If you use the scientific notation to simplify these bigger numbers it will make it easier
        
             
        
        
        
The original functions are: f(n) = 500 and g(n) = [9/10]^(n-1)
A geometric sequence combining them is: An = f(n)*g(n) = 500*[9/10]^(n-1):
Some terms are:
A1= 500
A2 = 500*[9/10]
A3 = 500*[9/10]^2
A4 = 500*[9/10]^3 
....
A11 = 500*[9/10]^10 ≈ 174.339
Answer: the third option, An = 500[9/10]^(n-1); A11 = 174.339
 
        
                    
             
        
        
        
Just in case:
This slope goes through (0,0) or more formally, the origin.
 
        
                    
             
        
        
        
Answer:
C. 
Step-by-step explanation:
I think the equation meant  ?
?
Anyways, to factor these kinds of quadratic, keep into consideration: 

ONLY if: 

Start off by finding factors of c, which in this case, -18: 
±(1, 2, 3, 6, 9, 18)
If one of the numbers is negative then the other number must be positive. 
Find which two factors will sum up to b, which in this case, is 3. 

The only two factors that work are 6 and -3. 
Replace them into the factored form: 

 
        
                    
             
        
        
        
There is only one answer, x=7