Part A: The slope of f(x) is three times as great as the slope of g(x).
Part B: The y-intercept of g(x) is 12 larger than the y-intercept of f(x).
In order to find these two answers, you need to find a model for f(x). You can do that by first finding the slope. The formula is below.
slope (m) = (y2 - y1)/(x2 - x1)
In this equation (x1, y1) is the first point and (x2, y2) is a second point. For this purpose, we'll pick (1, 0) and (0, -6)
slope (m) = (-6 - 0)/(0 - 1)
m = -6/-1
m = 6
Now we know that the slope is 6, which is 3 times as great as the first slope. Now to find the y-intercept, we can use either point and the slope in slope intercept form.
y = mx + b
0 = 6(1) + b
0 = 6 + b
-6 = b
So we know the y-intercept is -6, which is 12 less than the y-intercept of g(x).
The maximum value it going to be 12 which will be 16 in the end that is going to be corrrct
The volume of the box as a polynomial in the variable x is x(12 - 2x)(7 - 2x)
<h3>How to determine the volume?</h3>
The complete question is added as an attachment
From the attached image, we have:
Length = 12 - 2x
Width = 7 - 2x
Height = x
The volume is calculated as:
Volume = Length * Width * Height
Substitute the known values in the above equation
Volume = (12 - 2x) * (7 - 2x) * x
This gives
Volume = x(12 - 2x)(7 - 2x)
Hence, the volume of the box as a polynomial in the variable x is x(12 - 2x)(7 - 2x)
Read more about polynomial at:
brainly.com/question/4142886
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This might not be correct but....
I’m going to use rounding,
42 x 2 = 84
84 divides by 3 = 28,
Which is near 30......So the number of people in the group is rounding to about 2 people.
