Step-by-step explanation:
its answer is 94 bro
I pray it will helful to you
Answer:
![\huge\boxed{\sf x\leq 2}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7B%5Csf%20x%5Cleq%202%7D)
Step-by-step explanation:
<h3><u>Given inequality:</u></h3>
![56-10x\geq 20+8x\\\\Subtract \ 20 \ from \ both \ sides\\\\56-20-10x\geq 8x\\\\36-10x\geq 8x\\\\Add \ 10x \ to \ both \ sides\\\\36\geq 8x+10x\\\\36\geq 18x\\\\Divide \ 18 \ to \ both \ sides\\\\2 \geq x\\\\OR\\\\x\leq 2\\\\\rule[225]{225}{2}](https://tex.z-dn.net/?f=56-10x%5Cgeq%2020%2B8x%5C%5C%5C%5CSubtract%20%5C%2020%20%5C%20from%20%5C%20both%20%5C%20sides%5C%5C%5C%5C56-20-10x%5Cgeq%208x%5C%5C%5C%5C36-10x%5Cgeq%208x%5C%5C%5C%5CAdd%20%5C%2010x%20%5C%20to%20%5C%20both%20%5C%20sides%5C%5C%5C%5C36%5Cgeq%208x%2B10x%5C%5C%5C%5C36%5Cgeq%2018x%5C%5C%5C%5CDivide%20%5C%2018%20%5C%20to%20%5C%20%20both%20%5C%20sides%5C%5C%5C%5C2%20%5Cgeq%20x%5C%5C%5C%5COR%5C%5C%5C%5Cx%5Cleq%202%5C%5C%5C%5C%5Crule%5B225%5D%7B225%7D%7B2%7D)
Answer:
It will take 25.6 years for the mass of the sample to reach 400 grams.
Step-by-step explanation:
Element X is a radioactive isotope such that every 25 years, its mass decreases by half.
This means that the amount of the substance after t years can be modeled by a function in the following format:
![A(t) = A(0)(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
In which A(0) is the initial amount.
Initial mass of a sample of Element X is 910 grams.
This means that ![A(0) = 910](https://tex.z-dn.net/?f=A%280%29%20%3D%20910)
So
![A(t) = A(0)(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
![A(t) = 910(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20910%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
How long would it be until the mass of the sample reached 400 grams?
This is t for which ![A(t) = 400](https://tex.z-dn.net/?f=A%28t%29%20%3D%20400)
So
![A(t) = 910(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20910%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
![400 = 910(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=400%20%3D%20910%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
![(0.5)^{\frac{t}{25}} = \frac{400}{910}](https://tex.z-dn.net/?f=%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D%20%3D%20%5Cfrac%7B400%7D%7B910%7D)
![(0.5)^{\frac{t}{25}} = 0.43956](https://tex.z-dn.net/?f=%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D%20%3D%200.43956)
![\log{(0.5)^{\frac{t}{25}}} = \log{0.43956}](https://tex.z-dn.net/?f=%5Clog%7B%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D%7D%20%3D%20%5Clog%7B0.43956%7D)
![\frac{t}{25}\log{0.5} = \log{0.43956}](https://tex.z-dn.net/?f=%5Cfrac%7Bt%7D%7B25%7D%5Clog%7B0.5%7D%20%3D%20%5Clog%7B0.43956%7D)
![t = \frac{25\log{0.43956}}{\log{0.5}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B25%5Clog%7B0.43956%7D%7D%7B%5Clog%7B0.5%7D%7D)
![t = 25.6](https://tex.z-dn.net/?f=t%20%3D%2025.6)
It will take 25.6 years for the mass of the sample to reach 400 grams.
First find midpoint:
Find slope of line that passes through R and S: slope =
Negative reciprocal of slope to get slope of perpendicular: new slope = 6
Line will be: