Here is my essay for math lesson 38:

**Rates with Zero**

**For what values are the following expressions equal to zero? For what values are they undefined?**

*a)* **t-15/t+4**

- t=15. If t=15, then the nominator would be equal to zero. The denominator will not matter as long as the nominator is zero, because when they are both divided, the answer will turn out to be zero.
- t=-4. It would not make sense if t=-4, because that would mean the denominator is zero, and there would be nothing to divide by. Here is an example:

**15mi/0sec**

- That would mean we would be someplace 15 miles away in the same instant. It doesn’t make sense. Therefore, it is undefined.

*b) ***8/x-3**

- You cannot do anything to the nominator, so it will never be equal to zero.
- x=3. The three would cancel out, and it would be undefined.

*c) ***p+100/18**

- p=-100. The 100 would go POOF, and the nominator would become zero.
- The denominator cannot be changed, so this equation can never be undefined.

**Rates of Change**

A rate is a quotient of two quantities.

**x2-x1/t2-t1**

Here is an example of what it would look like:

1.** 5 miles (x1) –> 12 miles (x2)**

** 12 mi.(x2) – 5 mi.(x1) = 7 mi.**

2. **0 hrs (t1) –> 3.5 hrs (t2)**

** 3.5 hrs (t2) – 0 hrs (t1) = 3.5 hrs**

3. Summary of what happened above: **x2 -x1, t2 -t1**.

Now we divide them:

4. **7 mi./3.5 hrs. = 2 mi/hr or 2mph or x2-x1/t2-t1**

I hope you find this helpful!

~Caitlin 📝📚

PS. this is in 8th grade math.

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Good job(even though I dont know what any of this means)!!!

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really? I thought I made it simple.

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