point-slope form of the equation of the line with m = 7 that passes through the point (1, negative-2).
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a. Find the graph of their common region in the attachment
b. The area of the common region of the graphs is 8 units²
<h3>a. How to sketch the region common to the graphs?</h3>Since we have x ≥ 2, y ≥ 0, and x + y ≤ 6, we plot each graph separately and find their region of intersection.
- The graph of x ≥ 2 is the region right of the line x = 2.
- The graph of y ≥ 0 is the region above the line y = 0 or x-axis.
- To plot the graph of x + y ≤ 6, we first plot the graph of x + y = 6 ⇒ y = -x + 6. Then the graph of x + y ≤ 6 is the graph of y ≤ - x + 6.
So, the graph of x + y ≤ 6 is the region below the line y = - x + 6
From the graph, the regions intersect at (2, 0), (2, 4) and (6, 0)
Find the graph of their common region in the attachment
<h3>b. The area of the common region</h3>From the graph, we see that the common region is a right angled triangle with
- height = 4 units and
- base = 4 units
So, its area = 1/2 × height × base
= 1/2 × 4 units × 4 units
= 1/2 × 16 units²
= 8 units²
So, the area of the common region of the graphs is 8 units²
Learn more about region common to graphs here:
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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.
#SPJ1
