Answer:
 
    
 
    
Step-by-step explanation:
Given
 
        
 
        
Required
The new coordinates after reflected across y-axis and shifted 2 units down
When a point is reflected across the y-axis, the rule is:

So:
 
 
 
 
 
 
 
 
When a point is translated 2 units down, the rule is:

So:
 
  
 
 
  
 
 
 

 
  
 
So, the new coordinates are:
 
    
 
    
 
        
             
        
        
        
Answer:
it should replace how many numbers 
Step-by-step explanation:
we need a pick
 
        
                    
             
        
        
        
Answer:
X= 5, -9
Step-by-step explanation:
(X+2)² =49
Expand the bracket,
(X+2) (X+2)= 49
Apply the distributive property;
X(X+2) +2 (X+2) =49
X²+2X+2X+4=49
X²+4X+4=49
Move 49 to the left side of the equation;
X²+4X+4-49=0
X²+4X-45=0
Apply Factorisation method;
Consider the form
a²+bx+c=0  
Find two numbers whose sum is equal to b and whose product is equal to c.
Comparing with our equation;
B =4 and C =45
We can use 9 and -5, this is because ;
9+(-5)=4 and 9*(-5)= 45.
Replace X +4X-45=0 with (X-5) (X+9)=0
Therefore;
X-5=0
X+9=0
Moving to the left side of the equation;
Therefore X= 5 and -9
 
        
                    
             
        
        
        
Answer:
Step-by-step explanation:
<u>To make the given piecewise function continuous we need:</u>
- ax² - b = 6 and 5ax + b = 6 at x = 1 
<u>It gives us the system:</u>
- a(1²) - b = 6 ⇒ a - b = 6
- 5a(1) + b = 6 ⇒ 5a + b = 6
<u>Sum of the two:</u>
- a - b + 5a + b = 6 + 6
- 6a = 12
- a = 2
<u>Then b is:</u>