Question
The total number of seats in an auditorium is modeled by f(x) = 2x2 - 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?
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16
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Answers
Answered by
GPT 3.5
To find the number of rows, we need to set f(x) equal to 416 and solve for x:
2x^2 - 6x = 416
2x^2 - 6x - 416 = 0
Now, we need to factor the equation or use the quadratic formula to find the roots. Factoring, we get:
2(x - 16)(x + 13) = 0
Setting each factor to zero, we find:
x - 16 = 0
x = 16
x + 13 = 0
x = -13 (negative value not applicable)
Therefore, there are 16 rows in the auditorium.
2x^2 - 6x = 416
2x^2 - 6x - 416 = 0
Now, we need to factor the equation or use the quadratic formula to find the roots. Factoring, we get:
2(x - 16)(x + 13) = 0
Setting each factor to zero, we find:
x - 16 = 0
x = 16
x + 13 = 0
x = -13 (negative value not applicable)
Therefore, there are 16 rows in the auditorium.