Step-by-step explanation:
Recall that a parabola is the graph representing a quadratic equation, which is standard form is as follows:
y = ax2 + bx + c
where the value of 'a' determines whether the parabola opens upwards of downwards (i.e., the parabola opens upwards if a>0 and opens downwards if a<0) and the axis of symmetry is given by the line x = -b/(2a).
The vertex form of a parabola's (or a quadratic) equations is given by the following formula:
y = a(x - h)2 + k , where (h, k) is the vertex and the axis of symmetry is given by the line x = h.
Given that the vertex is at (0, 3), then ..... h = 0 and k = 3 ..... thus,
y = a(x - 0)2 + 3
y = a(x)2 + 3
With a point at (-4, -45), then ..... x = -4 and y = -45 ..... therefore,
-45 = a(-4)2 + 3
-45 = a(16) + 3
Solve for a by first subtracting 3 from both sides of the equation then dividing both sides of the equation by 16:
-45 - 3 = a(16) + 3 - 3
-48 = a(16)
-48/16 = 16a/16
-3 = a
With a vertex (h, k) at (0, 3) and given that a = -3, then the equation of this parabola in vertex form is as follows:
y = a(x - h)2 + k
y = -3(x - 0)2 + 3
y = -3x2 + 3
Answer:
If an object moves along a straight line, the distance traveled can be represented by a distance-time graph. In a distance-time graph, the gradient of the line is equal to the speed of the object. The greater the gradient (and the steeper the line) the faster the object is moving.
Step-by-step explanation:
First, compute the mean:
Next compute the absolute deviations for each datapoint:
|75-95.555|=20.555
|89-95.555|=6.555
|145-95.555|=49.445
|85-95.555|=10.555
|80-95.555|=15.555
|92-95.555|=3.555
|104-95.555|=8.445
|90-95.555|=5.555
|100-95.555|=4.445
Next we'll take the mean of these deviations:
The mean absolute deviation of your data is 13.8517
Answer: While there are plenty of quality options on the shelves that fall between the $15 and $30 range, “trendy” olive oils like Brightland and Fat Gold cost more, at $37 and $44.75, respectively. Some even have price tags in the three digits.
Step-by-step explanation:
Answer:
777.5
Step-by-step explanation:
777.54418176347
