<h3>
Answer: Choice A</h3>
The graph has <u>no</u> vertical asymptote
===========================================================
Explanation:
Let's simplify the function by factoring each piece.
![f(x) = \frac{x^2-64}{8x-64}\\\\f(x) = \frac{(x-8)(x+8)}{8x-64}\\\\f(x) = \frac{(x-8)(x+8)}{8(x-8)}\\\\f(x) = \frac{x+8}{8}\\\\](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7Bx%5E2-64%7D%7B8x-64%7D%5C%5C%5C%5Cf%28x%29%20%3D%20%5Cfrac%7B%28x-8%29%28x%2B8%29%7D%7B8x-64%7D%5C%5C%5C%5Cf%28x%29%20%3D%20%5Cfrac%7B%28x-8%29%28x%2B8%29%7D%7B8%28x-8%29%7D%5C%5C%5C%5Cf%28x%29%20%3D%20%5Cfrac%7Bx%2B8%7D%7B8%7D%5C%5C%5C%5C)
In the 2nd step, I used the difference of squares rule to factor the numerator. In the 4th step, the (x-8) terms cancel.
The simplified version doesn't have any variables in the denominator. This indicates the denominator is always 8, and never 0. So it's impossible to divide by zero in this simplified form. Consequently it means this graph <u>has no vertical asymptotes.</u>
However, there is a hole at x = 8 because this input causes a division by zero error in the original non-simplified function. Why? Because the calculator will use PEMDAS to evaluate the expression after replacing every copy of x with 8. It likely won't attempt to simplify like shown in the steps above. This is what causes the hole at x = 8.
The value x = -8 is perfectly fine in either the original function or the simplified one. It doesn't cause the denominator to be zero.
Answer:
If so, there are two numbers less than 3: 1 and 2. There are 6 total possible results, so the probability of rolling a number less than 3 is 2/6 or 1/3 or 0.3333
Step-by-step explanation:
<h2>
Explanation:</h2><h2>
</h2>
As I understand the question you have the following expressions given in scientific notation:
<u>Expression A:</u>
<u></u>
<u></u>
<u></u>
<u></u>
<u>Expression B:</u>
<u></u>
<u></u>
<u></u>
<u></u>
So we need to compare both expression in order to know how much times is expression A bigger than B. So:
![\frac{9\times 10^2}{3\times 10^{-2}}=\frac{9}{3}\times10^{2-(-2)}=3\times 10^4=30,000 \\ \\ \\ *\frac{a^n}{b^m}=a^{n-m}](https://tex.z-dn.net/?f=%5Cfrac%7B9%5Ctimes%2010%5E2%7D%7B3%5Ctimes%2010%5E%7B-2%7D%7D%3D%5Cfrac%7B9%7D%7B3%7D%5Ctimes10%5E%7B2-%28-2%29%7D%3D3%5Ctimes%2010%5E4%3D30%2C000%20%5C%5C%20%5C%5C%20%5C%5C%20%2A%5Cfrac%7Ba%5En%7D%7Bb%5Em%7D%3Da%5E%7Bn-m%7D)
In conclusion
is
times as much as ![3\times10^{-2}](https://tex.z-dn.net/?f=3%5Ctimes10%5E%7B-2%7D)
This is actually good, because it helps improvement more. They may do a ¨good¨ landing, but there could still be flaws. Due to my own experiences in reacting to criticism and praise, praise will make you calm down, and think you are perfect, making you more lazy the second time you do it, thinking it will all be okay. Criticism toughens you up, and helps you do better everytime you do what you do.