Answer:
16,249 years old
Explanation:
The exponential decay model for carbon-14 is given below:
![A=A_0e^{-0.000121t}](https://tex.z-dn.net/?f=A%3DA_0e%5E%7B-0.000121t%7D)
The paint contained 14% of the original carbon-14.
• A=14% = 0.14
,
• Ao = 100% = 1
![\begin{gathered} 0.14=e^{-0.000121t} \\ \text{ Take the ln of both sides} \\ ln(0.14)=ln(e^{-0.000121t}) \\ ln(0.14)=-0.000121t \\ \text{ Divide both sides by -0.000121} \\ t=\frac{ln(0.14)}{-0.000121} \\ t=16248.9 \\ t\approx16,249 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%200.14%3De%5E%7B-0.000121t%7D%20%5C%5C%20%5Ctext%7B%20Take%20the%20ln%20of%20both%20sides%7D%20%5C%5C%20ln%280.14%29%3Dln%28e%5E%7B-0.000121t%7D%29%20%5C%5C%20ln%280.14%29%3D-0.000121t%20%5C%5C%20%5Ctext%7B%20Divide%20both%20sides%20by%20-0.000121%7D%20%5C%5C%20t%3D%5Cfrac%7Bln%280.14%29%7D%7B-0.000121%7D%20%5C%5C%20t%3D16248.9%20%5C%5C%20t%5Capprox16%2C249%20%5Cend%7Bgathered%7D)
The paintings are approximately 16,249 years old.
Answer:
128
Step-by-step explanation:
Side a
11.314
cm
Area
128
cm²
Diagonal
16
cm
Perimeter
45.255
cm
Rearrange the first system to get x = -3y + 14. Substitute that into the other system.
![-5x+6y=-28\\\\-5(-3y+14)+6y=-28\\\\15y-70+6y=-28\\\\15y-70+6y=-28\\\\21y-70=-28\\\\21y=42\\\\y=2](https://tex.z-dn.net/?f=-5x%2B6y%3D-28%5C%5C%5C%5C-5%28-3y%2B14%29%2B6y%3D-28%5C%5C%5C%5C15y-70%2B6y%3D-28%5C%5C%5C%5C15y-70%2B6y%3D-28%5C%5C%5C%5C21y-70%3D-28%5C%5C%5C%5C21y%3D42%5C%5C%5C%5Cy%3D2)
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Answer:
3(x + 1) + 6 = 33
3x+3+6=33
3x+9=33
3x=33-9
3x=24
x=24/3
x=8
Step-by-step explanation:
hope it help ^_^