Answer:
39 years
Step-by-step explanation:
Adapt the formula A = P(1 + r)^n, letting P represent the original population, r the growth rate as a decimal fraction, and n the number of years.
Solve this for n:
2 billion = (1.353 billion)(1 + 0.01)^n
After simplification, we have:
2
--------- = 1.01^n
1.353
Taking the log of both sides, we get:
log 2 - log 1.353 = n log 1.01, or
log 2 - log 1.353 0.1697
------------------------ = -------------- = 39 years (rounded off from 39.28)
log 1.01 0.0043
The answers in C are inverses of each other.
In order to find the inverse of any equation, you simply switch the x and f(x) values and then solve for the new f(x). What it will result in is your new inverse function. If we do this for each of the problems above, only one will produce the second equation properly. See the work below for how to do it for C.
f(x) = 11x - 4 ---> Switch the x and f(x)
x = 11f(x) - 4 ----> Add 4 to both sides
x + 4 = 11f(x) ----> Divide both side by 11
= f(x) ----> Now put in the correct order
f(x) =
Since our inverse matches the g(x) function, this means that C is the correct answer.
Answer:
y=-1/4x+8
Step-by-step explanation:
To find the equation of a line that is perpendicular to a line, you would take the opposite reciprocal of the slope.
Before that, we need to change the equation into slope-intercept form.
-4x+y=10
y=4x+10
The opposite reciprocal of the slope is -1/4.
Now, let's use the point-slope formula to find our equation of the line that passes through (-4,9).
y-y1=m(x-x1)
y-9=-1/4(x-(-4))
y-9=-1/4x-1
y=-1/4x+8
Amount of fuel in the tank before the story begins . . . . . zero.
Total amount poured in . . . . . 3/4 gallon.
Total amount burned:
on Friday . . . . . 1/4 gallon
on Sunday . . . . 1/4 gallon
Total used . . 1/2 gallon .
Amount remaining in the tank on Monday:
(3/4 gallon in) - (1/2 gallon burned) = 1/4 gallon left.
==> NOT empty
The tank would have been empty on Monday IF Becky
had poured in only 1/2 gallon, instead of 3/4 of a gallon
before the first flakes began to fly.
40.6 is the answer to the problem
