ANSWER
b=1, c=81, and d=9.
EXPLANATION
The given function is:
This function is the same as:
To find the inverse of this function, we interchange x and y.
Solve for y:
Take square root of both sides:
Hence,
b=1, c=81, and d=9.
The first one and the second one are the correct sums
<em>a</em> = 8 - a train arrives at the station once every 8 minutes, so for any given 8 minute interval, a randomly selected train has uniform probability of arriving at the station at some point in this time.
<em>f(x)</em> = 1/8 - the area under the graph of <em>f(x)</em> must be equal to 1. This area corresponds to a rectangle with length <em>a</em> = 8 and height <em>x</em> such that 8<em>x</em> = 1. Solving for <em>x</em> gives 1/8.
<em>P</em> = 5/8 - this is equal to the area under the graph over the interval [0, 5], which is the area of a rectangle with length 5 and height 1/8.
There are 5 options. Let's figure out which ones are wrong, and why:
<span>y + y + y = y(1 + 1 + 1)
This one is correct, because of the distributive property. Another equivalent is 3y.
2a + 2b = 4ab
This one is incorrect, as you are not multiplying the numbers.
3 · (2 + x) = 6 + 3x
This one is correct, because of the distributive property
2t + 3t = 5t
This is correct, as you can add variables together as long as all the variables are the same
x + 3 = 4x
This is not correct, as 4x is 4 x's.
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