Answer:
y = -16.9
Step-by-step explanation:
<u>→Add 0.8y to both sides:</u>
-0.8y + 5.49 = -19.86 - 2.3y
5.49 = -19.86 - 1.5y
<u>→Add 19.86 to both sides:</u>
25.35 = -1.5y
<u>→Divide both sides by -1.5:</u>
-16.9 = y
Answer:
2(5) + 3 = 13
Step-by-step explanation:
x=5
y=3
2x+y=13
2(5)+3=13
10 +3 =13
![\displaystyle\\Answer:\ x=\sqrt{2}\ \ \ \ \ x=-\sqrt{2}\ \ \ \ \ x=\frac{ln5}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5C%5CAnswer%3A%5C%20x%3D%5Csqrt%7B2%7D%5C%20%5C%20%5C%20%5C%20%5C%20x%3D-%5Csqrt%7B2%7D%5C%20%5C%20%5C%20%5C%20%5C%20x%3D%5Cfrac%7Bln5%7D%7B2%7D)
Step-by-step explanation:
![5x^2-x^2e^{2x}+2e^{2x}=10](https://tex.z-dn.net/?f=5x%5E2-x%5E2e%5E%7B2x%7D%2B2e%5E%7B2x%7D%3D10)
![Let:\ x^2=t \ \ \ \ \ e^{2x}=v\\Hence,\\5t-tv+2v^2=10\\5t-tv+2v^2-10=10-10\\5t-tv-10+2v^2=0\\t(5-v)-2(5-v)=0\\(5-v)(t-2)=0\\5-v=0\\5-v+v=0+v\\5=v\\5=e^{2x}](https://tex.z-dn.net/?f=Let%3A%5C%20x%5E2%3Dt%20%20%5C%20%5C%20%5C%20%5C%20%5C%20e%5E%7B2x%7D%3Dv%5C%5CHence%2C%5C%5C5t-tv%2B2v%5E2%3D10%5C%5C5t-tv%2B2v%5E2-10%3D10-10%5C%5C5t-tv-10%2B2v%5E2%3D0%5C%5Ct%285-v%29-2%285-v%29%3D0%5C%5C%285-v%29%28t-2%29%3D0%5C%5C5-v%3D0%5C%5C5-v%2Bv%3D0%2Bv%5C%5C5%3Dv%5C%5C5%3De%5E%7B2x%7D)
<em>Prologarithmize both parts of the equation:</em>
![ln5=lne^{2x}\\ln5=2x*lne\\ln5=2x*1\\ln5=2x\\](https://tex.z-dn.net/?f=ln5%3Dlne%5E%7B2x%7D%5C%5Cln5%3D2x%2Alne%5C%5Cln5%3D2x%2A1%5C%5Cln5%3D2x%5C%5C)
<u><em> Divide both parts of the equation by 2:</em></u>
![\displaystyle\\x=\frac{ln5}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5C%5Cx%3D%5Cfrac%7Bln5%7D%7B2%7D)
![t-2=0\\t-2+2=0+2\\t=2\\x^2=2\\x=\sqrt{2} \\x=-\sqrt{2}](https://tex.z-dn.net/?f=t-2%3D0%5C%5Ct-2%2B2%3D0%2B2%5C%5Ct%3D2%5C%5Cx%5E2%3D2%5C%5Cx%3D%5Csqrt%7B2%7D%20%5C%5Cx%3D-%5Csqrt%7B2%7D)
Answer:
x=24
Step-by-step explanation:
y = x*c
x=2, y=7
2*c=7 => c=7/2
x*7/2 = 84
x = 84*2/7
x = 12*2
x = 24