Slove x: 9x - 6 = 4x + 19

Answer:

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Final answer:

To find the remaining area of the paperboard, calculate the area of the rectangle, subtract the area of the semicircle. The area of the rectangle is 336 square inches, and the area of the semicircle is 32π square inches. The remaining area is approximately 236.05 square inches.

Explanation:

To answer this question, we first need to calculate the area of the entire paperboard, and then calculate the area of the semi-circle that was cut out. We then subtract the area of the semi-circle from the area of the paperboard to get the remaining area.

The area of a rectangle is calculated by multiplying its length by its width. For the paperboard, we find the area by multiplying 21 inches (length) by 16 inches (width), which gives us 336 square inches.

Next, we have to calculate the area of the semi-circle that was cut out. Assuming the cut was made along the width of the paperboard, the diameter of the semi-circle would be 16 inches. The radius, therefore, is 8 inches. The area of a circle is given by the formula πr², where r is the radius. For a semi-circle, we simply take half of this. This gives us an area of half of π(8)² = 32π square inches.

So, to find the remaining area of the paperboard, we subtract the area of the semi-circle from the area of the rectangle: 336 square inches - 32π square inches = approximately 236.05 square inches.

Learn more about Area Calculation here:

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