Respuesta :
Answer:
[tex]m = \dfrac{a^2-99}{2a}[/tex]
Step-by-step explanation:
on a number line, m is the point that is the midpoint of two other points.
the distance between each of the points to the midpoint is 10 units..
if a is the point 10 units less than m
and b is the point 10 units greater than m,
then,
[tex]m = a+10[/tex]
[tex]m = b-10[/tex]
we can add the two equations to form the midpoint formula.
[tex]2m = a+b[/tex]
we also know that the product of both numbers equal -99.
[tex]ab = -99[/tex]
we can substitute either 'a' or 'b' to the equation of m.
[tex]2m = a-\dfrac{99}{a}[/tex]
[tex]m = \dfrac{a^2-99}{2a}[/tex]
and this is the equation for the midpoint of the two numbers.
