Write the equation of the circle with center (3, 2) and radius r = 7. Use the ^ key for the exponents. Write your answer as the example:
(x - 4)^2+(y+8)^2=25
 
        
             
        
        
        
<u>Answer:</u>
2(-5 - 7j) = -10 - 14j
<u>Step-by-step explanation:</u>
Using the distributive property means that we have to multiply both -5 and -7j by 2:
2(-5 - 7j)
⇒ 2 × -5  +  2 × -7j
⇒ -10 - 14j
 
        
             
        
        
        
Answer:
.
Step-by-step explanation:
 
        
             
        
        
        
Answer:
11,880 different ways.
Step-by-step explanation:
We have been given that from a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer will be filled. We are asked to find the number of ways in which the offices can be filled.
We will use permutations for solve our given problem.
 , where,
, where, 
n = Number of total items,   
r = Items being chosen at a time.         
For our given scenario  and
 and  .
.





Therefore, offices can be filled in 11,880 different ways.
       
     
 
        
             
        
        
        
Start by writing the system down, I will use  to represent
 to represent 

Substitute the fact that  into the first equation to get,
 into the first equation to get,

Simplify into a quadratic form ( ),
),

Now you can use Vieta's rule which states that any quadratic equation can be written in the following form,

which then must factor into

And the solutions will be  .
.
Clearly for small coefficients like ours  , this is very easy to figure out. To get 5 and 6 we simply say that
, this is very easy to figure out. To get 5 and 6 we simply say that  .
.
This fits the definition as  and
 and  .
.
So as mentioned, solutions will equal to  but these are just x-values in the solution pairs of a form
 but these are just x-values in the solution pairs of a form  .
. 
To get y-values we must substitute 3 for x in the original equation and then also 2 for x in the original equation. Luckily we already know that substituting either of the two numbers yields a zero.
So the solution pairs are  and
 and  .
.
Hope this helps :)