Multiply 5.8 by 100 to convert to percent:
<span>5.8 × 100 = </span>580 %
5a, because both are divided by 5 as the greatest common factor, and a to the first power (not a squared or cubed) is the greatest variable power they share :)
Answer:
150 bikes, $10,500 minimum manufacturing cost
Step-by-step explanation:
5x^2 - 1500x + 123000 is represented by a parabolic graph that opens up. You could easily estimate the x value at which C(x) is at a minimum, as well as the smallest C(x) value.
Or you could do this problem algebraically by finding the vertex of the parabola. The results MUST be the same as before.
-b
The equation of the axis of symmetry of this curve is x = ---------
2a
... which here is x = 1500
--------- = 150 units (150 bikes)
2(5)
Evaluating C(x) (see the problem statement) at x = 150 leads to finding the minimum cost. I like to use synthetic division to evaluate polynomials. Here, the divisor would be 150 and the coefficients of the quadratic would be
5 -1500 123000
Setting up synthetic division, we get:
150 / 5 -1500 123000
750 -112500
--------------------------------------
5 -750 10500
The remainder is $10,500. This is the minimum cost of this manufacturing operation.
Answer:
last option: y = (-2/3)x + 5
Step-by-step explanation:
slope-intercept equation: y = mx + b
where m is the slope and b is the y-intercept
if slope m = -2/3, then y = (-2/3)x + b
if point (3, 3) is on the line, substitute x=3 and y=3 into the equation and solve for b:
3 = (-2/3)3 + b
⇒ 3 = -2 + b
⇒ b = 5
Therefore, equation: y = (-2/3)x + 5
