Answer:
1 3 6 10 15
Step-by-step explanation:
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Consider the attached figure. The whole rectangle is ABCD, while AEGF is the part located in the third quadrant. In fact, this quadrant is composed by all the points with both coordinates negative.
To answer the question, let's compute the area of the two rectangles and see what part of ABCD is AEGF.
A and B have the same x coordinate, so the length of AB is given by the absolute difference of their y coordinates:
![\overline{AB} = |A_y-B_y| = |-3-7| = |-10| = 10](https://tex.z-dn.net/?f=%20%5Coverline%7BAB%7D%20%3D%20%7CA_y-B_y%7C%20%3D%20%7C-3-7%7C%20%3D%20%7C-10%7C%20%3D%2010%20)
Similarly, but exchanging the role of x and y, we compute the length of BC:
![\overline{BC} = |B_x-C_x| = |-4-1| = |-5| = 5](https://tex.z-dn.net/?f=%20%5Coverline%7BBC%7D%20%3D%20%7CB_x-C_x%7C%20%3D%20%7C-4-1%7C%20%3D%20%7C-5%7C%20%3D%205%20)
So, the area of the rectangle is ![\overline{AB} \cdot \overline{BC} = 10\cdot 5 = 50](https://tex.z-dn.net/?f=%20%5Coverline%7BAB%7D%20%5Ccdot%20%5Coverline%7BBC%7D%20%3D%2010%5Ccdot%205%20%3D%2050%20)
The same procedure allows us to compute width and height of the sub-rectangle in the third quadrant:
![\overline{AE} = |A_y-E_y| = |-3-0| = |-3| = 3](https://tex.z-dn.net/?f=%20%5Coverline%7BAE%7D%20%3D%20%7CA_y-E_y%7C%20%3D%20%7C-3-0%7C%20%3D%20%7C-3%7C%20%3D%203%20)
![\overline{EG} = |E_x-G_x| = |-4-0| = |-4| = 4](https://tex.z-dn.net/?f=%20%5Coverline%7BEG%7D%20%3D%20%7CE_x-G_x%7C%20%3D%20%7C-4-0%7C%20%3D%20%7C-4%7C%20%3D%204%20)
So, the area of the portion located in the third quadrant is ![\overline{AE} \cdot \overline{EG} = 3\cdot 4 = 12](https://tex.z-dn.net/?f=%20%5Coverline%7BAE%7D%20%5Ccdot%20%5Coverline%7BEG%7D%20%3D%203%5Ccdot%204%20%3D%2012%20)
This means that the ratio between the two area is
![\cfrac{\text{area }AEGF}{\text{area }ABCD} = \cfrac{12}{50}](https://tex.z-dn.net/?f=%20%5Ccfrac%7B%5Ctext%7Barea%20%7DAEGF%7D%7B%5Ctext%7Barea%20%7DABCD%7D%20%3D%20%5Ccfrac%7B12%7D%7B50%7D%20)
If we want this ratio to be a percentage, just make sure that the denominator is 100:
![\cfrac{12}{50} = \cfrac{12}{50}\cdot \cfrac{2}{2} = \cfrac{24}{100} = 24\%](https://tex.z-dn.net/?f=%20%5Ccfrac%7B12%7D%7B50%7D%20%3D%20%5Ccfrac%7B12%7D%7B50%7D%5Ccdot%20%5Ccfrac%7B2%7D%7B2%7D%20%3D%20%5Ccfrac%7B24%7D%7B100%7D%20%3D%2024%5C%25%20)
The perimeter of the regular polygon is 70 inches
<h3>How to determine the perimeter of the regular polygon?</h3>
The sides of the regular polygon is given as:
Side = 10 in
The regular polygon has 7 sides
So, the perimeter of the polygon is calculated as:
P = Side lengths * Number of sides
This gives
P = 10 inches * 7
Evaluate
P = 70 inches
Hence, the perimeter of the regular polygon is 70 inches
Read more about perimeter at
brainly.com/question/24571594
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Answer:
53
Step-by-step explanation:
5+3=8, 53 flipped is 35, and 53-35=18
Exponential functions are known to increase geometrically. An example of exponential function is p(x) = 500(1.02)^x
<h3>Exponential functions</h3>
Exponential functions are known to increase geometrically. The standard exponential function is given as:
y = ab^x
a is the base
x is the exponent
From the given options, the function written in this form is
p(x) = 500(1.02)^x. Hence an example of exponential function is
p(x) = 500(1.02)^x
Learn more on exponential function here: brainly.com/question/12940982
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