A newly drilled water well produces 50,000 quarts of water per week. With no new water feeding the well, the production drops by
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Answer:
The true statements about the graph of the function are:
The range of the function is {y : y ≤ 6} ⇒ 2nd
The function is increasing over the interval (–∞ , –2) ⇒ 3rd
The function has a positive y-intercept ⇒ 5th
Step-by-step explanation:
* Lets explain how to solve the problem
- The function f(x) = -x² - 4x + 2 is a quadratic function represented
graphically by a downward parabola with maximum vertex
∵ The form of the quadratic function is f(x) = ax² + bx + c
∵ The coordinates of the vertex of the parabola are (h , k) where
h = -b/2a and k = f(h)
∵ a = -1 , b = -4
∴ h = -(-4)/2(-1) = 4/-2 = -2
∵ k = f(h)
∴ k = -(-2)² - 4(-2) + 2 = -(4) - (-8) + 2
∴ k = -4 + 8 + 2 = 6
∴ The vertex of the parabola is (-2 , 6)
* Look to the attached figure to find the true statements
∵ The greatest value of the function is 6 ⇒ y-coordinate of the vertex
∵ The range of the function is the values y-coordinates of the points
on the parabola
∴ The range of the function is {y : y ≤ 6}
- The domain of the function is {x : x ∈ R} or (-∞ , ∞)
∵ The value of y increasing after -∞ to the x-coordinate of the vertex
∵ x-coordinate of the vertex is -2
∴ The function is increasing over the interval (–∞ , –2)
- The parabola intersect the y-axis at point (0 , 2)
∵ The y-intercept is the intersection between the parabola and the
y-axis
∵ The parabola intersect the y-axis at point (0 , 2)
∴ The y-intercept is 2
∴ The function has a positive y-intercept
I found a similar problem to your problem here, which is shown in the attached picture. So, from the picture, we have to find the equation for the red line. All we have to do is find two points of the line. That would be: Point 1(2,0) and Point 2(-2,3). The general equation would be:
y - y₁ = (y₂-y₁)/(x₂ - x₁) * (x - x₁)
Substituting the coordinates to the equation,
y - 0 = (3-0)/(-2 - 2) * (x - 2)
y = -3(x -2)/4
Rearranging,
<em>4y = -3x + 6 or 4y + 3x = 6</em>
y - y₁ = (y₂-y₁)/(x₂ - x₁) * (x - x₁)
Substituting the coordinates to the equation,
y - 0 = (3-0)/(-2 - 2) * (x - 2)
y = -3(x -2)/4
Rearranging,
<em>4y = -3x + 6 or 4y + 3x = 6</em>
Answer:
The co variance of the midterm and final exam scores is 58.76.
Step-by-step explanation:
The formula to compute the sample co variance is:
The values are computed in the table below.
Compute the co variance as follows:
Thus, the co variance of the midterm and final exam scores is 58.76.
