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The total cost of producing 6 widgets is $24 if the company also discovered that it costs $16 to produce 2 widgets, $18 to produce 4 widgets, and $48 to produce 10 widgets.
<h3>What is a quadratic equation?</h3>Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
Let's suppose the quadratic function is:
c(x) = ax² + bx + c
Plug c(x) = $16
x = 2
16 = 4a + 2b + c ...(1)
Plug c(x) = $18
x = 4
18 = 16a + 4b + c ...(2)
Plug c(x) = $48
x = 10
48 = 100a + 10b + c ...(3)
After solving equations (1), (2), and (3) by substitution method:
a = 0.5
b = -2
c = 18
c(x) = 0.5x² -2x + 18
Plug x = 6 widgets:
c(6) = 0.5(36) - 12 + 18 = $24
Thus, the total cost of producing 6 widgets is $24 if the company also discovered that it costs $16 to produce 2 widgets, $18 to produce 4 widgets, and $48 to produce 10 widgets.
Learn more about quadratic equations here:
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