Hey there! I'm happy to help!
First, we need to rotate our points 180° about the origin. To find the coordinates after such a rotation, we simply find the negative version of each number in the ordered pair, which can be written as (x,y)⇒(-x,-y).
Let's convert this below
A: (1,1)⇒(-1,-1)
B: (5,4)⇒(-5,-4)
C: (7,1)⇒(-7,-1)
D: (3,-2)⇒(-3,2)
Now, we need to translate these new points five units to the right and one unit down. This means we will add 5 to our x-value and subtract 1 from our y-value. This will look like (x,y)⇒(x+5,y-1). Let's do this below.
A: (-1,-1)⇒(4,-2)
B: (-5,-4)⇒(0,-5)
C: (-7,-1)⇒(-2,-2)
D: (-3,2)⇒(2,1)
Therefore, this new parallelogram has coordinates of A'(4,-2), B'(0,-5), C'(-2,-2), and D'(2,1)
Now you know how to find the coordinates of translated figures! Have a wonderful day! :D
Cost per bottle
6 pack is 3.79 so the cost per bottle is 3.79/6=$0.631666666666667 per bottle
9 pack is 4.50 so the cost per bottle is 4.50/9=$0.50 per bottle
12 pack is 6.89 so the cost per bottle is 6.89/12=$0.574166666667 per bottle
0.63>0.57>0.50
the one that costs the least per bottle is the 9 pack which costs $0.50 per bottle
For a single payment with compound interest, the equation to use is F=P(1+i)^n where F is the value after n periods, P is the present value, and i is the interest rate.
If we want the final value F to double in 5 years, F is then equal to P then n=5. The equation is now:
2P=P(1+i)^5
2=(1+i)^5
i=14.87% per year
