Answer: The answer is C
The transformations are a horizontal translation 2 units left then a vertical translation 6 units down.
We are told in the question that 1 carat is equal to 200 mg.
The Hope Diamond is 44.5 carats. Let's multiply the weight of 1 carat by 44.5 to get the weight of the Hope Diamond in mg:

The total weight of the Hope Diamond is 8,900 mg. However the question asks for the weight in grams. There are 1000 mg in 1 gram, so let's divide the known weight of the Hope Diamond in mg by 1000 to get the weight converted to grams:

Now we know that
the weight of the Hope Diamond is equal to 8.9 grams.
Answer:
- 1/3
- y-axis
- (1, -2)
Step-by-step explanation:
The length AC is 3, but the corresponding length FD is 1, so the dilation factor is FD/AC = 1/3.
The reflection is a left/right reflection, so it is across a vertical line. We suspect the only vertical line you are interested in is the y-axis. (It could be reflected across x=1/2, and then the only translation would be downward.)
The above transformations will put C' at (1, 0). Since the corresponding point D is at (2, -2), we know it is C' is translated by (1, -2) to get to D.
C' + translation = D
(1, 0) +(1, -2) = (2, -2)
One side of the rectangle is x=2, the other side is 2x-5
Add up all the four sides: (x+2) +(x+2)+(2x-5)+(2x-5)=54
6x-6=54
x=10
#3: suppose the first integer is x, then the second one is x+2
x(x+2)=255
x^2 +2x -255 =0
factor the quadratic equation: (x+17)(x-15)=0
x=-17, which is impossible, or x=15
so the two positive integers are 15 and 17