Answer:
The new amount is 36
Step-by-step explanation:
we know that
100%+20%=120%
Let
x-----> the new amount
The number 30 represent the 100%
so
by proportion
30/100%=x/120%
x=120*30/100=36
Let f(x) = p(x)/q(x), where p and q are polynomials and reduced to lowest terms. (If p and q have a common factor, then they contribute removable discontinuities ('holes').)
Write this in cases:
(i) If deg p(x) ≤ deg q(x), then f(x) is a proper rational function, and lim(x→ ±∞) f(x) = constant.
If deg p(x) < deg q(x), then these limits equal 0, thus yielding the horizontal asymptote y = 0.
If deg p(x) = deg q(x), then these limits equal a/b, where a and b are the leading coefficients of p(x) and q(x), respectively. Hence, we have the horizontal asymptote y = a/b.
Note that there are no obliques asymptotes in this case. ------------- (ii) If deg p(x) > deg q(x), then f(x) is an improper rational function.
By long division, we can write f(x) = g(x) + r(x)/q(x), where g(x) and r(x) are polynomials and deg r(x) < deg q(x).
As in (i), note that lim(x→ ±∞) [f(x) - g(x)] = lim(x→ ±∞) r(x)/q(x) = 0. Hence, y = g(x) is an asymptote. (In particular, if deg g(x) = 1, then this is an oblique asymptote.)
This time, note that there are no horizontal asymptotes. ------------------ In summary, the degrees of p(x) and q(x) control which kind of asymptote we have.
I hope this helps!
Answer:
(3) y = 4x
Step-by-step explanation:
In order for the equation not to change, the point (0, 0) must be on the original line and so on the line after dilation. The only equation with (0, 0) as a point on the line is y=4x.
Dilation about the origin moves all points away from the origin some multiple of their distance from the origin. If a point is on the origin, it doesn't move. We call that point the "invariant" point of the transformation. For the equation of the line not to change, the invariant point must be on the line to start with.
Answer:
Rounding to the nearest minute, it would take 95 minutes, or 1 hour and 35 minutes.
Step-by-step explanation:
Let's convert each time to minutes:
3.2 hours = 192 minutes
80 minutes = 80 minutes
2 hr 20 min = 140 minutes
Next, let's find the least common multiple:
LCM(192, 80, 140) = 6720
So let's say the volume of the tank is 6720 units. The speed of each pump is therefore:
Pump 1 = 6720 units / 192 minutes = 35 units/minute
Pump 2 = 6720 units / 80 minutes = 84 units/minute
Pump 3 = -6720 units / 140 minutes = -48 units/minute
Their combined speed is:
35 + 84 − 48 = 71 units/minute
So the time to fill the tank is:
6720 units / (71 units/minute) = 94.65 minutes
Rounding to the nearest minute, it would take 95 minutes, or 1 hour and 35 minutes.
First you subtract 6 from both sides to get:
4h=24
Then divide by 4:
h=6
With these problems, use the steps of either
PEDMAS, or <em></em>Please Excuse My Dear Aunt Sally.
the P stands for Parenthesis, the E for exponents, the M for multiplication, the D for division, the A for addition, and the S for subtraction
