Answer:
The answer is B) b
Step-by-step explanation:
According to the Trapezoid area formula, the area of the trapezoid is [(2d+a+b) × c] ÷ 2, however the area also equals (d+b) × c.
So d+(a+b)/2=d+b
(a+b)/2=b
a+b=2b
a=b
hope this helps <3
Answer:
30
Step-by-step explanation:
It says that the triangles are congruent (same size). Also, a triangle's angles add up to 180 degrees. In both of these triangles, one angle is 90° and another angle is 52°. The other angle is 180°-90°-52°=38°.
Solve these equations to find x and y: 2x+18=38, 3y+11=38
![2x+18=38\\2x=20\\x=10](https://tex.z-dn.net/?f=2x%2B18%3D38%5C%5C2x%3D20%5C%5Cx%3D10)
![3y+11=38\\3y=27\\y=9](https://tex.z-dn.net/?f=3y%2B11%3D38%5C%5C3y%3D27%5C%5Cy%3D9)
If
is the amount of strontium-90 present in the area in year
, and it decays at a rate of 2.5% per year, then
![S(t+1)=(1-0.025)S(t)=0.975S(t)](https://tex.z-dn.net/?f=S%28t%2B1%29%3D%281-0.025%29S%28t%29%3D0.975S%28t%29)
Let
be the starting amount immediately after the nuclear reactor explodes. Then
![S(t+1)=0.975S(t)=0.975^2S(t-1)=0.975^3S(t-2)=\cdots=0.975^{t+1}S(0)](https://tex.z-dn.net/?f=S%28t%2B1%29%3D0.975S%28t%29%3D0.975%5E2S%28t-1%29%3D0.975%5E3S%28t-2%29%3D%5Ccdots%3D0.975%5E%7Bt%2B1%7DS%280%29)
or simply
![S(t)=0.975^ts](https://tex.z-dn.net/?f=S%28t%29%3D0.975%5Ets)
So that after 50 years, the amount of strontium-90 that remains is approximately
![S(50)=0.975^{50}s\approx0.282s](https://tex.z-dn.net/?f=S%2850%29%3D0.975%5E%7B50%7Ds%5Capprox0.282s)
or about 28% of the original amount.
We can confirm this another way; recall the exponential decay formula,
![S(t)=se^{kt}](https://tex.z-dn.net/?f=S%28t%29%3Dse%5E%7Bkt%7D)
where
is measured in years. We're told that 2.5% of the starting amount
decays after 1 year, so that
![0.975s=se^k\implies k=\ln0.975](https://tex.z-dn.net/?f=0.975s%3Dse%5Ek%5Cimplies%20k%3D%5Cln0.975)
Then after 50 years, we have
![S(50)=se^{50k}\approx0.282s](https://tex.z-dn.net/?f=S%2850%29%3Dse%5E%7B50k%7D%5Capprox0.282s)
This year
2:7
18:?
well 2*9=18
so 7*9=63
18/63
(18+63=total 81 students)
Last year
1/8
multiply by 9
9/72
9 less students this year