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Answer:
The ratio of AC/CB=1/3
Step-by-step explanation:
We use the section formula:
![(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})](https://tex.z-dn.net/?f=%28%5Cfrac%7Bmx_2%2Bnx_1%7D%7Bm%2Bn%7D%2C%5Cfrac%7Bmy_2%2Bny_1%7D%7Bm%2Bn%7D%29)
We substitute the point A(-1.5,0) and B(4.5,8).
We plug in the points to get:
![(\frac{4.5m - 1.5n}{m+n},\frac{8m+n \times 0}{m+n})](https://tex.z-dn.net/?f=%28%5Cfrac%7B4.5m%20-%201.5n%7D%7Bm%2Bn%7D%2C%5Cfrac%7B8m%2Bn%20%5Ctimes%200%7D%7Bm%2Bn%7D%29)
This is supposed to be equal to: (0,2).
![(\frac{4.5m - 1.5n}{m+n},\frac{8m+n \times 0}{m+n}) = (0,2)](https://tex.z-dn.net/?f=%28%5Cfrac%7B4.5m%20-%201.5n%7D%7Bm%2Bn%7D%2C%5Cfrac%7B8m%2Bn%20%5Ctimes%200%7D%7Bm%2Bn%7D%29%20%3D%20%280%2C2%29)
We can equate, corresponding coordinates to find m and n.
![\frac{4.5m - 1.5n}{m + n} = 0](https://tex.z-dn.net/?f=%20%5Cfrac%7B4.5m%20-%201.5n%7D%7Bm%20%2B%20n%7D%20%20%3D%200)
This implies that:
![4.5m - 1.5n = 0](https://tex.z-dn.net/?f=4.5m%20-%201.5n%20%3D%200)
![4.5m = 1.5n](https://tex.z-dn.net/?f=4.5m%20%20%3D%201.5n)
![\frac{m}{n} = \frac{1.5}{4.5}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bm%7D%7Bn%7D%20%20%3D%20%20%5Cfrac%7B1.5%7D%7B4.5%7D%20)
![\frac{m}{n} = \frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bm%7D%7Bn%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20)
Therefore the ratio is m:n=1:3
Answer:
B
Step-by-step explanation:
Answer:
To find the price per spoon of brand A, divide the cost by the amount of spoons:
1.99 / 25 = 0.0796
Repeat this process for brand B:
3.89 / 42 = 0.0926
Brand A, at $0.08 a unit, is the better buy of brands A and B.