Find the total cost of producing 5 widgets. Widget Wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x. The company also discovered that it costs $15.50 to produce 3 widgets, $23.50 to produce 7 widgets, and $56 to produce 12 widgets.
OK...so we have
a(7)^2 + b(7) + c = 23.50 → 49a + 7b + c = 23.50 (1)
a(3)^2 + b(3) + c = 15.50 → 9a + 3b + c = 15.50 subtracting the second equation from the first, we have
40a + 4b = 8 → 10a + b = 2 (2)
Also
a(12)^2 + b(12) + c = 56 → 144a + 12b + c = 56 and subtracting (1) from this gives us
95a + 5b = 32.50
And using(2) we have
95a + 5b = 32.50 (3)
10a + b = 2.00 multiplying the second equation by -5 and adding this to (3) ,we have
45a = 22.50 divide both sides by 45 and a = 1/2 and using (2) to find b, we have
10(1/2) + b = 2
5 + b = 2 b = -3
And we can use 9a + 3b + c = 15.50 to find "c"
9(1/2) + 3(-3) + c = 15.50
9/2 - 9 + c = 15.50
-4.5 + c = 15.50
c = 20
So our function is
c(x) = (1/2)x^2 - (3)x + 20
And the cost to produce 5 widgets is = $17.50
The <em><u>correct answer</u></em> is:
D) Closed circle on 8, shading to the right.
Explanation:
First we must solve the inequality:
x - 3 ≥ 5
Add 3 to each side:
x - 3 + 3 ≥ 5 + 3
x ≥ 8
To graph this, we want a circle on 8 Since it is "greater than or equal to," 8 is included in the solution set. This means the circle will be closed.
Since it is "greater than," we want the numbers to the right of 8 on the number line.
This means the inequality will be a closed circle and shaded to the right.
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If i was you i would look up every box in the word bank then find examples of each box and do the best I could.
-hope this helps!
The correct answer is C
to get 5 to 100, multiply by 20, so multiply 3 by 20 as well.
