Here we are given the x intercepts at x=3 and x=9
So let us try to make quadratic equation for this using given information.
We have factors in the form (x-a)(x-b)
where a and b are x intercepts given to us.
So rewriting in factored form:

Now let us simplify it:

Let us find the vertex now,
For a quadratic equation of the form:

For x coordinate , we have the formula,

So using this formula for our equation,

So x = 6
Answer: The x-coordinate of the parabola's vertex is 6.
Answer:
See solutions for detail.
Step-by-step explanation:
a.
is the instantaneous rate of change of volume given with respect to time, t.
The volume's rate of change is written as a function of time.
-
is the rate of change in the height of water in the tank with respect to time, t.
b.
is the only constant. Water flows into the constant at a constant rate, say
per minute.
c.
is positive. Volume water in the take is increasing from time to time.
-The volume at time t=1 is greater than the volume at t=0, hence, it's a positive rate of change.
d.
is a positive rate. The initial height of water in the tank is zero.
-The final height at time t is 0.25h. The height is increasing with time.
Hence, it is positive.
Answer:
Time required by Machine B to create a widget = 4 hours
Step-by-step explanation:
Time taken by Machine A (
) = 3 hours
Time taken by Machine B (
)= x hours
Time taken by both machines by working together = 12 hours
The time required to both machines by working together to finish a task is given by the formula = 
Put the values in above formula we get
⇒ T = 
⇒ 12 = 
⇒ 36 + 12 x = 3 x
⇒ x = - 4 hours
This is the time required by Machine B to create a widget.