Answer:
Step-by-step explanation:
12x-6/3
=12x/3 - 6/3
=4x-2
or
12x-6/3
take 6 common
6(2x-1)/3
2(2x-1)
4x-2
![\bf y=\cfrac{2}{x}\implies y=\cfrac{2x^0}{x}](https://tex.z-dn.net/?f=%5Cbf%20y%3D%5Ccfrac%7B2%7D%7Bx%7D%5Cimplies%20y%3D%5Ccfrac%7B2x%5E0%7D%7Bx%7D)
now, the denominator has a higher degree, a degree of 1, than the numerator's, therefore the horizontal asymptote for this function is at y = 0.
now, the vertical asymptotes of it, are at the zeros of the denominator, namely x = 0, when is x = 0? at 0, so the vertical asymptote for this function is at x = 0, the y-axis.
now, if we want the horizontal asymptote moved over from its position at 0, over to x = 5, simply translate it by 5 units,
![\bf y=\cfrac{2}{x-5}](https://tex.z-dn.net/?f=%5Cbf%20y%3D%5Ccfrac%7B2%7D%7Bx-5%7D)
.
and if we want the vertical asymptote to move down from 0 to -3, simply translate the function vertically 3 units,
Answer:
(5,-1)
Step-by-step explanation:
rotate the point
Answer:
n = 121
Step-by-step explanation:
Given,
Amount invested = $250,000
Quarterly payment (P) = $5500
Interest Rate (Quarterly) (r) = 8% /4 = 2%
Account balance = $ 0
Present value of Annuity formula ,
Present value = ![P\times\dfrac{1-(1+r)^{-n}}{r}](https://tex.z-dn.net/?f=P%5Ctimes%5Cdfrac%7B1-%281%2Br%29%5E%7B-n%7D%7D%7Br%7D)
![250000 = 5500\times\dfrac{1-(1+0.02)^{-n}}{0.02}](https://tex.z-dn.net/?f=250000%20%3D%205500%5Ctimes%5Cdfrac%7B1-%281%2B0.02%29%5E%7B-n%7D%7D%7B0.02%7D)
1.02⁻ⁿ = 0.091
-n ln(1.02) = ln (0.091)
n = 121
Hence it will take 121 Quarters to account balance $0.