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Threr is only ONE value of n = 21 that satisfies the expression:

Sub 21 for n =12*21^2 + 12*21 + 11 =5,292 + 252 + 11 =5,555

Hint:    A_ABD = A_ABC - (A_BCE + A_ADE)

There is no way to get negative numbers, so the only way to not get a sum that is greater than 0 is when the sum = 0

$\dfrac{1}{2} * \dfrac{1}{3} * \dfrac{1}{5} * \dfrac{1}{7} * \dfrac{1}{11} = \dfrac{1}{2310}$

This is the chance that Bob gets 0 for all five games, since the chance of picking 0 out of n numbers is $\dfrac{1}{n}$

His chances of getting a sum of greater than 0 is

$1 - \dfrac{1}{2310} = \dfrac{2309}{2310}$

suppose you add $x$ green marbles

$\dfrac{green}{total} = \dfrac{5 + x}{4 + 3 + 5 + x} = \dfrac{5 + x}{12 + x} = 0.79$

multiply both sides by $12 + x$

$5 + x = 9.48 + 0.79x$

$0.21x = 4.48$

$x = 21.\overline{3}$

You need to add at least $21.\overline{3}$ green marbles, but that doesnt make sense here, since you can't have a fractional amount.

Rounding up, at least $22$ green marbles must be added

Right triangle ABC has one leg of length 6 cm, one leg of length 10 cm, and a right angle at A. A square has one side on the hypotenuse of triangle ABC and a vertex on each of the two legs of triangle ABC. What is the length of one side of the square in cm? Express your answer as a common fraction. 

Let the side of the square be  x

x / tan(B) + x + x / tan(C) = sqrt(6² + 10²)

x = 3.56997  

The 8th number is 26.

The area is 65/8.

What do you get when you multiply both sides of this inequality by -1? -8x+9y≤17     

I think you don't have any problem with changing polarity. 

I think you're wondering how it would affect the < inequality. 

Try it with a simpler inequality. 

What do you have to do to the symbol if you multiply both sides of 1 < 2 by –1..... 

_.

tThis is my explanation in image form. It has been explained clearly. 

So that would mean

the second one is 5-3 =2 

the third is 9-8 = 1

right?

painted surface   3 x 5 x 2    +  5 x 8 x 2    + 8x 3 x 2    = 158 cm²  = 158 painted surfaces

total cubes   3 x 5 x 8

   total surfaces   3x 5 x 8 x 6 =720 sufaces  

        unpainted =   720- 158 = 562 unpainted   =   562 cm²

his is not a difficult question Qwertyzz

Have you drawn it?

I count more than that   

You need to put it in brackets. Otherwise, it will do the order of operation wrong.

Here are a couple of examples:

To enter  $2\frac34$ ,   type:     2 + 3/4

To enter  $256\frac{15}{16}$ ,   type:     256 + 15/16

Go to this link and examine the answers given:

https://www.wolframalpha.com/input/?i=2x%5E2y%5E3+%2B+4y%5E3+%3D+149+%2B+3x%5E2%2C+integer+solution

Let the original number of chocolates in the box =C

C - 1/4C = 3/4C left

3/4C / 2 = 6 pieces left

3/8C = 6

C = 6 / (3/8) =6 x (8/3) =48 / 3 = 16 - Original number of chocolates in the box.

Go to this link and inspect the answers given:

https://www.wolframalpha.com/input/?i=1%5E5+%2B+2%5E5+%2B+3%5E5+%2B+...+%2B+n%5E5+%3D+f%28n%29%2C+write+f%28n%29+as+descending+polynomial

This is a pretty simple question. We know for sure the number is most probably under 30. So you can guess in check. Such as this: 

Number: 28

1/4 of 28 = 7

21 - 1/2 = 10.5

So it doesnt fit the equation, so it isn't number 29

Number: 18

1/4 of 18 = 4.5

1/2 of 14.5 = 7.25

So it doesnt fit the equation, so it isn't number 18. Since 7.25 is close to six it's probably around the range 12-17

Number: 12

1/4 of 12 = 3

1/2 of 9 = 4.5

So it doesnt fit the equation, so it isn't number 12. Since the number was under, and 18 was above, it probably is 14-17

Number: 14

1/4 of 14: 3.5

1/2 of 11.5: 5.75

So it doesnt fit the equation. So it isn't number 14. Since the number was under, and 18 was above, it is probably 17

Number: 17

1/4 of 17: 4.25

1/2 of 13.75

This is above, but if you can round, as this is a decimal, this can count. Now though you should try decimals like this:

16.1,16.2,16.3,16.4, but if you can round the answer is the number 17 READ MY EXPLANATION IK YOU PROBABLY WONT

There are 3!*5!/4 = 180 ways of distributing the pets.

The answer is 8 squares.