Question

The sum of a number and 20 is no more than the sum of the square of the number and 9.

Which of the following inequalities can be used to determine this unknown number?

A) x + 20 ≤ x2 + 9

B) x + 20 < x2 + 92

C) x + 20 < (x + 9)2

D) x + 20 ≤ (x + 9)2

Answer 1

Option A is correct

`x+20 \leq x^2+9`

Explanation:

Let the number be x.

As per the statement:

The sum of a number and 20 is no more than the sum of the square of the number and 9.

"sum of a number and 20" translated to x + 20

"no more than" means
`\leq`

"sum of the square of the number and 9" translated to
`x^2+9`

then;

`x+20 \leq x^2+9`

Therefore, the following inequalities can be used to determine this unknown number is,
`x+20 \leq x^2+9`