Answer:
t≈8.0927
Step-by-step explanation:
h(t) = -16t^2 + 128t +12
We want to find when h(t) is zero ( or when it hits the ground)
0 = -16t^2 + 128t +12
Completing the square
Subtract 12 from each side
-12 = -16t^2 + 128t
Divide each side by -16
-12/-16 = -16/-16t^2 + 128/-16t
3/4 = t^2 -8t
Take the coefficient of t and divide it by 8
-8/2 = -4
Then square it
(-4) ^2 = 16
Add 16 to each side
16+3/4 = t^2 -8t+16
64/4 + 3/4= (t-4)^2
67/4 = (t-4)^2
Take the square root of each side
±sqrt(67/4) =sqrt( (t-4)^2)
±1/2sqrt(67) = (t-4)
Add 4 to each side
4 ±1/2sqrt(67) = t
The approximate values for t are
t≈-0.092676
t≈8.0927
The first is before the rocket is launched so the only valid answer is the second one
Answer:
Step-by-step explanation:
we have

This is the equation of a vertical parabola open downward
The vertex represent a maximum
Convert the quadratic equation into vertex form
step 1
Factor -2

step 2
Complete the square


step 3
Rewrite as perfect squares
----> equation in vertex form
The vertex is the point (1,5)
Answer:
2.5
Step-by-step explanation:
Answer:
The third one, y=x-3
Step-by-step explanation:
A linear equation is any equation that can be written in the form. ax+b=0. Meaning it will not have a radical or be squared.
Answer:
y= (-6/5)x -2
Step-by-step explanation:
y=mx+b , where m is the slope, and b is the y -intercept
the y -intercept is where the line intersects the y-axis so b = -2
the slope m= y(rise) /x(run) = 6/-5 = -6/5 ( to find the slope you have to know how to get from any point on the line to another point on the same line; start at point (0,-2) go up 6(y-rise) and to the left 5(x-run) at point (-5,4))
y= (-6/5)x -2