Which of the following is an accurate analysis of the fundamental obligations
Without specific context or information provided, it is impossible to accurately analyze the fundamental obligations. The nature of the obligations will depend on the situation or context in which they arise. It is important to have more information in order to provide a meaningful analysis.
The total number of seats in an auditorium is modeled by f(x) = 2x^2 - 6x, where x represents the number of rows of seats. How many rows are there in the auditorium if it has a total of 416 seats?
A. 32
B. 13
C. 20
D. 16
To find the number of rows in the auditorium, we need to set the total number of seats equal to 416 and solve for x in the equation f(x) = 2x^2 - 6x.
So, we have:
2x^2 - 6x = 416
Rearranging the equation:
2x^2 - 6x - 416 = 0
Now, we can either factorize the quadratic equation or use the quadratic formula to find the value of x. Factoring is not straightforward here, so let's use the quadratic formula:
x = [-(-6) ± √((-6)^2 - 4*2*(-416))] / 2*2
x = [6 ± √(36 + 3328)] / 4
x = [6 ± √3364] / 4
x = [6 ± 58] / 4
Now, we have two possible solutions:
1. x = (6 + 58) / 4 = 64 / 4 = 16
2. x = (6 - 58) / 4 = -52 / 4 = -13
Since rows of seats cannot be negative, the number of rows in the auditorium is 16.
So, the correct answer is D. 16.