A sidewalk of width 2 feet is being built around a pool. Which expression represents the area of the sidewalk?
2 answers:
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Answer:
5. A) two solutions
6. one solution
Step-by-step explanation:
5. A graph shows the curve has two x-intercepts, so two solutions. You can also figure this by looking at the discriminant:
b^2 -4ac = (7)^2 -4(-4)(8) . . . . a positive number
When the discriminant is positive, there are two real solutions.
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6. The equation factors as ...
0 = 3(x +3)^2
This will have one real solution at x=-3.
Answer:
-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
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:
which simplifies a bit to
and
-1 = a(1) - 3. Therefore, a = 2 and our parabola is
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:
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!