Answer:
To find f-¹(x) of f(x) equate f(x) to y
That's
f(x) = y
So we have
Next interchange the variables that's x becomes y and y becomes x
That's
Next make y the subject
Cross multiply
We have
4y - 7 = 10x
Move -7 to the right side of the equation
4y = 10x + 7
Divide both sides by 4
We have the final answer as
So
Hope this helps you
Answer:
The sum of the first 37 terms of the arithmetic sequence is 2997.
Step-by-step explanation:
Arithmetic sequence concepts:
The general rule of an arithmetic sequence is the following:
In which d is the common diference between each term.
We can expand the general equation to find the nth term from the first, by the following equation:
The sum of the first n terms of an arithmetic sequence is given by:
In this question:
We want the sum of the first 37 terms, so we have to find 
Then
The sum of the first 37 terms of the arithmetic sequence is 2997.
Answer:
Rate of change = -12
Step-by-step explanation:
y − 3 = −12(x + 4)
Expanding, we have;
y - 3 = -12x - 48
y = -12x - 48 + 3
y = -12x - 45
Now, formula for rate of change is;
Rate of change = (y(x + h) - y)/h
y(x + h) is; y = -12(x + h) - 45
This gives;
Rate of change = (-12(x + h) - 45 + 12x + 45)/h
Rate of change = (-12x - 12h - 45 + 12x + 45)/h
Rate of change = -12h/h
Rate of change = -12
Answer:
A rectangle is defined by its length = L, and its width = W.
So the perimeter of the of the rectangle can be written as:
Perimeter = 2*L + 2*W.
In this case, we want to leave the perimeter fixed, so we have:
24ft = 2*L + 2*W.
Now, we do not have any other restrictions, so to know the different dimensions now we can write this as a function, by isolating one of the variables.
2*L = 24ft - 2*W
L = 12ft - W.
or:
L(W) = 12ft - W.
Such that:
W must be greater than zero (because we can not have negative or zero width).
And W must be smaller than 12ft (because in that case we would have zero or negative length)
Then the possible different dimensions are given by:
L(W) = 12ft - W
0ft < W < 12ft.
