The area of the convex polygon is 43/2 square units
<h3>How to determine the area of the convex polygon?</h3>
The vertices are given as:
(0,5), (-1,2), (4,4), (-3,-4) and (2,0)
The area is then calculated as:
![A = \frac 12(\left[\begin{array}{cc}x_1&x_2\\y_1&y_2\end{array}\right] + \left[\begin{array}{cc}x_2&x_3\\y_2&y_3\end{array}\right] + ....+\left[\begin{array}{cc}x_n&x\\y_n&y\end{array}\right] )](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%2012%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dx_1%26x_2%5C%5Cy_1%26y_2%5Cend%7Barray%7D%5Cright%5D%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dx_2%26x_3%5C%5Cy_2%26y_3%5Cend%7Barray%7D%5Cright%5D%20%2B%20....%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dx_n%26x%5C%5Cy_n%26y%5Cend%7Barray%7D%5Cright%5D%20%29)
So, we have:
Evaluate
Remove the absolute bracket
This gives
Hence, the area of the convex polygon is 43/2 square units
Read more about convex polygon at:
brainly.com/question/14522707
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I think the correct answer from the choices listed above is the last option. The number of points that lie on a period at the end of a sentence are infinite. <span>Thus, an infinite amount of them can reside on a finite sized period at the end of a sentence. Hope this answers the question.</span>
Part A.
The set of equations can be solved by substitution. Use the expression one equation gives for y as the value of y in the other equation. This gives
2x²-15 = 3x-6
Subtracting the right side gives a quadratic in standard form that can be solved by any of several methods.
2x² -3x -9 = 0
(2x+3)(x-3) = 0 . . . . factor the above equation
x = -3/2, x = 3 . . . . .use the zero product rule to find x
Now, these x-values can be substituted into either equation for y. The linear equation is often easier to evaluate.
y = 3(-3/2) -6 = -10.5
y = 3(3)-6 = 3
The solutions to the system are (-1.5, -10.5) and (3, 3).
Part B.
The two equations can be graphed. The solutions are where the graphs intersect. The graphs intersect where the (x, y) values that satisfy one equation are the same (x, y) values that satisfy the other equation. Those points of intersection are (-1.5, -10.5) and (3, 3).
