Answer
78.75
Step-by-step explanation:
75.00 × 0.05
= 78.75
![\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:
<u>Infotron should produce each day 13 hockey and 6 soccer games</u>
Step-by-step explanation:
x = Number of hockey games Infotron should produce
y = Number of soccer games Infotron should produce
Number of labor-hours for assembly = 2x + 3y
Number of labor-hours for testing = 2x + y
Now we can write our equations system, this way:
2x + 3y = 44
2x + y = 32
*********************
Expressing y in terms of x in the 2nd equation:
2x + y = 32
y = 32 - 2x
********************
Substituting y and solving for x in the 1st equation:
2x + 3y = 44
2x + 3 * ( 32 - 2x) = 44
2x + 96 - 6x = 44
-4x = 44 - 96
-4x = - 52
x = -52/-4
x = 13
*****************
Solving for y in the 2nd equation:
2x + y = 32
2 * 13 + y = 32
26 + y = 32
y = 32 - 26
y =<u> 6</u>
<u>Infotron should produce each day 13 hockey and 6 soccer games</u>
Answer:
It should be the first on the list 17 - 12/6
Step-by-step explanation:
if I replace the words in your sentence, you have
17 minus the 12/6
get
17 - 12/6