Question

Given 4y2 + x – 32y + 68 > 0, which ordered pair is part of the solution set? (–3, 5.7) (–5.9, 4) (–8, 5) (–13, 3)

Answer 1

Answer:

A. (-3, 5.7)

Step-by-step explanation:

Answer 2

Inequalities help us to compare two unequal expressions. The ordered pair that satisfies the given inequality is (–3, 5.7).

What are inequalities?

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

The ordered pair that satisfies the given inequality is the solution set of the inequalities, the inequality can be written as,

$4y^2+x-32y+68 > 0\\\\4y^2-32y+68 > -x$

Now, let's substitute the value of the first ordered pair, (–3, 5.7),

$4(5.7)^2-32(5.7)+68 > -(-3)\\\\129.96-178.24+68 > 9\\\\19.72 > 9$

Since the inequality is satisfied the ordered pair is a set of solutions.

For the second ordered pair (-5.9,4),

$4y^2-32y+68 > -x\\\\4(4)^2-32(4)+68 > -(-5.9)\\\\64-128+68 > 5.9\\\\4 > 5.9$

Since inequality is not true it is not the solution to the problem.

For the third ordered pair (-8, 5),

$4y^2-32y+68 > -x\\\\4(5)^2-32(5)+68 > -(-8)\\\\64-128+68 > 8\\\\8 > 8$

Since inequality is not true it is not the solution to the problem.

For the fourth ordered pair (-13, 3),

$4y^2-32y+68 > -x\\\\4(3)^2-32(3)+68 > -(-13)\\\\64-128+68 > 13\\\\8 > 13$

Since inequality is not true it is not the solution to the problem.

Learn more about Inequality:

https://brainly.com/question/19491153