Answer:
-0.9090... can be written as 
.
Explanation:
Any <em>repeating </em>decimal can be written as a fraction by dividing the section of the pattern to be repeated <em>by </em>9's.
We can start by listing out
0.909090... = 9/10 + 0/100 + 9/1000 + 0/10000 + 9/100000 + 0/1000000 + ...
Now. we let this series be equal to x, that is
= 9/10 + 0/100 + 9/1000 + 0/10000 + 9/100000 + 0/1000000 + ...
Now, we'll multiply both sides by 100
.
= 90 + 0 + 9/10 + 0/100 + 9/1000 + 0/10000 + ...
Then, subtract the 1st equation from the second like so:
= 90 + 0 + 9/10 + 0/100 + 9/1000 + 0/10000 + 9/100000 + 0/1000000 + ...
= - 9/10 - 0/100 - 9/1000 - 0/10000 - 9/100000 - 0/1000000 - ...
And we end up with this:
Finally, we divide both sides by 99 in order to isolate x and get the fraction we're looking for.
Which can be reduced and simplified to
Hope this helps!
Answer:
square root of 8
Step-by-step explanation:
Step-by-step explanation:
let's look at the full numbers under the square roots when bringing the external factors back in :
sqrt(9×9×2) - sqrt(3×3×7) + sqrt(8) - sqrt(28)
and let's present these numbers as the product of their basic prime factors
sqrt(3×3×3×3×2) - sqrt(3×3×7) + sqrt(2×2×2) - sqrt(2×2×7)
now we see that we have 2 pairs of square roots : 1 pair ends with a factor of 2, and one pair with a factor of 7.
let's combine these
sqrt (3×3×3×3×2) + sqrt(2×2×2) - sqrt(3×3×7) - sqrt (2×2×7)
and now we move the factors of 2 and 7 back out in front (of course, we need to apply the square root on these factors) :
9×sqrt(2) + 2×sqrt(2) - 3×sqrt(7) - 2×sqrt(7) =
= (9+2)×sqrt(2) - (3+2)×sqrt(7) = 11×sqrt(2) - 5×sqrt(7)
and that is the first answer option.
The midpoint formula is basically (averaging the x coordinates, averaging the y coordinates).
Point A: (3, 7)
Point B: (2, -1)
Midpoint x: (3 + 2) / 2 = 5 / 2
Mindpoint y: (7 - 1) / 2 = 3
Therefore, the midpoint of the segment is choice C (5/2, 3)
Answer:
B
Step-by-step explanation:
in table B if x = 1 y cannot equal both 1 and -1
no function can have x equal to two or more unique y's
