John has about 1.09 m of rope.
31 cm is 0.31 m
soo 0.33 + 0.45 + 0.31 = 1.09
Answer: f^{-1}(x) = 3-x/3
Step-by-step explanation: Let y = f(x) and rearrange making x the subject, that is...
1. y = - 3x + 3 ( add 3x to both sides )
2. 3x + y = 3 ( subtract y from both sides )
3. 3x = 3 - y ( divide both sides by 3 )
4. x = 3-y/3
Change x back into terms of y
f^{-1}(x) = 3-x/3
Answer:
I invested $ 10,000 at 7% per year, and $ 1,000 at 3% per year.
Step-by-step explanation:
Given that I invested $ 11,000 in two accounts paying 3% and 7% annual interest, respectively, if the total interest earned for the year was $ 730, to determine how much was invested at each rate, the following calculation must be performed:
5,000 x 0.07 + 6,000 x 0.03 = 530
8,000 x 0.07 + 3,000 x 0.03 = 650
10,000 x 0.07 + 1,000 x 0.03 = 730
Therefore, I invested $ 10,000 at 7% per year, and $ 1,000 at 3% per year.
There's some unknown (but derivable) system of equations being modeled by the two lines in the given graph. (But we don't care what equations make up these lines.)
There's no solution to this particular system because the two lines are parallel.
How do we know they're parallel? Parallel lines have the same slope, and we can easily calculate the slope of these lines.
The line on the left passes through the points (-1, 0) and (0, -2), so it has slope
(-2 - 0)/(0 - (-1)) = -2/1 = -2
The line on the right passes through (0, 2) and (1, 0), so its slope is
(0 - 2)/(1 - 0) = -2/1 = -2
The slopes are equal, so the lines are parallel.
Why does this mean there is no solution? Graphically, a solution to the system is represented by an intersection of the lines. Parallel lines never intersect, so there is no solution.
