Question

Which of the points (s, t) is inside the shaded region of the set of inequalities shown below?

s<24 - 0.66t
s>12 - t
s< 30 - t
s>0
t>0

O A. (1,8)
O B. (-9,21)
O C. (9,4)
O D. (30, 10)​

Answer 1

Answer:9,4

Explanation:

Answer 2

Only point C. (9,4)

Explanation:

To check if the points are inside the region of the inequalities, we just need to use the values of the point in each inequation, and if the point satisfy all inequations, the point is inside the region.

point A = (1,8): s = 1 and t = 8

first inequation: s<24 - 0.66t

1 < 24 - 0.66*8

1 < 18.72 (true)

second inequation: s>12 - t

1 > 12 - 8

1 > 4 (false)

So point A is not inside the region.

point B = (-9,21): s = -9 and t = 21

As we can see from the fourth inequation, the s value needs to be greater than 0, and point B has s negative, so point B is not inside the region.

point C = (9,4): s = 9 and t = 4

first inequation: s<24 - 0.66t

9 < 24 - 0.66*4

9 < 21.36 (true)

second inequation: s>12 - t

9 > 12 - 4

9 > 8 (true)

third inequation: s< 30 - t

9 < 30 - 4

9 < 26 (true)

fourth inequation: s>0

9 > 0 (true)

fifth inequation: t>0

4 > 0 (true)

As all conditions are true, point C is inside the region.

point D = (30,10): s = 30 and t = 10

first inequation: s<24 - 0.66t

30 < 24 - 0.66*10

30 < 17.4 (false)

So point D is not inside the region.