Question

Three times the square of a number is greater than a second number. The square of the second number increased by 6 is greater than the first number. Which system of inequalities represents these criteria?

Answer 1

Given:

Three times the square of a number is greater than a second number.

The square of the second number increased by 6 is greater than the first number.

To find:

The system of inequalities represents these criteria.

Solution:

Let the first number be x and the second number be y.

Three times the square of a number is greater than a second number.

$3\times x^2>y$

$3x^2>y$           ...(i)

The square of the second number increased by 6 is greater than the first number.

$y^2+6>x$       ...(ii)

Therefore, the system of inequalities represents these criteria has inequalities $3x^2>y$ and $y^2+6>x$, where x is first number and y is second number.

Answer 2

The system of inequalities represents given criteria are $3x^{2} > y$ and $y^{2} +6 > x$.

Let us take the numbers as x and y respectively.

First number = x

Second number = y

What is inequality?

Inequality is the relationship between two expressions that are not equal to one another.

Three times the square of the first number is greater than a second number:

This means, $3x^{2} > y$

The square of the second number increased by 6 is greater than the first number:

This means, $y^{2} +6 > x$

Therefore, the system of inequalities represents given criteria are $3x^{2} > y$ and $y^{2} +6 > x$.

To get more about inequalities visit:

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