Mathematics, 05.02.2020 03:53 robertcoe426

What is the average rate of change from x = −3 to x = −4?

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Answer from: ninja12302

-2

Step-by-step explanation:

Since it would be immensely helpful to know the equation of this parabola, we need to figure it out before we can continue. We have the work form of a positive upwards-opening parabola as

y=a(x-h)^2+k

where a is the leading coefficient that determines the steepness of lack thereof of the parabola, x and y are coordinates of a point on the graph, and h and k are the coordinates of the vertex. We know the vertex: V(-3, -3), and it looks like the graph goes through the point P(-2, -1). Now we will fill in the work form equation and solve for a:

-1=a(-2-(-3))^2-3

which simplifies a bit to

-1=a(1)^2-3

and

-1 = a(1) - 3. Therefore, a = 2 and our parabola is

y=2(x+3)^2-3

Now that know the equation, we can find the value of y when x = -3 (which is already given in the vertex) and the value of y when x = -4. Do this by subbing in the values of x one at a time to find y. When x = -3, y = -3 so the coordinate of that point (aka the vertex) is (-3, -3). When x = -4, y = -1 so the coordinate of that point is (-4, -1). The average rate of change between those 2 points is also the slope of the line between those 2 points, so we will use the slope formula to find it:

$m=\frac{-1-(-3)}{-4-(-3)} =\frac{2}{-1}=-2$

And there you have it! I'm very surprised that this question sat unanswered for so very long! I'm sorry I didn't see it earlier!

Answer from: Quest

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes.

step-by-step explanation:

Answer from: Quest

the final price would be 29.6925

step-by-step explanation:

39.59 minus 25% equals 29.6925

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