The <em>second order</em> polynomial that involves the variable <em>x</em> (border inside the rectangle) and associated to the <em>unshaded</em> area is x² - 62 · x + 232 = 0.
<h3>How to derive an expression for the area of an unshaded region of a rectangle</h3>
The area of a rectangle (<em>A</em>), in square inches, is equal to the product of its width (<em>w</em>), in inches, and its height (<em>h</em>), in inches. According to the figure, we have two <em>proportional</em> rectangles and we need to derive an expression that describes the value of the <em>unshaded</em> area.
If we know that <em>A =</em> 648 in², <em>w =</em> 22 - x and <em>h =</em> 40 - x, then the expression is derived below:
<em>A = w · h</em>
(22 - x) · (40 - x) = 648
40 · (22 - x) - x · (22 - x) = 648
880 - 40 · x - 22 · x + x² = 648
x² - 62 · x + 232 = 0
The <em>second order</em> polynomial that involves the variable <em>x</em> (border inside the rectangle) and associated to the <em>unshaded</em> area is x² - 62 · x + 232 = 0. 
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Answer:
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Step-by-step explanation:
The slope would be 1/1x, or just 1x or 1.
We will first find the volume of the base:
V 1 = 9² · 5 = 81 · 5 = 405 in³
Then the volume of the upper solid - pyramid. We must find the height of the pyramid:
h² = 11² - 4.5² = 121 - 20.25 = 100.75
h = √100.75
h = 10.037429
V 2 = 1/3 · 9² · 10.037429 = 271.01
Finally, the volume of the composite solid:
V = V 1 + V 2 = 405 + 271.01 = 676.01
Answer: C. 676.01 in³
Answer:
126
Step-by-step explanation: