Answer:
![\huge\boxed{x=\sqrt{70}}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7Bx%3D%5Csqrt%7B70%7D%7D)
Step-by-step explanation:
ΔABC and ΔADB are similar (AAA).
Therefore the corresponging sides are in proportion:
![\dfrac{AB}{AD}=\dfrac{AC}{AB}](https://tex.z-dn.net/?f=%5Cdfrac%7BAB%7D%7BAD%7D%3D%5Cdfrac%7BAC%7D%7BAB%7D)
Substitute:
![AB=x\\AC=7+3=10\\AD=7](https://tex.z-dn.net/?f=AB%3Dx%5C%5CAC%3D7%2B3%3D10%5C%5CAD%3D7)
<em>cross multiply</em>
![(x)(x)=(7)(10)\\\\x^2=70\to x=\sqrt{70}](https://tex.z-dn.net/?f=%28x%29%28x%29%3D%287%29%2810%29%5C%5C%5C%5Cx%5E2%3D70%5Cto%20x%3D%5Csqrt%7B70%7D)
Answer:
35.9 grams
Step-by-step explanation:
We use the formula:
![q=m*C_p*\Delta T](https://tex.z-dn.net/?f=q%3Dm%2AC_p%2A%5CDelta%20T)
Where
q is heat released
m is mass
C_p is the constant 2.44
ΔT is change in temperature
We put the info in the formula and solve for m (mass):
![q=m*C_p*\Delta T\\-3.12 = m*2.44(12.3-47.9)\\-3.12*10^3=m*(-86.864)\\m=35.9](https://tex.z-dn.net/?f=q%3Dm%2AC_p%2A%5CDelta%20T%5C%5C-3.12%20%3D%20%20m%2A2.44%2812.3-47.9%29%5C%5C-3.12%2A10%5E3%3Dm%2A%28-86.864%29%5C%5Cm%3D35.9)
The mass of ethanol is 35.9 grams
We know that they have:
2 entrences
3 ways to chose (escalator,elevator and stairs)
8 gates
and again 3 ways to chose (escalator, elevator and stairway)
now you have to multiply it:
![2*3*8*3=6*8*3=48*3=144](https://tex.z-dn.net/?f=2%2A3%2A8%2A3%3D6%2A8%2A3%3D48%2A3%3D144)
There are 144 different ways that Anita and Terry can go from street level to the trains:)