Answer: In general, a solution of a system in two variables is an ordered pair that makes BOTH equations true. In other words, it is where the two graphs intersect, what they have in common. So if an ordered pair is a solution to one equation, but not the other, then it is NOT a solution to the system
I find it easier just to graph this sort of question rather than multiply it all out.
x = 3.5
_____
(x^2 +2x +1) -(x^2 -6x +9) = 20
.. 8x -8 = 20
.. x = 28/8 = 3.5
For P(t) = 920*1.06^(2t), the current population is 920, the percentage growth rate is 6% semiannually, and the population in 4 years will be 920*1.06^8 = 1466.
Selection B is appropriate.
_____
The 2 in the exponent means the growth factor 1.06 is applied twice for each increment of t, that is, twice in 1 year (semiannually).
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.
The circle is open if the inequality is greater than (>) or less than (<) and closed if the inequality is greater than or equal to (≥) or less than or equal to (≤)
If the arrow points to the right (—>) towards bigger numbers, x (whatever number is on the line) will be GREATER (> or ≥)
If the arrow o points to the left (<—) towards smaller numbers, x will be LESSER (< or ≤)
1. Starts at -2 with a closed circle and goes in the positive direction —>
So x ≥ -2
2. Starts at 2 with an open circle and goes in the negative direction <—
So x<2
And the rest use the same method.
