Answer: Coffiecent is 26
Step-by-step explanation
the travel from Sun to Jupiter it will take more than 43 minutes . depending on whether are on the same side of the Sun as well as Jupiter or on the other side
another point always sun and Jupiter are not nearest so only changes in the light travels
Answer:
x
21
Step-by-step explanation:
(-2/3)x+13≥ -1
(-2/3)x≥ -14 (I subtracted by 13 on both sides)
x
-14*(-3/2) (I divided by -2/3 on both sides)
x
21
Answer:
When x=10 , y= 120
When x = 1\2 , y = 6
Step-by-step explanation:
X=2/4,y=6
10 *6 = 0.5y
10*6 *2 =y
120=y
0.5 (6)= 0.5 y
Y=6
Answer:
![\cos(\alpha +\beta)=\frac{2}{3}(1-\frac{\sqrt{5}}{5})](https://tex.z-dn.net/?f=%5Ccos%28%5Calpha%20%2B%5Cbeta%29%3D%5Cfrac%7B2%7D%7B3%7D%281-%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B5%7D%29)
Step-by-step explanation:
Let the hypotenuse of the smaller triangle be h units.
Then; from the Pythagoras Theorem.
![h^2=4^2+2^2](https://tex.z-dn.net/?f=h%5E2%3D4%5E2%2B2%5E2)
![h^2=16+4](https://tex.z-dn.net/?f=h%5E2%3D16%2B4)
![h^2=20](https://tex.z-dn.net/?f=h%5E2%3D20)
![h=\sqrt{20}](https://tex.z-dn.net/?f=h%3D%5Csqrt%7B20%7D)
![h=2\sqrt{5}](https://tex.z-dn.net/?f=h%3D2%5Csqrt%7B5%7D)
From the smaller triangle;
and ![\sin(\alpha)=\frac{2}{2\sqrt{5} }=\frac{1}{\sqrt{5} }](https://tex.z-dn.net/?f=%5Csin%28%5Calpha%29%3D%5Cfrac%7B2%7D%7B2%5Csqrt%7B5%7D%20%7D%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B5%7D%20%7D)
From the second triangle, let the other other shorter leg of the second triangle be s units.
Then;
![s^2+4^2=6^2](https://tex.z-dn.net/?f=s%5E2%2B4%5E2%3D6%5E2)
![s^2+16=36](https://tex.z-dn.net/?f=s%5E2%2B16%3D36)
![s^2=36-16](https://tex.z-dn.net/?f=s%5E2%3D36-16)
![s^2=20](https://tex.z-dn.net/?f=s%5E2%3D20)
![s=\sqrt{20}](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B20%7D)
![s=2\sqrt{5}](https://tex.z-dn.net/?f=s%3D2%5Csqrt%7B5%7D)
![\cos(\beta)=\frac{2\sqrt{5} }{6}=\frac{\sqrt{5} }{3}](https://tex.z-dn.net/?f=%5Ccos%28%5Cbeta%29%3D%5Cfrac%7B2%5Csqrt%7B5%7D%20%7D%7B6%7D%3D%5Cfrac%7B%5Csqrt%7B5%7D%20%7D%7B3%7D)
and
![\sin(\beta)=\frac{4}{6}=\frac{2}{3}](https://tex.z-dn.net/?f=%5Csin%28%5Cbeta%29%3D%5Cfrac%7B4%7D%7B6%7D%3D%5Cfrac%7B2%7D%7B3%7D)
We now use the double angle property;
![\cos(\alpha +\beta)=\cos(\alpha)\cos(\beta) -\sin(\alpha)\sin(\beta)](https://tex.z-dn.net/?f=%5Ccos%28%5Calpha%20%2B%5Cbeta%29%3D%5Ccos%28%5Calpha%29%5Ccos%28%5Cbeta%29%20-%5Csin%28%5Calpha%29%5Csin%28%5Cbeta%29)
we plug in the values to obtain;
![\cos(\alpha +\beta)=\frac{2}{\sqrt{5} }\times \frac{\sqrt{5} }{3}-\frac{1}{\sqrt{5} }\times \frac{2}{3}](https://tex.z-dn.net/?f=%5Ccos%28%5Calpha%20%2B%5Cbeta%29%3D%5Cfrac%7B2%7D%7B%5Csqrt%7B5%7D%20%7D%5Ctimes%20%5Cfrac%7B%5Csqrt%7B5%7D%20%7D%7B3%7D-%5Cfrac%7B1%7D%7B%5Csqrt%7B5%7D%20%7D%5Ctimes%20%5Cfrac%7B2%7D%7B3%7D)
![\cos(\alpha +\beta)=\frac{2}{3}(1-\frac{\sqrt{5}}{5})](https://tex.z-dn.net/?f=%5Ccos%28%5Calpha%20%2B%5Cbeta%29%3D%5Cfrac%7B2%7D%7B3%7D%281-%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B5%7D%29)
Answer:
I believe it is -17.5. Tell me if I am wrong
Step-by-step explanation:
3x + 5 = x - 10
-x -5 -x -5
2x = -15
x = -7.5
3(7.5) + 5
= 22.5 + 5
= -17.5