the function f(x) = 4(x+3) − 5
Lets find the inverse function f^-1(x)
step 1: Replace f(x) with y
y = 4(x+3) − 5
step 2: Replace x with y and y with x
x = 4(y+3) - 5
step 3: Solve for y
x = 4(y+3) - 5
x = 4y +12 -5
x= 4y + 7 (subtract 7 on both sides)
x - 7 = 4y (divide by 4 on both sides)
Given : x = 3
We plug in 3 for x in the inverse function
= -1
the inverse function when x = 3 is -1
To dig the pool, he rents a small backhoe for $95.50 a day. If his total bill comes to $286.50, for 3 days does he rent the backhoe.
What is backhoe?
A backhoe, also known as a rear actor or back actor, is a type of digging apparatus, often known as a digger, that has a digging bucket attached to the end of a two-part articulated arm. Usually, it is attached to the rear of a tractor or front loader, the latter of which is known as a "backhoe loader."
$286.50/$95.50= 3
Henry is building an in-ground pool at his house. He is doing most of the work himself to save money. To dig the pool, he rents a small backhoe for $95.50 a day. If his total bill comes to $286.50, for 3 days does he rent the backhoe.
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Answer:
Step-by-step explanation:
2y+3=5x-18
2y+21 = 5x
x = ⅖y + 21/5
Answer:
The y-coordinates are the same
Step-by-step explanation:
Answer:
rate of the plane in still air is 33 miles per hour and the rate of the wind is 11 miles per hour
Step-by-step explanation:
We will make a table of the trip there and back using the formula distance = rate x time
d = r x t
there
back
The distance there and back is 264 miles, so we can split that in half and put each half under d:
d = r x t
there 132
back 132
It tells us that the trip there is with the wind and the trip back is against the wind:
d = r x t
there 132 = (r + w)
back 132 = (r - w)
Finally, the trip there took 3 hours and the trip back took 6:
d = r * t
there 132 = (r + w) * 3
back 132 = (r - w) * 6
There's the table. Using the distance formula we have 2 equations that result from that info:
132 = 3(r + w) and 132 = 6(r - w)
We are looking to solve for both r and w. We have 2 equations with 2 unknowns, so we will solve the first equation for r, sub that value for r into the second equation to solve for w:
132 = 3r + 3w and
132 - 3w = 3r so
44 - w = r. Subbing that into the second equation:
132 = 6(44 - w) - 6w and
132 = 264 - 6w - 6w and
-132 = -12w so
w = 11
Subbing w in to solve for r:
132 = 3r + 3(11) and
132 = 3r + 33 so
99 = 3r and
r = 33
