(2x-3)^2 - (3x-2)^2
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Let's start with 22-C!
To figure out the problem, let's establish what it's asking. It wants to know the one time fee of using the trash dumpster. Your teacher may have taught you a better way to do this, but I'll show you how to solve it via logic.
We first need to set up a basic equation. X will be the unknown fee, 195 will act as the total, and 9(15) will represent the remaining cash (you get this from 15$ an hour for 9 hours).
The equation should look something like this:
x + 9(15) = 195 OR (simplified) x + 135 = 195.
At this point we can solve it like a regular equation. Subtract 135 on both sides:
x = 60. Therefore, the fee for using the dumpster is 60$.
Now we can move on to 23-A & B!
First, let's go over 2 basics: point slope formula and slope intercept.
Point slope formula: <em>y - y</em>
Slope intercept: <em>y = mx + b</em>
We know that .5 is the slope because it's dependent on an amount of time (or dependent in general). 64 can be used as y1 and 48 as x1.
The formula would be: y - 64 = .5(x - 48).
As for part B, we plug in the same numbers! We've previously found that .5 is the slope (m) and it appears you already know that the y-intercept (b) is 40. Plug it in like so:
y = .5x + 40
All of the answers are bolded, I hope this helped!