Answer:
Step-by-step explanation:
S56=56/2[2(-8)+(56-1)7]
S56=10332
 
        
             
        
        
        
Answer:
a. A customer earns 1 free night per 10 nights stayed.  
Step-by-step explanation:
The missing function is:
f(x) = x/10  
The missing options are:
<em>
a. A customer earns 1 free night per 10 nights stayed.  </em>
<em>
b. A customer starts with 1 free night and then earns another free night after every 10 nights stayed.
</em>
<em>
c.A customer earns x – 10 free nights for every 10 nights stayed.  </em>
<em>
d. A customer earns 10 free nights after x number of nights stayed.
</em>
The function means that after a customer stayed 10 nights, a free night is earned. That is, replacing x = 10 into the function, we get:
f(10) = 10/10  = 1
which means 10 nights are equivalent to 1 free night.
 
        
             
        
        
        
Answer:

Step-by-step explanation:
The expression to transform is:
![(\sqrt[6]{x^5})^7](https://tex.z-dn.net/?f=%28%5Csqrt%5B6%5D%7Bx%5E5%7D%29%5E7)
Let's work first on the inside of the parenthesis.
Recall that the n-root of an expression can be written as a fractional exponent of the expression as follows:
![\sqrt[n]{a} = a^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%7D%20%3D%20a%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
Therefore ![\sqrt[6]{a} = a^{\frac{1}{6}}](https://tex.z-dn.net/?f=%5Csqrt%5B6%5D%7Ba%7D%20%3D%20a%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D)
Now let's replace  with
 with  which is the algebraic form we are given inside the 6th root:
 which is the algebraic form we are given inside the 6th root:
![\sqrt[6]{x^5} = (x^5)^{\frac{1}{6}}](https://tex.z-dn.net/?f=%5Csqrt%5B6%5D%7Bx%5E5%7D%20%3D%20%28x%5E5%29%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D)
Now use the property that tells us how to proceed when we have  "exponent of an exponent":

Therefore we get:  
Finally remember that this expression was raised to the power 7, therefore:
^7=(x^\frac{5}{6})^7=x^\frac{35}{6}](https://tex.z-dn.net/?f=%5Btex%5D%28%5Csqrt%5B6%5D%7Bx%5E5%7D%29%5E7%3D%28x%5E%5Cfrac%7B5%7D%7B6%7D%29%5E7%3Dx%5E%5Cfrac%7B35%7D%7B6%7D) [/tex]
[/tex]
An use again the property for the exponent of a exponent:
 
 
        
             
        
        
        
Write the equation of the first train: x = 12t
Write the equation of the second train: y = -20t+72, assuming the train one is at the origins when t = 0. 
Now solve the equation: 12t=-20t+72, 
32t = 72, then t = 2.25 hours. The two train meet after 2.25 hours. 
Now the equation of the <span>pigeon is like this: x = 48t. 
</span>Then for t = 2.25, we get 

<span>
The Hyde has flown 108 km when the trains meet.</span>
 
        
        
        
Answer:
1,824 sq inches
Step-by-step explanation:
area of rectangle: 48 x 32 = 1536
area of triangle: (48 x 12) / 2 = 288