Question

Two numbers are 10 units away in different directions from

their midpoint, m, on a number line. The product of the
numbers is -99.
Which equation can be used to find m, the midpoint of the
two numbers?
(m - 5)(m + 5) = 99
O (m-10)(m + 10) = 99
m2 - 25 = -99
O m- 100 = -99

Answer 1

Answer: Option D

(D) m2 – 100 = –99

Explanation:

Answer 2

The equation can be used to find m, the midpoint of the

two numbers is:

`m^2-100 = -99`

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:

`x_1=m+10\\\\x_2=m-10`

The product of the numbers is -99. This can be written as:

`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`