Question

2. Write a system of inequalities to represent the shaded portion of the graph.

Answer 1

The shaded area is 34.66 sq. units.

Linear system

It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.

To find

The shaded area is shown in the graph.

How to find a shaded area?

A line y = mx + c

For dashed line, the slope (m) is given by

$\rm m = \dfrac{y_{2} -y_{1} }{x_{2} -x_{1} } \\\\m = \dfrac{3-0}{1-0} \\\\m = 3$

And c = 0  because the line is passing through the origin.

so the equation is 3y = x

For x = -1 then y = -1/3

Then

The base and height of the triangle will be 16/3 and 4.

And the height of the trapezium and the sum of the parallel side are 4 and 12.

Then the shaded area will be

$\rm Shaded\ area\ =\ area\ of\ trapezium\ +\ area\ of\ triangle\\\\Shaded\ area\ = \dfrac{1}{2} (sum\ of\ parallel\ sidess)* height +\dfrac{1}{2} base *height\\\\Shaded\ area\ = \dfrac{1}{2} *12*4 +\dfrac{1}{2} * \dfrac{16}{3} *4\\\\Shaded\ area\ = 34.66$

Thus, the shaded area is 34.66 sq. units.

More about the linear system link is given below.

brainly.com/question/20379472