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
○ (m - 10)(m + 10) = 99
○ m² - 25 = -99
○ m² - 100 = -99

Explanation:

Step1: Define the two numbers

Let the midpoint be \( m \). Since the two numbers are 10 units away from \( m \) in different directions, the two numbers are \( m + 10 \) and \( m - 10 \).

Step2: Find the product of the two numbers

The product of the two numbers is \( (m + 10)(m - 10) \). We know from the difference of squares formula that \( (a + b)(a - b)=a^{2}-b^{2} \), so \( (m + 10)(m - 10)=m^{2}-10^{2}=m^{2}- 100 \).

Step3: Set up the equation

We are given that the product of the two numbers is - 99. So we set up the equation \( m^{2}-100=-99 \).

Answer:

\( m^{2}-100 = - 99 \) (the fourth option)