Question

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

Answer 1

Answer:

Option D

Step-by-step 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, $(s,t)\neq (7.5,0)$