Answer:
m=rise over run
so it would be ![\frac{2}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B5%7D)
Step-by-step explanation:
Answer:
Where’s the graph?
Step-by-step explanation:
Answer:
x²y²+xy²+3+xy+2y²
Step-by-step explanation:
(2x²y²+x²y+xy²+3)-(x²y²+x²y²+x²y-xy-2y²)
1. remove the parentheses (when there’s - in front of an expression in parentheses change the sign of each term of the expression)
2x²y² + x²y + xy² + 3-x²y² - x²y² - x²y + xy - 2y²
2. eliminate the opposites
2x²y² + xy² + 3 -x²y² + xy +2y²
3. collect like terms
x²y² + xy² + 3 + xy + 2y²
Answer:
![h(t)=-6(t-2)^2+24](https://tex.z-dn.net/?f=h%28t%29%3D-6%28t-2%29%5E2%2B24)
Step-by-step explanation:
Given function:
![h(t)=-6t^2+24t](https://tex.z-dn.net/?f=h%28t%29%3D-6t%5E2%2B24t)
where:
- h = height (in feet)
- t = times (in seconds)
Rewrite in the form ![h(t)=a(t-h)^2+k](https://tex.z-dn.net/?f=h%28t%29%3Da%28t-h%29%5E2%2Bk)
The quickest way to do this is to expand
and compare coefficients with the original function.
![\begin{aligned}h(t)& =a(t-h)^2+k\\ & = at^2-2aht+ah^2+k\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dh%28t%29%26%20%3Da%28t-h%29%5E2%2Bk%5C%5C%20%26%20%3D%20at%5E2-2aht%2Bah%5E2%2Bk%5Cend%7Baligned%7D)
Comparing coefficients with ![h(t)=-6t^2+24t](https://tex.z-dn.net/?f=h%28t%29%3D-6t%5E2%2B24t)
![\begin{aligned}\implies at^2& =-6t^2\\ a &=-6\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20at%5E2%26%20%3D-6t%5E2%5C%5C%20a%20%26%3D-6%5Cend%7Baligned%7D)
![\begin{aligned}\implies -2aht & =24t\\ -2(-6)ht& =24t\\ 12ht & = 24t\\ 12h & = 24\\ h & = 2\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20-2aht%20%26%20%3D24t%5C%5C%20-2%28-6%29ht%26%20%3D24t%5C%5C%2012ht%20%26%20%3D%2024t%5C%5C%2012h%20%26%20%3D%2024%5C%5C%20h%20%26%20%3D%202%5Cend%7Baligned%7D)
![\begin{aligned}\implies ah^2+k & = 0\\(-6)(2)^2+k &=0\\ -24+k & =0\\ k &=24 \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20ah%5E2%2Bk%20%26%20%3D%200%5C%5C%28-6%29%282%29%5E2%2Bk%20%26%3D0%5C%5C%20-24%2Bk%20%26%20%3D0%5C%5C%20k%20%26%3D24%20%5Cend%7Baligned%7D)
Therefore, substituting the found values into the equation:
![h(t)=-6(t-2)^2+24](https://tex.z-dn.net/?f=h%28t%29%3D-6%28t-2%29%5E2%2B24)