Respuesta :
Answer:
The equation can be used to find m, the midpoint of the
two numbers is:
[tex]m^2-100 = -99[/tex]
Step-by-step explanation:
Two numbers are 10 units away in different directions from their midpoint, m, on a number line.
Then, we can define the two numbers as:
[tex]x_1=m+10\\\\x_2=m-10[/tex]
The product of the numbers is -99. This can be written as:
[tex]x_1\cdot x_2=-99\\\\(m-10)(m+10)=-99\\\\m^2-10m+10m-100=-99\\\\m^2-100=-99\\\\m^2=-99+100=1\\\\m=\pm1[/tex]
