Which statement is true about the given function? a. f(x) < 0 over the intervals (-infinity, -2,7) and (0.8, infinity) b. f(x) < 0 over the intervals (-infinity, -2.7) and (-1 ,0.8) c. f(x) > 0 over the intervals (-infinity, -2.7) and (-1, 0.8) d. f(x) > 0 over the intervals (-infinity, -1) and (0.8, infinity)

For the shown graph, let us make some notes to get the correct option.

First let us see that are the positive and what are the negative values of y's in the shown graph.

Note: The values of y's down the x-axis are negative and up the x-axis are positive.

From (-infinity to -2.7) it has negative values of y, that is less than 0 because it's down the x-axis.

From (-1 to 0.08) it also has negative values of y, that is less than 0.

Therefore, correct option is option B). f(x) < 0 over the intervals (-infinity, -2.7) and (-1 ,0.8).

{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