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Calculate the total area of the region described. Do not count area beneath the x-axis as negative. bounded by the line y = x, the x-axis, and the lines x = 0 and x = 9 Calculate the total area of the region described. Do not count area beneath the x-axis as negative.

User Nikki
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Final answer:

The total area of the region bounded by the line y = x, the x-axis, and the lines x = 0 and x = 9 is 40.5 square units. This is calculated as the area of a right triangle with base and height of 9 units each.

Step-by-step explanation:

To calculate the total area of the region described, we consider the area bounded by the line y = x, the x-axis, and the lines x = 0 and x = 9. As the question instructs not to count the area beneath the x-axis as negative, we are essentially calculating the area of a triangle where the altitude and the base are both equal to 9, since the line y = x implies the height at x = 9 is also 9.

The area of a triangle is given by the formula ½ × base × height, which in this case translates to ½ × 9 × 9. Therefore, the total area is ½ × 81, or 40.5 square units.

User Darriel
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