Answer:
Option A. x < -4
Step-by-step explanation:
The given function is f(x) = -(x + 6)(x + 2)
General form of the function will be,
f(x) = -(x² + 2x + 6x + 12)
= -(x² + 8x + 12)
Vertex form of the function will be,
f(x) = -[x² + 2(4)x + 12]
= -[(x² + 2(4)x + 16) - 16 + 12]
= -(x + 4)² + 4
Therefore, parabola for the function above will open down with vertex (-4, 4) as shown in the graph attached.
Graph shows the function is increasing in x < -4 and decreasing in x > -4.
Therefore, Option A. is the correct answer.
Answer:
Step-by-step explanation:
The x-intercept exists when y = 0; the coordinate that results from our x-intercept is (4, 0).
The y-intercept exists when x = 0; the coordinate that results from our y-intercept is (0, -2).
We can use these 2 coordinates to find the slope of the line we need to write:
Now we can use that slope along with one of our points to write the equation of the line. I am going to use the point-slope form, then we will solve it for y to put it into slope-intercept. Let's use the coordinate (4, 0). Keep in mind that regardless of which point we choose to use to write our equation, we will get the same equation.
y - 0 = 1/2(x - 4) and
y = 1/2x - 2
That's your equation!
Answer:
x = 1/2
Step-by-step explanation:
6x - 8 + 4x = -6x
10x - 8 = -6x
16x = 8
x = 8/16
x = 1/2
The ounce per cost of the tomato sauce is: $0.04 per ounce
Answer:
W = 21.44*10⁶J
Step-by-step explanation:
Given
y = x² (0 < x < 4)
γ = 10000 N/m³
W = ?
If we apply
y = 4² = 16 = h
y = x² ⇒ x = √y
then
V = π*(√y)²*dy = π*y*dy
W = (γ*V) *(16-y) = γ*π*y*dy*(16-y)
⇒ W = γ*π*∫y*(16-y)dy = γ*π*(8y²-(y³/3))
finally we obtain (0 < y < 16)
W = γ*π*(8y²-(y³/3)) = 10000*π*(8*16²-(16³/3)) = 21.44*10⁶J
