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

Question

asked Nov 4, 2021 65.9k views

2 Answers

Chandel · Answer 1 · 2021-11-08T02:52:34+0000

Answer:

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,
$(s,t)\\eq (7.5,0)$