Answer: The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.
Step-by-step explanation:
<h3>Answer:</h3>
y = -3(x -2)² -5
<h3>Explanation:</h3>
The equation of a parabola with vertex (h, k) is given by ...
... y = a(x -h)² +k . . . . . . . for some vertical scale factor "a".
We can find the value of "a" by substituting the coordinates of a point that is not the vertex. Here, that point is the y-intercept: (0, -17).
... y = a(x -2)² -5 . . . . . initial form of the equation for the parabola
... -17 = a(-2)² -5 . . . . . substitute y-intercept values
... -12 = 4a . . . . . . . . . . add 5, simplify
... -12/4 = a = -3
The desired equation is ... y = -3(x -2)² -5.
By definition, a rectangle is a quadrilateral (4-sided polygon) containing two sets of equal and parallel sides called the length and the width. For determining the area of a rectangle, you simply have to multiply length times width. In this problem, let L be the length and W be the width. Then, we formulate the two independent formulas: formula for area, and formula relating L and W
A = LW = 33
L = 2W-5
Substituting the second equation to the first,
A = 33 = (2W - 5)W
33 = 2W² - 5W
2W² - 5W -33 = 0
W = 5.5 and -3
Since the equation is quadratic, there are two possible roots: 5.5 and -3. However, we can only use the positive value. Thus, W=5.5 m. Consequently,
L = 2(5.5)-5
L = 6 m
Therefore, the dimensions of the rectangle is 6 m by 5.5 m.