Find the value of k given that both points lie on a line passing through the origin (5,10)and(-3,k)

The value of 'k' is -6.

Step-by-step explanation:

Given:

A line passing through the origin.

The points lying on the line are:

(5, 10) and

A line that passes through the origin is given as:

Where 'm' is the slope of the line.

Now, (5, 10) lies on the line. So, the point will satisfy the equation.

Therefore, plugging in in the above equation, we get:

So, the slope of the line is 2.

Now, the equation becomes

Now, point (-3, k) will also satisfy the equation. So, plugging in , we get

Therefore, the value of 'k' is -6.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

the answer is y < -3 or   y > 3

-3y > 7 + 2

-3 y > 9

y < -3