Answer:
10 square units.
Step-by-step explanation:
Area of Polygon C = 40 square units.
Scale factor used in obtaining polygon D = ![\dfrac12](https://tex.z-dn.net/?f=%5Cdfrac12)
To obtain the area of the new polygon, we multiply the area of the polygon from which it was derived by the square of the scale factor.
Therefore:
Area of Polygon D
![=40 \times (\frac12)^2\\\\=40 \times \frac14\\\\=10$ square units](https://tex.z-dn.net/?f=%3D40%20%5Ctimes%20%28%5Cfrac12%29%5E2%5C%5C%5C%5C%3D40%20%5Ctimes%20%5Cfrac14%5C%5C%5C%5C%3D10%24%20square%20units)
The area of polygon D is 10 square units.
Answer:
![3v^2\left(5v^6-7v^3\right)=15v^8-21v^5](https://tex.z-dn.net/?f=3v%5E2%5Cleft%285v%5E6-7v%5E3%5Cright%29%3D15v%5E8-21v%5E5)
Step-by-step explanation:
Given the expression
![3v^2\left(5v^6-7v^3\right)](https://tex.z-dn.net/?f=3v%5E2%5Cleft%285v%5E6-7v%5E3%5Cright%29)
Apply the distributive law
![a\left(b-c\right)=ab-ac](https://tex.z-dn.net/?f=a%5Cleft%28b-c%5Cright%29%3Dab-ac)
![a=3v^2,\:b=5v^6,\:c=7v^3](https://tex.z-dn.net/?f=a%3D3v%5E2%2C%5C%3Ab%3D5v%5E6%2C%5C%3Ac%3D7v%5E3)
![=3v^2\cdot \:5v^6-3v^2\cdot \:7v^3](https://tex.z-dn.net/?f=%3D3v%5E2%5Ccdot%20%5C%3A5v%5E6-3v%5E2%5Ccdot%20%5C%3A7v%5E3)
![=3\cdot \:5v^6v^2-3\cdot \:7v^3v^2](https://tex.z-dn.net/?f=%3D3%5Ccdot%20%5C%3A5v%5E6v%5E2-3%5Ccdot%20%5C%3A7v%5E3v%5E2)
![=15v^8-21v^5](https://tex.z-dn.net/?f=%3D15v%5E8-21v%5E5)
Thus, we conclude that
![3v^2\left(5v^6-7v^3\right)=15v^8-21v^5](https://tex.z-dn.net/?f=3v%5E2%5Cleft%285v%5E6-7v%5E3%5Cright%29%3D15v%5E8-21v%5E5)
The first step is to Prepare. Heidi wants to make a 30 pounds of molasses solution. She mixes and solution together. How much mixture does she make?
It will. Be the third one