What is the area of angle ABC? Round to the nearest tenth
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First of all, when I do all the math on this, I get the coordinates for the max point to be (1/3, 14/27). But anyway, we need to find the derivative to see where those values fall in a table of intervals where the function is increasing or decreasing. The first derivative of the function is 
. Set the derivative equal to 0 and factor to find the critical numbers. 
, so x = -3 and x = 1/3. We set up a table of intervals using those critical numbers, test a value within each interval, and the resulting sign, positive or negative, tells us where the function is increasing or decreasing. From there we will look at our points to determine which fall into the "decreasing" category. Our intervals will be -∞<x<-3, -3<x<1/3, 1/3<x<∞. In the first interval test -4. f'(-4)=-13; therefore, the function is decreasing on this interval. In the second interval test 0. f'(0)=3; therefore, the function is increasing on this interval. In the third interval test 1. f'(1)=-8; therefore, the function is decreasing on this interval. In order to determine where our points in question fall, look to the x value. The ones that fall into the "decreasing" category are (2, -18), (1, -2), and (-4, -12). The point (-3, -18) is already a min value.
The first mistake of Ana is sum of interior is 180° that is given by the definition. Then the correct option is A.
The statements, reasons, and options are attached below.
<h3>What is the triangle?</h3>A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
Linear angle – If the total of two angles is 180 degrees, they are said to be linear angles.
Ana tried to prove that an exterior triangle angle measure equals the sum of the measures of the two interior angles not adjacent to it.
∠1 + ∠2 + ∠3 = 180° (By definition of triangle)
∠3 + ∠4 = 180° (By definition of linear angle)
∠1 + ∠2 + ∠3 = ∠3 + ∠4 (Substitution)
∠1 + ∠2 = ∠4 (Subtraction on both side by ∠3)
The first mistake of Ana is sum of interior is 180° that is given by the definition.
Then the correct option is A.
More about the triangle link is given below.
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