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Sum formulas to the rescue! 

It is a formula that the sum of the first n odd numbers is n^2. There are (203+1)/2 = 102 odd numbers here, so our numerator is 102^2.

Our denominator is 2*(1+2+3+...+102), which, by the triangular number theorem, is 102(103). 

Thus, our answer is 102^2/(102*103) = 102/103

Oh, so convenient! (a^3+b^3+c^3) - (a+b+c)^3 = -3(a+b)(b+c)(a+c).

How convenient! (a+b)(b+c)(a+c) + abc = (a+b+c)(ab+ac+bc).

With these elusive factoring tricks down, we substitute numbers.

(a^3+b^3+c^3) - 216 = -3(30 - 12) = -54

216-54 = 162.

2x-73+11 = 180

do -73+11

2x - 62 = 180

      +62     +62

2x=242

--- = ----

2  =  2

x= 121

Es ist nicht zwölf.  Es ist zwölf minus eins.  

Ja, ich habe dich erwischt.   LOL  

This is not a geometric sequence, but we can break it down into two.

Call the sum S. Then S = (1 + 1/4 + 1/16 + 1/64 + ...) + (i/2 + i/8 + i/32 + i/128 + ...).

Evaluating each of these separately, by the geometric series formula, the first part of the sum is 1/(1-1/4) = 4/3.

The second part of the sum is i/(2 * (1-1/4)) = 2i/3. 

The answer is (4+2i)/3.

yes, you click on the heart.  :)

x = (180-11+73)/2 = 121.

There is only one way we get x: multiplying 1 by x. 

Thus, we look only at the x+1 terms.

(x+1)^5, and by pascal's triangle rules, we have that this expression is equal to \(x^5 + 5 x^4 + 10 x^3 + 10 x^2 + 5 x + 1.\)

The answer is 5. 

3x+9-6x(6+8)=7(7+3)

Simplify everything inside the parenthesis.

3x+9-6x*14 = 7*10.

Combine like terms.

-81x+9 = 70.

Isolate x. 

-81x = 61

x=-61/81 --> 1 solution

velocity is m/s     36 m / 6s   = 6 m/s

30 m/s  *  120 s  = .......... m       ( see how the 's' cancels out and you are left with 'm' )

third and fourth ones are similar to the second one...you can do them I am sure !

Ahhhhhhhhhhhhhhhh

That's the best explanation I could give!!!!!

🥳🥳🥳🥳🥳🥳🥳🥳

5/8 ÷ 9/7 = 35/72

Result in decimals: 0.48611111111111

Calculation steps:

5/8 ÷ 9/7

= 5/8 × 7/9

= 5 × 7/8 × 9

= 35/72

Further explanation:

5/8 ÷ 9/7 = ?

Division of fractions is equivalent to multiplication by the reciprocal of the second fraction:

5/8÷9/7 = 5/8 × 7/9

Once rearranged, multiply all of the numerators by each other. Do the same with the denominators and form a new fraction with these values:

5 × 7/8 × 9 = 35/72

The result is:

5/8 ÷ 9/7 = 35/72

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Just  divide

                                2x^3  - x^2  +  x   +  3  

x^2  +  2x  + 3    [    2x^5  + 3x^4  + 5x^3  + 2x^2  + 9x  + 9  ]

                                2x^5  + 4x^4  + 6x^3

                             __________________________________

                                            -x^4  -  x^3   + 2x^2

                                           -x^4   - 2x^3  -  3x^2

                                         ______________________

                                                        x^3  + 5 x^2  +  9x

                                                        x^3  + 2 x^2  +  3x

                                                       ___________________

                                                                 3x^2   + 6x   + 9

                                                                  3x^2  + 6x   + 9

                                                               ________________

🥳🥳🥳🥳🥳🥳🥳🥳🥳

oh, okay

Vertical      =   1200 sin 28^o    f/s

Horizontal  =   1200 cos 28^o   f/s

There are 4 solutions.

f(x) = 2 at exactly one point.

The area is 20.

x = total visitors

.40 (x) = 1600

x = 1600/ .4   = ............. visitors for the month

Hello asinus.....   The arrow reaches the target in 1/2 second.... not 2 seconds .....

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