using the digits 0,1,2,2,3 how many numbers greater than 20000 can be made ?

Assuming digits are to be used only once then as long as the first digit is greater than 1, any number formed will be greater than 20000:
3*4*3*2*1=72

Solve the equation by using the square root property. Express the radical in simplest form: (m+12)^2=-9

 or 
 or 

indicates the sets to which the number belongs -144/4

This number belongs to an infinite number of sets, but if you mean "major" set of numbers, then -144/4 belongs to the negative rational numbers, and thus every set for which the negative rational numbers is a subset.

Give the coordinates of the vertex for the graph of the equation: y=x^2+6x+9

In general...


v(-3,0)

but there is an easier way if we use the fact that it is a perfect square...


so that , 

---

separate 30 into two parts such that the larger is 6 less than twice the smaller. find the working equation of this and the answer.

1) 2x-6=y
2) x+y=30 

then we write... 
x+(2x-6)=30
3x=36
x=12 



and so y=18

|x-1| = 5x+10

absolute value means...
1) x-1=5x+10 
or 
2) x-1=-5x-10 

so for case 1)...
4x=-11
x=-11/4 (extraneous)


and for case 2)...
-6x=9
x=-3/2

how do i do this: 1 /loga(abc) +1 /logb(abc) +1 /logc(abc) ?

use the change of base identity: 
1 /loga(abc) +1 /logb(abc) +1 /logc(abc)=
(log(a)+log(b)+log(c))/log(abc)