Answer:
7 - 2 = 5
Step-by-step explanation:
pls give me brainliest i need it to level up
Fun Fact: The hagfish is the only animal that has a skull but no spine.
Answer:
15
Step-by-step explanation:
Answer:
![(a)-\dfrac{11\sqrt{5}}{25} \\(b) -\dfrac{2\sqrt{5}}{25} \\(c)\dfrac{11}{2}](https://tex.z-dn.net/?f=%28a%29-%5Cdfrac%7B11%5Csqrt%7B5%7D%7D%7B25%7D%20%5C%5C%28b%29%20-%5Cdfrac%7B2%5Csqrt%7B5%7D%7D%7B25%7D%20%5C%5C%28c%29%5Cdfrac%7B11%7D%7B2%7D)
Step-by-step explanation:
![\tan \alpha =\dfrac12, \pi < \alpha< \dfrac{3 \pi}{2}](https://tex.z-dn.net/?f=%5Ctan%20%5Calpha%20%3D%5Cdfrac12%2C%20%5Cpi%20%3C%20%5Calpha%3C%20%5Cdfrac%7B3%20%5Cpi%7D%7B2%7D)
Therefore:
![\alpha$ is in Quadrant III](https://tex.z-dn.net/?f=%5Calpha%24%20is%20in%20Quadrant%20III)
Opposite = -1
Adjacent =-2
Using Pythagoras Theorem
![Hypotenuse^2=Opposite^2+Adjacent^2\\=(-1)^2+(-2)^2=5\\Hypotenuse=\sqrt{5}](https://tex.z-dn.net/?f=Hypotenuse%5E2%3DOpposite%5E2%2BAdjacent%5E2%5C%5C%3D%28-1%29%5E2%2B%28-2%29%5E2%3D5%5C%5CHypotenuse%3D%5Csqrt%7B5%7D)
Therefore:
![\sin \alpha =-\dfrac{1}{\sqrt{5}}\\\cos \alpha =-\dfrac{2}{\sqrt{5}}](https://tex.z-dn.net/?f=%5Csin%20%5Calpha%20%3D-%5Cdfrac%7B1%7D%7B%5Csqrt%7B5%7D%7D%5C%5C%5Ccos%20%5Calpha%20%3D-%5Cdfrac%7B2%7D%7B%5Csqrt%7B5%7D%7D)
Similarly
![\cos \beta =\dfrac35, \dfrac{3 \pi}{2}](https://tex.z-dn.net/?f=%5Ccos%20%5Cbeta%20%3D%5Cdfrac35%2C%20%5Cdfrac%7B3%20%5Cpi%7D%7B2%7D%3C%5Cbeta%3C2%5Cpi%5C%5C%5Cbeta%20%24%20is%20in%20Quadrant%20IV%20%28x%20is%20negative%2C%20y%20is%20positive%29%2C%20therefore%3A%5C%5CAdjacent%3D%24-3%5C%5C%24Hypotenuse%3D5%5C%5COpposite%3D4%20%20%28Using%20Pythagoras%20Theorem%29)
![\sin \beta =\dfrac{4}{5}\\\tan \beta =-\dfrac{4}{3}](https://tex.z-dn.net/?f=%5Csin%20%5Cbeta%20%3D%5Cdfrac%7B4%7D%7B5%7D%5C%5C%5Ctan%20%5Cbeta%20%3D-%5Cdfrac%7B4%7D%7B3%7D)
(a)
![\cos(\alpha + \beta)=\cos\alpha\cos\beta-\sin \alpha\sin \beta\\](https://tex.z-dn.net/?f=%5Ccos%28%5Calpha%20%2B%20%5Cbeta%29%3D%5Ccos%5Calpha%5Ccos%5Cbeta-%5Csin%20%5Calpha%5Csin%20%5Cbeta%5C%5C)
![=-\dfrac{2}{\sqrt{5}}\cdot \dfrac{3}{5}-(-\dfrac{1}{\sqrt{5}})(\dfrac{4}{5})\\=-\dfrac{2\sqrt{5}}{5}\cdot \dfrac{3}{5}+\dfrac{\sqrt{5}}{5}\cdot\dfrac{4}{5}\\=-\dfrac{2\sqrt{5}}{25}](https://tex.z-dn.net/?f=%3D-%5Cdfrac%7B2%7D%7B%5Csqrt%7B5%7D%7D%5Ccdot%20%5Cdfrac%7B3%7D%7B5%7D-%28-%5Cdfrac%7B1%7D%7B%5Csqrt%7B5%7D%7D%29%28%5Cdfrac%7B4%7D%7B5%7D%29%5C%5C%3D-%5Cdfrac%7B2%5Csqrt%7B5%7D%7D%7B5%7D%5Ccdot%20%5Cdfrac%7B3%7D%7B5%7D%2B%5Cdfrac%7B%5Csqrt%7B5%7D%7D%7B5%7D%5Ccdot%5Cdfrac%7B4%7D%7B5%7D%5C%5C%3D-%5Cdfrac%7B2%5Csqrt%7B5%7D%7D%7B25%7D)
(b)
![\sin(\alpha + \beta)=\sin\alpha\cos\beta+\cos \alpha\sin \beta](https://tex.z-dn.net/?f=%5Csin%28%5Calpha%20%2B%20%5Cbeta%29%3D%5Csin%5Calpha%5Ccos%5Cbeta%2B%5Ccos%20%5Calpha%5Csin%20%5Cbeta)
![\sin(\alpha + \beta)=\sin\alpha\cos\beta+\cos \alpha\sin \beta\\=-\dfrac{1}{\sqrt{5}}\cdot\dfrac35+(-\dfrac{2}{\sqrt{5}})(\dfrac{4}{5})\\=-\dfrac{\sqrt{5}}{5}\cdot\dfrac35-\dfrac{2\sqrt{5}}{5}\cdot\dfrac{4}{5}\\=-\dfrac{11\sqrt{5}}{25}](https://tex.z-dn.net/?f=%5Csin%28%5Calpha%20%2B%20%5Cbeta%29%3D%5Csin%5Calpha%5Ccos%5Cbeta%2B%5Ccos%20%5Calpha%5Csin%20%5Cbeta%5C%5C%3D-%5Cdfrac%7B1%7D%7B%5Csqrt%7B5%7D%7D%5Ccdot%5Cdfrac35%2B%28-%5Cdfrac%7B2%7D%7B%5Csqrt%7B5%7D%7D%29%28%5Cdfrac%7B4%7D%7B5%7D%29%5C%5C%3D-%5Cdfrac%7B%5Csqrt%7B5%7D%7D%7B5%7D%5Ccdot%5Cdfrac35-%5Cdfrac%7B2%5Csqrt%7B5%7D%7D%7B5%7D%5Ccdot%5Cdfrac%7B4%7D%7B5%7D%5C%5C%3D-%5Cdfrac%7B11%5Csqrt%7B5%7D%7D%7B25%7D)
(c)
![\tan(\alpha + \beta)=\dfrac{\sin(\alpha + \beta)}{\sin(\alpha + \beta)}=-\dfrac{11\sqrt{5}}{25} \div -\dfrac{2\sqrt{5}}{25} =\dfrac{11}{2}](https://tex.z-dn.net/?f=%5Ctan%28%5Calpha%20%2B%20%5Cbeta%29%3D%5Cdfrac%7B%5Csin%28%5Calpha%20%2B%20%5Cbeta%29%7D%7B%5Csin%28%5Calpha%20%2B%20%5Cbeta%29%7D%3D-%5Cdfrac%7B11%5Csqrt%7B5%7D%7D%7B25%7D%20%5Cdiv%20-%5Cdfrac%7B2%5Csqrt%7B5%7D%7D%7B25%7D%20%3D%5Cdfrac%7B11%7D%7B2%7D)
I think the better buy is the 1.50 for 5oz