Question

Which of the points is NOT one of the vertices (s,t) of the shaded region of the set of inequalities shown below?

Please help

Answer 1

D.

Explanation:

Answer 2

Option D

Explanation:

Given: set of inequalities

To find: Points which do not satisfy all the inequalities

Solution:

For point
`(15,0)`:

`15\leq 30-3(0)=30\\15\geq 15-0=15\\15\leq 25-0=25\\15\geq 0\\0\geq 0`

So, (15, 0) satisfies all the inequalities

For point
`(7.5,7.5)`:

`7.5\leq 30-3(7.5)=30-22.5=7.5\\7.5\geq 15-7.5=7.5\\7.5\leq 25-7.5=17.5\\7.5\geq 0\\7.5\geq 0`

So, (7.5, 7.5) satisfies all the inequalities

For point (22.5,2.5):

`22.5\leq 30-3(2.5)=30-7.5=22.5\\22.5\geq 15-2.5=12.5\\22.5\leq 25-2.5=22.5\\22.5\geq 0\\2.5\geq 0\\`

So, (22.5,2.5) satisfies all the inequalities

For point (7.5 ,0):

Put s = 7.5 and t = 0 in
`s\geq 15-t`

`7.5\geq 15-0=15` which is false

So,
`(s,t)\\eq (7.5,0)`