This is a geometric sequence because each term is twice the value of the previous term. So this is what would be called the common ratio, which in this case is 2. Any geometric sequence can be expressed as:
a(n)=ar^(n-1), a(n)=nth value, a=initial value, r=common ratio, n=term number
In this case we have r=2 and a=1 so
a(n)=2^(n-1) so on the sixth week he will run:
a(6)=2^5=32
He will run 32 blocks by the end of the sixth week.
Now if you wanted to know the total amount he runs in the six weeks, you need the sum of the terms and the sum of a geometric sequence is:
s(n)=a(1-r^n)/(1-r) where the variables have the same values so
s(n)=(1-2^n)/(1-2)
s(n)=2^n-1 so
s(6)=2^6-1
s(6)=64-1
s(6)=63 blocks
So he would run a total of 63 blocks in the six weeks.
Answer:
(-9, -5)
Step-by-step explanation:
Ok, so when you move an image to the right, you are moving along the x-axis, and when you move up, you are moving up the y-axis. So if the altered image is (x,y) and the values are (-5, -1), you reverse what has been done to the image. In this case, since we moved to the right 4 units, we know that means we added 4 to x, so we subtract 4 to get -9. And then, for the y-value, because we added 4, we do the opposite, and subtract 4 to get -5. So the pre-image should be (-9, -5)
C is answer no explanation needed
As long as the new rectangle is not moved, just dilated, line EF will be parallel.
