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:
10.31 ft
Step-by-step explanation:
the base is 25 ft²
leaves 100 ft² for the 4 sides on top
so each triangle got 25ft²
the base length of the triangle is 5ft, bc it's the base length of the pyramid
so the height of the triangle is 10ft,
bc only then do we get a surface area of 25ft²
(b * h /2) for the triangle
now that we got base length and height,
let's look for the slant
we recall the pythagoras stuff to get the missing side of the triangle. but notice that we need to split the triangle in half to get a 90° angle.
leaving us with 10ft (height) and 2.5ft
slant² = 10² + 2.5²
slant² = 106.25
slant = sqrt(106.25)
slant = 10.31
Answer:
C
Step-by-step explanation:
Okay so on Saturday there is a 30% sale plus she comes early so +10% and that makes 40% off.
10% of 400=40
multiply by 4 to get 40%, 40*4=40%
40%=160
400-160=240
Hope this helps
Plug 8 into the equation and divide it by that equation but with 5 plugged in
Step-by-step explanation:
Sum of arithmetic terms = n/2 × [2a + (n - 1)×d], where 'a' is the first term, 'd' is the common difference between two numbers, and 'n' is the number of terms.
this is the same as n/2 × (a1 + an), because
an = a1 + (n-1)×d
so, for the series above :
a or a1 = 2
d = 7, as every new term is the previous term plus 7.
for n
37 = a1 + (n-1)×d = 2 + (n-1)×7
and now solve for n
35 = 7n - 7
42 = 7n
n = 6
so, the sum of all terms is
6/2 × (2+37) = 3×39 = 117
