The coordinates of A will be (2P +M)/3
= (2(16, 14) +(1, 4))/3 = (33/3, 32/3) = (11, 32/3)

The appropriate choice is
(C) (11, 32/3)

_____
You will note that the coordinates of A are the weighted average of the coordinates of the end points. The weighting is the reverse of the ratio of the line segments. That is, the point adjacent to the shortest segment gets the highest weighting. (This is typical of the solution to "mixture" problems.)

8 0

3 years ago

What is the relationship between the discriminant of a quadratic and its graph?

faltersainse [42]

Answer:

In a quadratic equation of the shape:

y = a*x^2 + b*x + c

we hate that the discriminant is equal to:

D = b^2 - 4*a*c

This thing appears in the Bhaskara's formula for the roots of the quadratic equation:

$x = \frac{-b +-\sqrt{b^2 - 4ac} }{2a}$

You can see that the determinant is inside a square root, this means that if D is smaller than zero we will have imaginary roots (the graph never touches the x-axis)

If D = 0, the square root term dissapear, and this implies that both roots of the equation are the same, this means that the graph touches the x axis in only one point, wich coincides with the minimum/maximum of the graph)

If D > 0 we have two different roots, so the graph touches the x-axis in two different points.

4 0

3 years ago