two numbers are 10 units away in different directions from their mid - point, m, on a number line. the…

two numbers are 10 units away in different directions from their mid - point, m, on a number line. the product of the numbers is - 99. which equation can be used to find m, the mid - point of the two numbers? (m - 5)(m + 5)=99 (m - 10)(m + 10)=99 m² - 25=-99 m² - 100=-99

two numbers are 10 units away in different directions from their mid - point, m, on a number line. the product of the numbers is - 99. which equation can be used to find m, the mid - point of the two numbers? (m - 5)(m + 5)=99 (m - 10)(m + 10)=99 m² - 25=-99 m² - 100=-99

Answer

Explanation:

Step1: Express the two numbers

If the mid - point is $m$ and the two numbers are 10 units away in different directions from the mid - point, the two numbers are $m - 10$ and $m+10$.

Step2: Set up the product equation

The product of the two numbers is $(m - 10)(m + 10)$. We know that the product of the two numbers is - 99. So, $(m - 10)(m + 10)=-99$.

Step3: Expand the left - hand side

Using the difference of squares formula $(a - b)(a + b)=a^{2}-b^{2}$, where $a = m$ and $b = 10$, we get $m^{2}-100=-99$.

Answer:

$m^{2}-100=-99$