Answer:
k = -1
Step-by-step explanation:
-3k + 6 = 10 + k
combine similar terms:
-3k - k = 10 - 6
simplify:
-4k = 4
simplify:
k = 4 / -4
k = -1
 
        
                    
             
        
        
        
5x+3y=12
Subtract 5x from both sides 
3y=-5x+12
Divide by 3
Y=-5/3x +4
        
             
        
        
        
Answer:
(1, 3)
Step-by-step explanation:
You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola.  The first few steps are as follows.  Set the parabola equal to 0 so you can solve for the vertex.  Separate the x terms from the constant by moving the constant to the other side of the equals sign.  The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out).  Let's start there.  The first 2 steps result in this polynomial:
 .  Now we factor out the -2:
.  Now we factor out the -2:
 .  Now we complete the square.  This process is to take half the linear term, square it, and add it to both sides.  Our linear term is 2x.  Half of 2 is 1, and 1 squared is 1.  We add 1 into the set of parenthesis.  But we actually added into the parenthesis is +1(-2).  The -2 out front is a multiplier and we cannot ignore it.  Adding in to both sides looks like this:
.  Now we complete the square.  This process is to take half the linear term, square it, and add it to both sides.  Our linear term is 2x.  Half of 2 is 1, and 1 squared is 1.  We add 1 into the set of parenthesis.  But we actually added into the parenthesis is +1(-2).  The -2 out front is a multiplier and we cannot ignore it.  Adding in to both sides looks like this:
 .  Simplifying gives us this:
.  Simplifying gives us this:

On the left we have created a perfect square binomial which reflects the h coordinate of the vertex.  Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:

From this form,

you can determine the coordinates of the vertex to be (1, 3)
 
        
                    
             
        
        
        
Answer:
TanA=  and sinA=36/45
 and sinA=36/45 
Step-by-step explanation:
Tan= opposite/adjacent
since 36 is opposite of A and 27 is adjancent to 36 your will use tanA= 36/27
Sin= opposite/hypotenuse 
36 is opposite of A and 45 is the hypotenuse 
 
        
             
        
        
        
Answer:
36 tiles
Step-by-step explanation:
First, find area of the square floor knowing the formula as;
Area= 
where s= side of a square.
If one side of the floor is 12 feet, then Area= 
Next, find the area of each tile using the same formula and given s=2 feet;
Area(tile) = 
To find the number of tiles needed to cover entire floor, divide area of the floor by area of one tile; 144 / 4 = 36 tiles