Which of the following is guaranteed by the Intermediate Value Theorem, if f is a continuous function on the closed interval [−13, −5] where f(−13) = 4 and f(−5) = 11? f(c) = −7 for at least one c in the open interval (4, 11)
f(c) = 7 for at least one c in the open interval (−13, −5)
f(c) = −7 for at least one c in the open interval (−13, −5)
f(c) = 7 for at least one c in the open interval (4, 11)

{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

d. corresponding side lengths in similar triangles are proportional in length.

step-by-step explanation: