Answer:

Step-by-step explanation:

 
        
             
        
        
        
Step-by-step explanation:
see the attachment...............
 
        
                    
             
        
        
        
Answer:

Step-by-step explanation:
Let be  , this expression is simplified by algebraic and trascendental means. As first step, the second order polynomial is simplified. Its roots are determined by the Quadratic Formula, that is to say:
, this expression is simplified by algebraic and trascendental means. As first step, the second order polynomial is simplified. Its roots are determined by the Quadratic Formula, that is to say:


The polynomial in factorized form is:

The function can be rewritten and simplified as follows:
![f(x,y) = \log_{4} [(x-5-\sqrt{25-6\cdot y})\cdot (x-5+\sqrt{25-6\cdot y})]](https://tex.z-dn.net/?f=f%28x%2Cy%29%20%3D%20%5Clog_%7B4%7D%20%5B%28x-5-%5Csqrt%7B25-6%5Ccdot%20y%7D%29%5Ccdot%20%28x-5%2B%5Csqrt%7B25-6%5Ccdot%20y%7D%29%5D)

 
        
             
        
        
        
Answer:
The man traveled 20km by train.
Step-by-step explanation:
If x is the distance he traveled by train, you can write this equation to represent the situation:

Then, you can simply solve for x:

The man traveled 20km by train.

 
        
             
        
        
        
Answer:
The total trip will be 4 hours long.
Step-by-step explanation:
The length of the trip decreases by 65/2 miles for every half hour. So in 2 half hours (or 1 hour), Aubree would have traveled the last 65 miles she needed.