a person can pay $27 for a membership to the science museum and then go to the stamp for just $1 per visit what is the maximum n
1 answer:
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Answer:
a. Slope of f(x) is greater than g(x)
b. y-intercept of f(x) is less than the y-intercept of g
Step-by-step explanation:
Function f(x)
Given the function f(x)
x f(x)
-3 -0.5
-2 0
-1 0.5
0 1
Finding the slope between any two points
Thus,
The slope of f(x) = 0.5
We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.
From the given point (0, 1), we can easily observe that at x = 0, the value of y = 1.
Thus, the y-intercept of f(x) = 1
Function g(x)
Taking two points from the given graph of g(x)
- (1, 0)
- (0, 2)
Finding the slope between (1, 0) and (0, 2)
Refine
Thus,
The slope of g(x) = -2
We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.
From the given point (0, 2), we can easily observe that at x = 0, the value of y = 2.
Thus, the y-intercept of g(x) = 2
Conclusion:
<u>FOR function f(x)</u>
The slope of f(x) = 0.5
The y-intercept of f(x) = 1
<u>FOR function gx)</u>
The slope of g(x) = -2
The y-intercept of g(x) = 2
Thus:
a. Slope of f(x) is greater than g(x)
b. y-intercept of f(x) is less than the y-intercept of g
Essentially, we are trying to find the missing constant term of (remember that we are subtracting
due to the negative sign in front of the second term). Let's expand this to see what we can work with:
- Set up
- FOIL and simplify
Now, we know the second term is , so let's set the second term in the polynomial we just found equal to
:
- Set up
- Divide both sides of the equation by
- Divide both sides of the equation by 2
We have found . We know the missing constant term is
, according to the polynomial we found earlier. Thus, the missing term is:
The missing constant term is 36.