the midpoint of line segment AB and E is the midpoint of luine segment AC.
Draw line segments FC and BE(medians of triangle). G is the point where line segment FC and BE meet. Now, Join AG.
Let H be the point outside the ΔABC and AG passs through the point H such that AG intersects BC at D. BH and HC are dashed lines.
We need to show that D is the midpoint of BC. The correct logical order for proof will be:
III. GC is parallel to line segment BH and line segment BG is parallel to line segment HC.
IV. Line segment FG is parallel to line segment BH and line segment GE is parallel to line segment HC.
I. BGCH is a parallelogram as opposite sides are parallel (from III.)
II. Since, diagnols of a parallelogram bisect each other. Henc, we get BD=DC.
Therefore, D is mid pont of BC.
It implies that AD is also a median.
Hence, all the three medians that are: BE,FC and AD passes through a common vertex G.
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Answer: a = 4
Step-by-step explanation: Area of a triangle is calculated as: .
The triangle formed by the parabola has base (b) equal to the distance between the points where the graph touches x-axis and height (h) is the point where graph touches the y-axis.
The points on the x-axis are the roots of the quadratic equation:
a(x-3)(x+2)=0
(x-3)(x+2)=0
x - 3 = 0
x = 3
or
x + 2 = 0
x = -2
So, base is the distance between (-2,0) and (3,0).
Since they are in the same coordinate, distance will be:
b = 3 - (-2)
b = 5
Area of the triangle is 10. So constant a is
5a = 10.2
a = 4
The constant a of the function y = a(x-3)(x+2) is 4.