Choice A is the correct answer.
y=x is the diagonal that goes between the two pentagons and is also the line of reflection.
I guess this reads
![\displaystyle\int_1^4f(x)\,\mathrm dx=19](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_1%5E4f%28x%29%5C%2C%5Cmathrm%20dx%3D19)
![\displaystyle\int_1^4g(x)\,\mathrm dx=12](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_1%5E4g%28x%29%5C%2C%5Cmathrm%20dx%3D12)
You want to compute
![I=\displaystyle\int_1^4(8f(x)-g(x)+7)\,\mathrm dx](https://tex.z-dn.net/?f=I%3D%5Cdisplaystyle%5Cint_1%5E4%288f%28x%29-g%28x%29%2B7%29%5C%2C%5Cmathrm%20dx)
By linearity of the definite integral,
![I=\displaystyle8\int_1^4f(x)\,\mathrm dx-\int_1^4g(x)\,\mathrm dx+7\int\mathrm dx](https://tex.z-dn.net/?f=I%3D%5Cdisplaystyle8%5Cint_1%5E4f%28x%29%5C%2C%5Cmathrm%20dx-%5Cint_1%5E4g%28x%29%5C%2C%5Cmathrm%20dx%2B7%5Cint%5Cmathrm%20dx)
![I=8\cdot19-12+7(4-1)=\boxed{161}](https://tex.z-dn.net/?f=I%3D8%5Ccdot19-12%2B7%284-1%29%3D%5Cboxed%7B161%7D)
Answer:
Step-by-step explanation:
k-2
It is A) strong positive, because the slope is graphing up
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![\large \sf \underline{Problem:}](https://tex.z-dn.net/?f=%5Clarge%20%5Csf%20%5Cunderline%7BProblem%3A%7D)
The weight of the rectangle is 80 grams.
The weight of the triangle is double the weight of the
circle.
Determine the weight of the circle.
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![\large \sf \underline{Answer:}](https://tex.z-dn.net/?f=%5Clarge%20%5Csf%20%5Cunderline%7BAnswer%3A%7D)
Rectangle has four sides. The total weight of the circle is 20 grams.
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![\large \sf \underline{Explanation:}](https://tex.z-dn.net/?f=%5Clarge%20%5Csf%20%5Cunderline%7BExplanation%3A%7D)
What is a rectangle?
A rectangle is a 2D shape that has four sides, and the pair of opposite sides are equal and parallel to each other.
As it is given that the weight of the rectangle is 80 grams, and a rectangle is made up of two triangles. Therefore, the weight of each triangle can be written as,
![Weight \: of \: the \: reactangle \: = \frac{80}{2} = 40 grams](https://tex.z-dn.net/?f=Weight%20%20%5C%3A%20of%20%20%5C%3A%20the%20%20%5C%3A%20reactangle%20%20%5C%3A%20%20%3D%20%20%5Cfrac%7B80%7D%7B2%7D%20%20%3D%2040%20grams)
It is given that the total weight of the triangle is double the weight of the circle. therefore, the relationship can be written as,
![Weight \: of \: the \: triangle = 2x \\ Weight \: of \: the \: circle \: \\ 40 = 2 \times Weight \: of \: the \: circle](https://tex.z-dn.net/?f=Weight%20%5C%3A%20%20of%20%20%5C%3A%20the%20%20%5C%3A%20triangle%20%20%3D%202x%20%20%5C%5C%20%20Weight%20%20%5C%3A%20of%20%20%5C%3A%20the%20%20%5C%3A%20circle%20%5C%3A%20%20%5C%5C%2040%20%3D%20%202%20%5Ctimes%20Weight%20%20%5C%3A%20of%20%20%5C%3A%20the%20%20%5C%3A%20circle%20%3C%2Fp%3E%3Cp%3E%20)
![Weight \: of \: the \: circle = 20 grams](https://tex.z-dn.net/?f=Weight%20%20%5C%3A%20of%20%20%5C%3A%20the%20%20%5C%3A%20circle%20%20%3D%2020%20%20%20%20grams)
Hence, the total weight of the circle is 20 grams.
Learn more about Rectangle:
brainly.com/question/994316
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