Evaluate $m+n^2$ if we know $m=2$ and $n=-2$
A) 8
B) -6
C) 6
D) -8
Answer (1)
Substitute m = 2 and n = − 2 into the expression m + n 2 .
Calculate ( − 2 ) 2 = 4 .
Add the results: 2 + 4 = 6 .
The final answer is 6 .
Explanation
Understanding the Problem We are given the expression m + n 2 and the values m = 2 and n = − 2 . Our goal is to substitute these values into the expression and evaluate it.
Substituting the Values First, we substitute the given values into the expression: m + n 2 = 2 + ( − 2 ) 2
Calculating n^2 Next, we calculate ( − 2 ) 2 . Since a negative number squared is positive, we have ( − 2 ) 2 = ( − 2 ) × ( − 2 ) = 4 . So the expression becomes: 2 + 4
Adding the Numbers Finally, we add the two numbers: 2 + 4 = 6 Therefore, the value of the expression m + n 2 when m = 2 and n = − 2 is 6.
Examples
In real life, this type of calculation can be used in various scenarios. For example, if you are calculating the total cost of an item where there is a fixed cost ( m ) and a variable cost that depends on the square of the quantity ( n 2 ), you would use this formula. Imagine a service charges a $2 base fee plus $1 per unit of data squared. If you use -2 units of data (in some abstract sense), the total charge would be calculated as $2 + (-2)^2 = 2 + 4 = $6.
