Another question. is very much appreciated! ! (see attachment)

The triangle inequality says the two smallest sides have to add up to strictly more than the biggest. So when 7 and 12 are the smaller sides the biggest can't be 19 or larger. When 12 is the largest side the smallest side can't be 5 or smaller. So we check those in the open interval (5,19):

A B C D

According to the triangle inequality theory the sum of 2 sides of a triangle need to be grater than the 3rd side.

If we sum 7 + 12 we obtain a result of 19. Since nineteen is the answer, we select all the options that summed with either 12 or 7 are lower than 19 but greater than 5 (because if you sum up 5 with the numbers, the answers won't match according to the theory):

A, B, C & D

Hope it helped,

Happy homework/ study/ exam!

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

you didn't give me the choices, so i will just give you the graph so you can look at your choices and choose the right one.