1 Subtract
9
y
9y from both sides
4
x
=
6
3
−
9
y
4x=63−9y
2 Divide both sides by
4
4
x
=
6
3
−
9
y
4
x=
4
63−9y
3 Factor out the common term
9
9
x
=
9
(
7
−
y
)
4
x=
4
9(7−y)
Done
Answer:
18% if it is the rate of change.
0 if solved
Step-by-step explanation:
Sorry, but you need more information
The quadratic formula is:
and
Let's identify our a, b, and c values:
a: -1
b: 1
c: 12
Plug in the values for a, b, and c into the equation. Let's do the first equation:
Simplify everything in the radical:
Simplify the radical:
Combine like terms:
Simplify:
This is one solution, now, let's solve for the other equation:
Since when simplified, everything is the same except the subtraction sign, we can skip the simplification again and change the sign to subtraction:
Combine like terms:
Simplify:
Your final answers are:
Answer:
434,470 gallons
Step-by-step explanation:
The exponential equation for the volume v remaining after t hours can be written as ...
v(t) = (initial amount)×(decay factor)^(t/(decay time))
v(t) = 500,000×(1 -10%)^(t/3)
Then after 4 hours, the remaining volume is ...
v(4) = 500,000×(0.90^(4/3)) ≈ 434,470 . . . . gallons
_____
<em>Comment on the form of the equation</em>
The decay factor is related to the decay rate by ...
decay factor = 1 - (decay rate)
and the decay time is the time applicable to that decay rate. Here, the rate is 10% every 3 hours, so the decay time is 3 hours for a decay rate of 10%.