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The total number of seats in an auditorium is modeled by f(x) = 2x2 – 6x, where x represents the number of rows. How many rows are there in the auditorium if it has a total of 416 seats?

Jose knows to solve for x to determine the number of rows. He decides to use his calculator. Under y =, he types in 2x^2-6x.

He gets the two solutions
x=0,x=3
Jose determines the auditorium has 3 rows.

Respuesta :

calculista

Answer:

Jose's solution is not correct, the auditorium has [tex]16[/tex] rows

Step-by-step explanation:

we have

[tex]f(x)=2x^{2} -6x[/tex]

where

f(x)------> is the total number of seats in the auditorium

x----> represents the number of rows

How many rows are there in the auditorium if it has a total of 416 seats?

so

Find the value of x for f(x)=416 seats

substitute the value of f(x) in the equation

[tex]416=2x^{2} -6x[/tex]

[tex]2x^{2} -6x-416=0[/tex]

Using a graphing calculator

The values of x are

[tex]x=-13, x=16[/tex]

The solution is

x=16 rows because the number of rows can not be a negative number

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