Area of the region `{(x,y)inR^(2): y ge sqrt(|x+3|), 5ylex+9le15}` is equal to

Options

A. `(1)/(6)`
B. `(4)/(3)`
C. `(3)/(2)`
D. `(5)/(3)`

Explanation

To find the area of the region defined by the inequalities \( y \geq \sqrt{|x + 3|} \) and \( 5y < x + 9 < 15 \), we will follow these steps:

### Step 1: Understand the inequalities
The first inequality \( y \geq \sqrt{|x + 3|} \) represents the area above the curve defined by \( y = \sqrt{|x + 3|} \). The second inequality \( 5y < x + 9 < 15 \) can be split into two parts:
1. \( 5y < x + 9 \) which simplifies to \( y < \frac{x + 9}{5} \)
2. \( x + 9 < 15 \) which simplifies to \( x < 6 \)