Answer:
The second one I think
Step-by-step explanation:
<h2>
Hello!</h2>
The answer is: ![g(x)=-\sqrt[3]{x-1}](https://tex.z-dn.net/?f=g%28x%29%3D-%5Csqrt%5B3%5D%7Bx-1%7D)
<h2>
Why?</h2>
Let's check the roots and the shown point in the graphic (2,-1)
First,
![0=-\sqrt[3]{x-1}\\\\0^{3}=(-\sqrt[3]{x-1})^{3}\\\\0=-(x-1)\\\\x=1](https://tex.z-dn.net/?f=0%3D-%5Csqrt%5B3%5D%7Bx-1%7D%5C%5C%5C%5C0%5E%7B3%7D%3D%28-%5Csqrt%5B3%5D%7Bx-1%7D%29%5E%7B3%7D%5C%5C%5C%5C0%3D-%28x-1%29%5C%5C%5C%5Cx%3D1)
then,
![g(0)=-\sqrt[3]{0-1}\\g(0)=-(-1)\\g(0)=1\\y=1](https://tex.z-dn.net/?f=g%280%29%3D-%5Csqrt%5B3%5D%7B0-1%7D%5C%5Cg%280%29%3D-%28-1%29%5C%5Cg%280%29%3D1%5C%5Cy%3D1)
So, we know that the function intercepts the axis at (1,0) and (0,1), meaning that the function match with the last given option
(
)
Second,
Evaluating the function at (2,-1)
![y=-\sqrt[3]{x-1}\\-1=-\sqrt[3]{2-1}\\-1=-\sqrt[3]{1}\\-1=-(1)\\-1=-1](https://tex.z-dn.net/?f=y%3D-%5Csqrt%5B3%5D%7Bx-1%7D%5C%5C-1%3D-%5Csqrt%5B3%5D%7B2-1%7D%5C%5C-1%3D-%5Csqrt%5B3%5D%7B1%7D%5C%5C-1%3D-%281%29%5C%5C-1%3D-1)
-1=-1
It means that the function passes through the given point.
Hence,
The equation which represents g(x) is ![g(x)=-\sqrt[3]{x-1}](https://tex.z-dn.net/?f=g%28x%29%3D-%5Csqrt%5B3%5D%7Bx-1%7D)
Have a nice day!
Answer:
Scale factor = 4
Step-by-step explanation:
Scale factor = 
Since, S is being dilated with a scale factor to form T,
So, the figure S is the preimage and figure T will be the image,
Length of one side of image T = 8
Length of one side of preimage = 2
Therefore, Scale factor = 
= 4
Scale factor by which figure S has been dilated to form figure T is 4.
Answer:
p(t) = 0.19e0.10t
=>p'(t) = 0.19e0.10t (0.10*1)
=>p'(t) = 0.019e0.10t
t = 0 represents 1994
for 2002, t=2002-1994 =8
in 2002
average price =p(8)
=>average price = 0.19e0.10*8
=>average price =0.422853... million
rate of increase =p'(8)
=>rate of increase = 0.019e0.10*8
=>rate of increase =0.0422853... million per year
p(8)=$ 0.42 million
p'(8)=$ 0.042 million per year
Simpe interest rate = PRT/100
— ( principal x rate x time ) / 100
$3,000 is the principal
3 years is the time
2% is the rate
so, PRT/100
(3,000 x 3 x 2) / 100
= $180
Answer : $180