Question

Given `k\left(x\right)=-x^{2}-2x+15,`which statement is true?
Answer
The number of seats in an auditorium is modeled by `f\left(x\right)=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?
Answer
Which ordered pair is in the solution set of `y<-\frac{3}{5}x+4`?
Answered by GPT 3.5
The function k(x) is a quadratic function.
Answered by GPT 3.5
To find the number of rows in the auditorium, we need to solve the equation f(x) = 416.

Given f(x) = 2x^2 - 6x and f(x) = 416:

2x^2 - 6x = 416.

Rearranging, we get:

2x^2 - 6x - 416 = 0.

Now, we solve this quadratic equation for x by factoring, completing the square, or using the quadratic formula.

By factoring or using the quadratic formula, we find the values of x.

Once we have the value(s) of x, we can determine the number of rows in the auditorium.
Answered by GPT 3.5
To find the ordered pair that is in the solution set of `y < -\frac{3}{5}x + 4`, we can test the given ordered pairs by substituting the x and y values into the inequality to see which pair satisfies the inequality.

Let's test the ordered pairs:
A) (-5, 2)
B) (0, 3)
C) (5, 0)

A) For (-5, 2):
Substitute x = -5 and y = 2 into the inequality:
2 < -\frac{3}{5}(-5) + 4
2 < 3 + 4
2 < 7

This is true, so the ordered pair (-5, 2) is in the solution set of the given inequality.

B) For (0, 3):
Substitute x = 0 and y = 3 into the inequality:
3 < -\frac{3}{5}(0) + 4
3 < 4

This is also true, so the ordered pair (0, 3) is in the solution set of the given inequality.

C) For (5, 0):
Substitute x = 5 and y = 0 into the inequality:
0 < -\frac{3}{5}(5) + 4
0 < -3 + 4
0 < 1

This is true, so the ordered pair (5, 0) is also in the solution set of the given inequality.

Therefore, all three ordered pairs are in the solution set of `y < -\frac{3}{5}x + 4`.