itsyaboi

\(0.\overline{123} = \frac{41}{333} \\ \text{So, } \frac{41}{333} \times 9= \boxed{\frac{41}{37}}\)

Just plug things in. You'll find that A is your answer. 

So, you want me to find f(2x)-2f(x), huh?

In the above equation, you can just plug in 2x, which yields:

2(2x)^2-5(2x) = 8x^2 - 10x

Now we find 2f(x), which is just 2(2x^2-5x) = 4x^2 - 10x

subtracting 4x^2 - 10x from 8x^2 - 10x, we get 4x^2.

x^3/27 - 3x^2 + 81x -729 = 25+30+9

multiply everything by 27 to clear the fraction

x^3 - 81x^2+2187x - 19683 = 1728

subtract by 1728

x^3 - 81x^2 + 2187x - 21411=0

factoring yields:

x^3 - 8x^2 + 2187x -21411 = (x-39)(x^2-42x+549)

since two of the solutions are complex/imaginary numbers, the only solution is 39.

Factoring the bottom yields (1-1/5) times 10^m

Now, you have the fraction: (5^(m-2 * 2^(m+2)))/((4/5)*10^m)

10^m can be expressed as 2^m * 5^m

Cancelling yields:

4/(5^2 times 4/5)

4/20 = 1/5

2) b + bx +bx^2 +bx^3 .... +bx^9 = 180, where x =7/4

Therefore, b= 47185920/93808891

Therefore, b_2+b_4+b_6+b_8+b_10 = 1260/11.

1) By the geometric series (finite) formula,

 \(\frac{8000(1-(-1.5)^n)}{2.5}=57875 \\ \text{where n is the number of terms}\)

n=7, so 8000 times -1.5^7 = -136687.5.

x/y = 5/3

and

x-4/y+2 = 8/7

So, x = 5/3y

\(\frac{\frac{5y}{3}-4}{y+2}=\frac{8}{7}\)

Solving this, we should get that y=12 and x=20

So, Og has 8 more.

The arithmetic sum formula shows that:

\(\text{sum} = 100(\frac{4+100}{2}) = 5200\)

\(\text{sum} = 100(\frac{3+100}{2}) = 5150\)

The difference is 5200 - 5150 = 50.

1) If x/2, x/3, and x/6 are angle measures of a triangle, they must add up to 180.

x/2 + x/3 + x/6 = 180

Find the common denominator:

3x/6+2x/6 + x/6 = 180

Multiply both sides by 6:

3x+2x+x=1080

6x=1080,

x = 180

x/6, the smallest angle, is 30.

2) Correct me if I'm wrong, but isn't it just 135?

3) 108/120 = 9/10

Can't you just plug in the value 3 for x?

What do you mean by formal definition of a limit?