Answer:
To determine the inverse of the given function, change f(x) to y, switch x and y and solve for y and f^-1(x)= ln(x+4)/2
Step-by-step explanation:
f(x) = e^2x - 4
to find the inverse let
y = e^2x - 4
Replace x and y
x = e^2y - 4
and now, solve to find value of y
x + 4 = e^2y
taking ln on both sides:
ln(x+4) = ln(e^2y)
ln(x+4) = 2y
=> y = ln(x+4)/2
=> f^-1(x)= ln(x+4)/2
So, To determine the inverse of the given function, change f(x) to y, switch x and y and solve for y and f^-1(x)= ln(x+4)/2
We have a question on motion with the elements of distance, time taken and speed.
This question in particular is asking us for distance per unit time (in this case, hours).
We are required to find out how much distnace is covered in on hour and our approach will be as follows:

This right here just tells us that 4 hours, Madeline covered 180 miles and since her rate was constant (equal distances in equal times), then she also covered 45 miles in an hour.
Now we plot our number line.
Answer:
feet tall
Step-by-step explanation:
Ajax is "5 and 1 fourth feet tall", which can be written as the mixed number
.
His sister is "3 eighths foot shorter", so she's 3/8 feet shorter than 5 1/4.
So, this is just a subtraction problem:

To solve this, we want to convert 5 1/4 into an improper fraction, which is:
. Now, we want to find a common denominator. In this case, that common denominator is 8, so
.
Finally, we subtract 3/8 from 42/8:
. So, Ajax's sister is 39/8 feet. Converting this into a mixed number, we have: 39/8 = 4
.
Therefore, Ajax's sister is
feet tall.
Hope this helps!
Here ya go!!! this should be correct
Answer:
<h2>5x-18</h2>
Step-by-step explanation:
lets simplify!
(3x+5)+(2x-9)-14
combine like terms..
5x+ -4 - 14
subtract numbers without exponents
therefore, the answer is
5x-18
hope this helps:)