The 1,000s place because she was in the 100s and you moved 6 to the left which makes the number higher.
{x+2y+2z=0
{2x+y+z=3
{x-3y-z=1
{x+2y+2z=0
-
{4x+2y+2z=6
{-3x=-6 → x=2
{-3y-z=-1
+
{y+z=-1
{-2y=-2 → y=1
{2+2+2z=0 → 2z=-4 → z=-2
Final triple is
(2; 1; -2)
Yes you always do.
eg x - 2 = 8
x - 2 + 2 = 8 + 2
x = 10
if we plug x = 10 into the original equation we se that this fits:-
10 - 2 = 8
The volume of a triangular prism is V = 1/2 x a x c x h where a is height of the triangle, c is the base of the triangle and h is the height of the prism.
120 = 1/2 x a x c x h; we write a from the previous equation in terms of c and h thus,
a = 240 / ( c x h)
If the dimensions where halved then a = a/2 ; c = c/2 ; h=h/2
We use the volume formula again and substitute the given values to find the new volume,
V = 1/2 x a/2 x c/2 x h/2
Substitute the previously determined a term,
V = 1/2 x (240/2ch) x c/2 x h/2
We cancel and evaluate the constants therefore the new volume is,
V= 15 cm^3
