Irresponsible. The responsible thing to do would to be first and formost only using a credit card for small, quick purchases that you could pay back immediately as the bill arrives. Paying the minimum payment and dragging it out for weeks can and will deplete your credit score and will make you pay more in interest.
Part a.
We have
![a_n = a_1 r^{n-1}](https://tex.z-dn.net/?f=a_n%20%3D%20a_1%20r%5E%7Bn-1%7D)
![a_3 = a_1 r^2 = -27](https://tex.z-dn.net/?f=a_3%20%3D%20a_1%20r%5E2%20%3D%20-27)
![a_5 = a_1 r^4 = -162](https://tex.z-dn.net/?f=a_5%20%3D%20a_1%20r%5E4%20%3D%20-162)
Dividing,
![r^2 = \dfrac{-162}{-27} = 6](https://tex.z-dn.net/?f=r%5E2%20%3D%20%5Cdfrac%7B-162%7D%7B-27%7D%20%3D%206)
Ugh. It would have killed them to choose a perfect square?
![r= \pm \sqrt 6](https://tex.z-dn.net/?f=%20r%3D%20%5Cpm%20%5Csqrt%206)
We can't really tell the sign on the common ratio; there's not enough information. Let's just pick the positive square root going forward.
Part b
![a_1 = a_3/r^2 = -27/6 = -3/2](https://tex.z-dn.net/?f=%20a_1%20%3D%20a_3%2Fr%5E2%20%3D%20-27%2F6%20%3D%20-3%2F2)
![a_n = -\frac 3 2 (\sqrt{6})^{n-1}](https://tex.z-dn.net/?f=%20a_n%20%3D%20-%5Cfrac%203%202%20%28%5Csqrt%7B6%7D%29%5E%7Bn-1%7D%20)
Part c
![a_8 = -\frac 3 2 (\sqrt{6})^{7} = -324 \sqrt{6}](https://tex.z-dn.net/?f=%20a_8%20%3D%20-%5Cfrac%203%202%20%28%5Csqrt%7B6%7D%29%5E%7B7%7D%20%3D%20-324%20%5Csqrt%7B6%7D%20)
Part d
![\displaystyle \sum_{k=1}^{n} a r^{k-1} = \dfrac{ a(1 - r^n)}{1 -r}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Csum_%7Bk%3D1%7D%5E%7Bn%7D%20a%20r%5E%7Bk-1%7D%20%3D%20%5Cdfrac%7B%20a%281%20-%20r%5En%29%7D%7B1%20-r%7D)
![\displaystyle s_8 = \sum_{k=1}^{8} a_k = \dfrac{ (-3/2)(1 - (\sqrt{6})^8)}{1 -\sqrt 6}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20s_8%20%3D%20%5Csum_%7Bk%3D1%7D%5E%7B8%7D%20a_k%20%3D%20%5Cdfrac%7B%20%28-3%2F2%29%281%20-%20%28%5Csqrt%7B6%7D%29%5E8%29%7D%7B1%20-%5Csqrt%206%7D)
![s_8 = - \dfrac{777}{2} (1 + \sqrt 6) ](https://tex.z-dn.net/?f=s_8%20%3D%20-%20%5Cdfrac%7B777%7D%7B2%7D%20%281%20%2B%20%5Csqrt%206%29%0A)
Answer: The system of equations are
30x + 15y = 330
x = y + 2
Step-by-step explanation:
Let x represent the number of hours that Caleb worked.
Let y represent the number of hours that Landon worked.
Caleb can iron 30 shirts per hour, and Landon can iron 15 shirts per hour. This means that the number of shirts that Caleb would iron in x hours is 30x and the number of shirts that Landon would iron in y hours is 15y. They ironed 330 shirts between them. This means that
30x + 15y = 330 - - -- - - - - - - - - - - -1
Caleb worked 2 more hours than Landon. This means that
x = y + 2 - - - -- - - - - - - -2
Answer:
1. (5y) = 35
2. (6y) = 1
3. (4y) = 2
4. (11y) = 15
5. 18, 24, 42, 60
The number of miles Henry rides his bike in 10 days is 60miles
Step-by-step explanation: