Answer:
<u>Translations</u>
![f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}](https://tex.z-dn.net/?f=f%28x%2Ba%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20left%7D)
![f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}](https://tex.z-dn.net/?f=f%28x-a%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20right%7D)
![f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}](https://tex.z-dn.net/?f=f%28x%29%2Ba%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20up%7D)
![f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}](https://tex.z-dn.net/?f=f%28x%29-a%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20down%7D)
![y=-\:f\:(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}](https://tex.z-dn.net/?f=y%3D-%5C%3Af%5C%3A%28x%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Breflected%20in%20the%7D%20%5C%3A%20x%20%5Ctextsf%7B-axis%7D)
![y=f\:(-\:x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}](https://tex.z-dn.net/?f=y%3Df%5C%3A%28-%5C%3Ax%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Breflected%20in%20the%7D%20%5C%3A%20y%20%5Ctextsf%7B-axis%7D)
Parent function: ![f\:(x) = \ln(x)](https://tex.z-dn.net/?f=f%5C%3A%28x%29%20%3D%20%5Cln%28x%29)
Translated right 1 unit: ![f\:(x\:-1) = \ln(x - 1)](https://tex.z-dn.net/?f=f%5C%3A%28x%5C%3A-1%29%20%3D%20%5Cln%28x%20-%201%29)
Then translated down 9 units: ![f\:(x\: -1)-9 = \ln(x - 1) - 9](https://tex.z-dn.net/?f=f%5C%3A%28x%5C%3A%20-1%29-9%20%3D%20%5Cln%28x%20-%201%29%20-%209)
The reflected over the x-axis: ![-\:[f\:(x\:-1) - 9] = -\ln(x - 1) + 9](https://tex.z-dn.net/?f=-%5C%3A%5Bf%5C%3A%28x%5C%3A-1%29%20-%209%5D%20%3D%20-%5Cln%28x%20-%201%29%20%2B%209)
Therefore, ![g(x) = -\ln\:(x\:- 1) + 9](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-%5Cln%5C%3A%28x%5C%3A-%201%29%20%2B%209)
⇒ g(30) = - ln(30 - 1) + 9
= -3.36729... + 9
= 5.6 (nearest tenth)
Answer:
(x+5)(x-4)(x-3)
Step-by-step explanation:
Divide (e+5) into e³-2e²-23e+60 using polynomial long division (picture attached below). Since it divides in evenly, we can see it is a factor.
So we can say e³-2e²-23e+60 = (e+5)(e²-7e+12)
To complete the factorisation, factorise e²-7e+12.
Note that (x+a)(x+b)=x²+(a+b)x+ab. So find the multiples or 12 which can be added or subtracted to get -7: -4 and -3.
e²-7e+12=(x-4)(x-3)
So e³-2e²-23e+60 = (x+5)(x-4)(x-3)
Answer:
it is the first answer
Step-by-step explanation:
too lazy lol
Answer:
121
Step-by-step explanation:
11 x 11 =121
If you multiply 11 and 11 you will get 121. Meaning 121 would be your perfect square for this problem
Its not letting me come to for some reason so I’m doing this on answers
But I think u need a little more info for someone to answer this maybe a picture would help