well, the sequence goes, 1100, to 1135, to 1170.... notice, is simply adding 35 to get the next term, so the common difference is 35, and the first term is 1100 of course.
![\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=1100\\ d=35\\ a_n=3725 \end{cases} \\\\\\ 3725=1100+(n-1)35\implies 3725=1100+35n-35 \\\\\\ 3725=1065+35n\implies 2660=35n\implies \cfrac{2660}{35}=n\implies 76=n](https://tex.z-dn.net/?f=%5Cbf%20n%5E%7Bth%7D%5Ctextit%7B%20term%20of%20an%20arithmetic%20sequence%7D%0A%5C%5C%5C%5C%0Aa_n%3Da_1%2B%28n-1%29d%5Cqquad%0A%5Cbegin%7Bcases%7D%0An%3Dn%5E%7Bth%7D%5C%20term%5C%5C%0Aa_1%3D%5Ctextit%7Bfirst%20term%27s%20value%7D%5C%5C%0Ad%3D%5Ctextit%7Bcommon%20difference%7D%5C%5C%5B-0.5em%5D%0A%5Chrulefill%5C%5C%0Aa_1%3D1100%5C%5C%0Ad%3D35%5C%5C%0Aa_n%3D3725%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0A3725%3D1100%2B%28n-1%2935%5Cimplies%203725%3D1100%2B35n-35%0A%5C%5C%5C%5C%5C%5C%0A3725%3D1065%2B35n%5Cimplies%202660%3D35n%5Cimplies%20%5Ccfrac%7B2660%7D%7B35%7D%3Dn%5Cimplies%2076%3Dn)
Cheyenne sells 7.1428% of her cards at the craft fair. I hope this helps you!
Answer:
The Slope is
![slope=m=\dfrac{-5}{4}](https://tex.z-dn.net/?f=slope%3Dm%3D%5Cdfrac%7B-5%7D%7B4%7D)
The Equation is
Step-by-step explanation:
Two Point Form
Given:
Let,
point A( x₁ , y₁) ≡ ( 0 ,-1)
point B( x₂ , y₂ )≡ (-4 , 4)
To Find:
Equation of Line AB =?
Solution:
![slope=m=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} }](https://tex.z-dn.net/?f=slope%3Dm%3D%5Cdfrac%7By_%7B2%7D-y_%7B1%7D%20%7D%7Bx_%7B2%7D-x_%7B1%7D%20%7D)
Substituting the point A( x₁ , y₁) ≡ ( 0 ,-1) and B( x₂ , y₂ )≡ (-4 , 4) we get
![slope=m=\dfrac{4--1}{-4-0}=\dfrac{5}{-4}=\dfrac{-5}{4}](https://tex.z-dn.net/?f=slope%3Dm%3D%5Cdfrac%7B4--1%7D%7B-4-0%7D%3D%5Cdfrac%7B5%7D%7B-4%7D%3D%5Cdfrac%7B-5%7D%7B4%7D)
Equation of a line passing through a points A( x₁ , y₁) and point B( x₂ , y₂ ) is given by the formula Two -Point Form,
Now on substituting the slope and point A( x₁ , y₁) ≡ ( 0 ,-1) and B( x₂ , y₂ )≡ (-4 , 4) we get
![(y--1})=\dfrac{4--1}{-4-0}\times (x-0)](https://tex.z-dn.net/?f=%28y--1%7D%29%3D%5Cdfrac%7B4--1%7D%7B-4-0%7D%5Ctimes%20%28x-0%29)
OR
Equation of a line passing through a points A( x₁ , y₁) and having slope m is given by the formula,
i.e equation in point - slope form
Substituting the values we get
Answer:
It is a Right angle triangle ,
So, Apply Pythagoras Theorem ,
![y = \sqrt{ {2x}^{2} + {(x + 3)}^{2} }](https://tex.z-dn.net/?f=y%20%3D%20%20%5Csqrt%7B%20%7B2x%7D%5E%7B2%7D%20%20%2B%20%20%7B%28x%20%2B%203%29%7D%5E%7B2%7D%20%7D%20)
![y = \sqrt{4 {x}^{2} + {x}^{2} + 3 + 6x }](https://tex.z-dn.net/?f=y%20%3D%20%20%5Csqrt%7B4%20%7Bx%7D%5E%7B2%7D%20%2B%20%20%7Bx%7D%5E%7B2%7D%20%2B%203%20%2B%206x%20%20%7D%20)
![y = \sqrt{5 {x}^{2} + 6x + 9}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Csqrt%7B5%20%7Bx%7D%5E%7B2%7D%20%20%2B%206x%20%2B%209%7D%20)
<h3>Now put X =2 </h3>
![y = \sqrt{5 \times 4 + 6 \times 2 + 9}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Csqrt%7B5%20%5Ctimes%204%20%2B%206%20%5Ctimes%202%20%2B%209%7D%20)
![y = \sqrt{41}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Csqrt%7B41%7D%20)
<h2>Hope it helps you...</h2>
Answer: The answer is: 3x^{3} -5x^{2} +10x -10 + {7}{x + 1}