Q33. - Algebra 2

Question

Graph the inequality $0.4x+0.6y\ge 90$where $x$ is midterm score and $y$ is the final term score.

Step-by-Step Solution

Answer

The graph of the inequality is

The inequality is $0.4x+0.6y\ge 90$

Step-1 – Describe the given data

Which Rosa’s professor says that the midterm exam will count for $40\%$of each students grade and final exam will count for means $60\%$

The Consider the inequality showing this situation as

$0.4x+0.6y\ge 90$

Here, the variables are respectively the midterm score and final exam score.

Step-2 – Check whether the inequality is true or not.

The graph of the above inequality is represented as follows:

The corresponding equation of the inequality is

$0.4x+0.6y\ge 90$

Since, the inequality sign is $\ge$so, the boundary will be solid.

Check the origin point $\left(0,0\right)$

On substituting the value $x=0$and $y=0$in the inequality.

$\begin{array}{l}0.4x+0.6y\ge 90\\ 0.4\left(0\right)+0.6\left(0\right)\ge 90\\ 0\ge 90\end{array}$

The origin does not satisfy the inequality, therefore, the shaded region not containing the origin side.

Therefore, all points lying above the solid  boundary satisfies the inequality.

Step-3 – Plot the graph of the given function

The graph of the inequality 

$0.4x+0.6y\ge 90$is represented as the shaded region as follows.