Variables are letters from the end of the alphabet
Economics always uses the firsts letter of whatever that letter is representing.
<span> An </span>expression<span> such as 4x</span>3<span> is a </span>variable<span>. It can assume different values because x can assume different values.</span>
2x + y = 3
x = 2y - 1
solve for y in the first equation;
2x + y = 3
y = 3 - 2x
x = 2y - 1
x = 2(3 - 2x) - 1
x = -4x + 5
solve for x;
x = -4x + 5
x + 4x = 5
5x = 5
x = 1
solve for y;
y = 3 - 2x
y = 3 - 2(1)
y = 1
the answer is: x = 1, y = 1
hope this helps, God bless!
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
Answer:
10
Step-by-step explanation:
-80 / -8 = 10
the negatives cancel each other out
