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BDI is not a triangle by the triangle inequality, please talk to your teacher/problem owner to tell them of this error/typo.

1 - [12 + 5 - 1] C [5 - 1] ==1820 ways without restrictions

2 - 1820  -  [listfor(n, 1, 7, ((10 - n) nCr (4 - 1))* 5)]

3 - 1820  -  [420+ 280+ 175+ 100+ 50+ 20+ 5] + 10 [Because 6 occurs twice 10 times]

4 - 780 ways to distribute 12 candies to 5 kids each having at most 5 candies.

By the quadratic formula, the roots are (3 + sqrt(101))/2 and (3 - sqrt(101))/2.  These add up to (3 + sqrt(101))/2 + (3 - sqrt(101))/2 = 3.

By the quadratic formula, the roots are (7 \pm sqrt(2449))/60.  Plugging in these value gives us

(r + 3)(s + 3) = ((7 + sqrt(2449))/60 + 3)((7 - sqrt(2449))/60 + 3) = 271/30

Let the original number ==N

[5N] / [N  -  4  +  7] == 18, solve for N

N = -54/13 == - 4  2/13 - the original number

The largest n is 30:

3x^2 + 30x + 72 = 3(x + 4)(x + 6)

Remember: (You can simplify by expanding out)

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

and

a^2 + b^2 = (a + b)^2 - 2ab

Substituting in, you get:

(a + b)(a^2 - ab + b^2) = 812 + (a + b)^2 - 2ab

14[(a + b)^2 - 2ab - ab] = 812 + 196 - 2ab

14(196 - 3ab) = 1008 - 2ab 

2744 - 42ab = 1008 - 2ab

1736 = 40ab

ab = 43.4

a + b = 14

Write a quadratic equation using vieta's formula:

x^2 - 14x + 43.4 = 0. x is the values of a and b.

a and b are 14 +- sqrt(22.4)) / 2

They have a common denominator so you can multiply both sides by a^3 + 7.

You obtain the equation 1 = -a^3, a = -1

Combine like terms, so combine the ones with the same variable or the ones with the same constant/normal numbers and you get:

5c + d + 1

Both of those are also incorrect, I'm so sorry. I appreciate your help though!

There are only two: (a,b) = (0,1) and (a,b) = (0,-1).

Sum of all possible value of z ==4 + 5 + 8 ==17

1 - (2 * 2 * 4) ==2 * (2 + 2 + 4) ==16 = 16

2 - (1 * 4 * 5) ==2 * (1 + 4 + 5) ==20 = 20

3 - (1 * 3 * 8) ==2 * ( 1+ 3 + 8) ==24 = 24

Thank you, but it says that is incorrect.

So would the answer be 

(2+2+4)+(1+4+5)+(1+3+8)?

1  = (2, 2, 4)
2  = (1, 4, 5)
3  = (1, 3, 8)

4 is also incorrect, guest. Thanks for your effort! 

22 is incorrect guest, but thanks for trying!

The answer is 22.

 318 , 415 , 514 , 813>> Total = 4

Whn lines are perpendicular, their slopes mutltiply to -1 in slope intercept form

We have: 

y=2x+13

6y+ax =6

y= 2x+13

6y = -ax+6

y=2x+13

y=-(a/6)x+1

-(a/6) = -1/2

a=3