Rewriting the question, the given lengths that were cut from the board were 30 3/4 inches, 12 1/4 inches, and 16 1/4 inches. To obtain the remaining length of the board, all of the measurements cut are to be added and subtracted from 72 inches. This is shown below:
30 3/4 + 12 1/4 + 16 1/4 = 237/4 = 59.25 inches.
Remaining length of board = 72 - 59.25 = 12.75 inches.
Therefore, there will be 12.75 inches remaining of the board.
Answer:
so whats u r question
Step-by-step explanation:
Answer:
Step-by-step explanation:
If two values are inversely proportional, their product must be maintained. That way, if one value goes up, the other goes down by the same extent.
Therefore, if 
and 
vary inversely, their product will be the same for all values of 
and 
.
Let 
and 
as given in the problem. Substitute values:
Hence, the maintained product is 
.
Thus, we have the following equation:
Substitute 
to find the value of 
when :
Answer:
- f⁻¹(x) = (x + 1) / (x - 2)
- f⁻¹(1 ) = - 2
Step-by-step explanation:
<u>Given function:</u>
- f(x) = (2x + 1) / (x - 1)
<u>Find its inverse, substitute x with y and f(x) with x, solve for y:</u>
- x = (2y + 1) / (y - 1)
- x(y - 1) = 2y + 1
- xy - x = 2y + 1
- xy - 2y = x + 1
- y(x - 2) = x + 1
- y = (x + 1) / (x - 2)
<u>Substitute y with f⁻¹(x):</u>
- f⁻¹(x) = (x + 1) / (x - 2)
<u>Find f⁻¹(1 ):</u>
- f⁻¹(1 ) = ( 1 + 1) / (1 - 2) = 2 / - 1 = - 2
Answer:
f(-3) = -2
f(-2.6) = -2
f(0.6) = 2.4
f(4.5) = 8.5
Step-by-step explanation:
(Whole question:
Evaluate the piecewise function for the given values.
Find f(-3), f(-2,6), f(0.6), and f(4.5) for f(x)={ -2 If x ≤ 0 4x. If 0 <x <1. x + 4. If x ≥ 1)
As the piecewise function shows, the function f(x) has the value of -2 for values of x lesser or equal than 0, has the value of 4x if the value of x is between 0 and 1, and has the value of x+4 for values of x greater or equal than 1.
So, for f(-3), the value of x is lesser than 0, so we have that f(-3) = -2
For f(-2.6), the value of x is lesser than 0, so we have that f(-3) = -2
For f(0.6), the value of x is between 0 and 1, so we have that f(0.6) = 4*0.6 = 2.4
For f(4.5), the value of x is greater than 1, so we have that f(4.5) = 4.5 + 4 = 8.5
