Complete the square:
F(x) = -3x² - 6x - 5
F(x) = -3 (x² + 2x) - 5
F(x) = -3 (x² + 2x + 1 - 1) - 5
F(x) = -3 ((x + 1)² - 1) - 5
F(x) = -3 (x + 1)² + 3 - 5
F(x) = -3 (x + 1)² - 2
The y-intercept has x-coordinate equal to 0, so it corresponds to the value of F(0) :
F(0) = -3 (0 + 1)² - 2 = -3 - 2 = -5
The axis of symmetry is the vertical line running through the vertex of this parabola, so we'll come back to this.
The vertex of the parabola is (-1, -2). This represents the maximum value of F(x), which follows from
(x + 1)² ≥ 0 ⇒ -3 (x + 1)² ≤ 0 ⇒ -3 (x + 1)² - 2 ≤ -2
This is to say, every point on the parabola has a y-coordinate no greater than -2.
As mentioned earlier, the axis of symmetry is the vertical line through the vertex, and its equation is determined by the x-coordinate of the vertex. Hence the AoS is the line x = -1.
v varies directly with height means
v/h=k were k is a constant
or also h/v=k where k is a constant (this is a different k than previous)
so if h=12 and v=300 then
h/v=12/300=1/25=k
so the relationhip could be h/v=1/25
if you di v/h, then
v/h=300/12=25/1=25=k
so the relationship could be v/h=25
1/3 + 7x = 1/3 + 7(5 )=
1/3+35
=1/3 + 105/3 =
106/3=
35 1/3
Step-by-step explanation:
2x/3 - x/3 = x/3
they both have the same denominators (number at the bottom of the fraction) so all you have to do it subtract the numerators (top of the fraction) together. 2x-x =x, that's why it's x on the numerator for the answer
hope this helps
