Zelda made 5 gallons of lemonade and gave each of her friends an equal amount. Write an expression that represents how much lemo
1 answer:
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The given function is a quadratic equation. Any quadratic equation can be written in the form :
The given points can be taken as (2,23) ,(4,55) and(10,247)
We form three equations with the given points
For point (2,23 ) the equation is
23 = 4a + 2b + c
For point (4,55) the equation is
55 = 16a + 4b + c
For point (10,247) the equation is:
247 = 100a+10b+c.
Solving the three equations for a,b,c we have :
32 = 12a + 2b
16 = 6a + b
and,
192 = 84 a + 6b
32 = 14a + b
Solving for a,b,c we have:
a=2 b=4 c=7
The quadratic equation is c(x)=
When x=8
c(x)=]
Option C. $167 is the right answer.
The average rate of change on the interval (5, 6) is 9. So the correct option is D.
<h3>How to find the average rate of change on the interval?</h3>
Here we want to find the average rate of change of f(x), the function on the table, on the interval (5, 6).
This is just:
I we look at the table we see that:
This is a system of equations.
If we subtract the second and first functions, we get:
From that we take two relations:
Now we can replace these two in the last equations so we get:
Now that we know the value of a:
The quadratic equation is:
Evaluating this in x = 6 we get:
And from the table we know that f(5) = 17, then the average rate of change is:
The correct option is D.
If you want to learn more about average rates of change:
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