Answer:
![f(x)=-2log(3x)+3](https://tex.z-dn.net/?f=f%28x%29%3D-2log%283x%29%2B3)
Step-by-step explanation:
we have
![f(x)=log(3x)](https://tex.z-dn.net/?f=f%28x%29%3Dlog%283x%29)
step 1
Reflecting the function f(x) over the x-axis
we know that
To reflect a function about the x-axis, multiply the function by -1
f(x) -----> -f(x)
so
![f(x)=-log(3x)](https://tex.z-dn.net/?f=f%28x%29%3D-log%283x%29)
step 2
Stretching the function f(x) vertically by a factor of two
To stretch a function vertically, multiply the function by two
f(x) -----> 2f(x)
![f(x)=-2log(3x)](https://tex.z-dn.net/?f=f%28x%29%3D-2log%283x%29)
step 3
Shifting the function f(x) up three units
To shift the function up, adds three units to the function
f(x) -----> f(x) +3
![f(x)=-2log(3x)+3](https://tex.z-dn.net/?f=f%28x%29%3D-2log%283x%29%2B3)
Answer:
Step-by-step explanation:
If you want to factor this, you have to use the quadratic formula to do so.
![x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%2B%2F-%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D)
For us, it looks like this:
![x=\frac{-3+/-\sqrt{(-3)^2-4(5)(4)} }{2(5)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-3%2B%2F-%5Csqrt%7B%28-3%29%5E2-4%285%29%284%29%7D%20%7D%7B2%285%29%7D)
which simplifies to
![x=\frac{-3+/-\sqrt{-71} }{10}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-3%2B%2F-%5Csqrt%7B-71%7D%20%7D%7B10%7D)
Since it breaks every mathematical rule to have a negative number under an even index radical, we have to deal with that using the imaginary "i". You should know at this point that ![i^2=-1](https://tex.z-dn.net/?f=i%5E2%3D-1)
so we will do a rewrite on that equation above:
![x=\frac{-3+/-\sqrt{i^2*71} }{10}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-3%2B%2F-%5Csqrt%7Bi%5E2%2A71%7D%20%7D%7B10%7D)
which simplifies further to
![x=\frac{-3+/-i\sqrt{71} }{10}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-3%2B%2F-i%5Csqrt%7B71%7D%20%7D%7B10%7D)
This is the answer but we can separate it into its proper standard form which is
and ![x=-\frac{3}{10}-\frac{\sqrt{71} }{10}i](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B3%7D%7B10%7D-%5Cfrac%7B%5Csqrt%7B71%7D%20%7D%7B10%7Di)
Answer:
-4 and 1/4
Step-by-step explanation:
They marked it up to 2979 since 993*3(aka 200%). You then multiply 2979 by 1.14 to get the total of $3396.06
A) AB is where plane P and plane R intersect.
B) A, D, B are collinear (on the same line).
C) plane ADG (three points on the plane)
D) F, D, G, A are all on plane R
E) D lies on both planes.