Q34. - Algebra 2

Question

It is to check whether Rosa will get an A If rosa scored $85$ scored in midterm and $95$ on final.

Step-by-Step Solution

Answer

If rosa scores $85$ on the midterm and $95$on the final then she will score A.

Step-1 – Describe the given data

Here it is given that following information

Rosa’s professor says that the midterm exam will count $40\%$ and final exam will count for $60\%$

Which Consider the inequality showing this situation $0.4x+0.6y\ge 90$

The variables are respectively the midterm score and final exam score. 

Step-2 – Plot the graph of the given function

The graph can be plot in inequality $0.4x+0.6y\ge 90$ shown below,

To find out whether Rosa can score an A if she gets $85$ get in midterm and $95$ in the final, the point $\left(85,95\right)$ final, the point it should lie in the shaded region represents as the feasible region.

Step-3 – Describe the points which satisfy the inequality

Consider boundary here is of graph Another way to find out whether she can score an A on getting $85$ in midterm and $95$in final is that the point $\left(85,95\right)$should satisfy the inequality.

Putting the value $x=85$ Putting the value and $y=95$ value and in the inequality,

$\begin{array}{l}0.4x+0.6y\ge 90\\ 0.4\left(85\right)+0.6\left(95\right)\ge 90\\ 34+57\ge 90\end{array}$

Therefore, 

$91\ge 90$

Hence, $\left(85,95\right)$lies in the shaded region which has the interpretation that Rosa will score an if she get $85$ in midterm $95$ and in the final.

Therefore, the answer is yes.