Intersecting chords theorem:
![7\cdot7=10x](https://tex.z-dn.net/?f=7%5Ccdot7%3D10x)
i.e. when two chords intersect, the products of the resulting line segments' lengths are equal. Then
![10x=49\implies x=\dfrac{49}{10}=\boxed{4.9}](https://tex.z-dn.net/?f=10x%3D49%5Cimplies%20x%3D%5Cdfrac%7B49%7D%7B10%7D%3D%5Cboxed%7B4.9%7D)
Answer:
The solution to the system of equations be:
![y=-3,\:x=2](https://tex.z-dn.net/?f=y%3D-3%2C%5C%3Ax%3D2)
Step-by-step explanation:
Given the system of equations
![\begin{bmatrix}y=3x-9\\ y=-2x+1\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7Dy%3D3x-9%5C%5C%20y%3D-2x%2B1%5Cend%7Bbmatrix%7D)
Let us solve the system by the elimination method
![\begin{bmatrix}y=3x-9\\ y=-2x+1\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7Dy%3D3x-9%5C%5C%20y%3D-2x%2B1%5Cend%7Bbmatrix%7D)
Arrange equation variables for elimination
![\begin{bmatrix}y-3x=-9\\ y+2x=1\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7Dy-3x%3D-9%5C%5C%20y%2B2x%3D1%5Cend%7Bbmatrix%7D)
subtracting the equations
![y+2x=1](https://tex.z-dn.net/?f=y%2B2x%3D1)
![-](https://tex.z-dn.net/?f=-)
![\underline{y-3x=-9}](https://tex.z-dn.net/?f=%5Cunderline%7By-3x%3D-9%7D)
![5x=10](https://tex.z-dn.net/?f=5x%3D10)
so the system of equations becomes
![\begin{bmatrix}y-3x=-9\\ 5x=10\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7Dy-3x%3D-9%5C%5C%205x%3D10%5Cend%7Bbmatrix%7D)
solve 5x for x
![5x=10](https://tex.z-dn.net/?f=5x%3D10)
Divide both sides by 5
![\frac{5x}{5}=\frac{10}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B5x%7D%7B5%7D%3D%5Cfrac%7B10%7D%7B5%7D)
![x = 2](https://tex.z-dn.net/?f=x%20%3D%202)
![\mathrm{For\:}y-3x=-9\mathrm{\:plug\:in\:}x=2](https://tex.z-dn.net/?f=%5Cmathrm%7BFor%5C%3A%7Dy-3x%3D-9%5Cmathrm%7B%5C%3Aplug%5C%3Ain%5C%3A%7Dx%3D2)
![y-3\cdot \:2=-9](https://tex.z-dn.net/?f=y-3%5Ccdot%20%5C%3A2%3D-9)
![y-6=-9](https://tex.z-dn.net/?f=y-6%3D-9)
Add 6 to both sides
![y-6+6=-9+6](https://tex.z-dn.net/?f=y-6%2B6%3D-9%2B6)
![y=-3](https://tex.z-dn.net/?f=y%3D-3)
Therefore, the solution to the system of equations be:
![y=-3,\:x=2](https://tex.z-dn.net/?f=y%3D-3%2C%5C%3Ax%3D2)
In the balanced reaction
2 Fe + O₂ → 2 FeO
2 moles of iron (Fe) react with 1 mole of molecular oxygen (O₂) to produce 2 moles of iron oxide (FeO). The ratio of Fe to FeO is 1-to-1, so if one starts with 42.4 mol of Fe, one will end up with the same amount of FeO, 42.4 mol.
Look up the molar mass of Fe and O:
• Fe = 55.845 g/mol
• O = 15.999 g/mol
Then the molar mass of FeO is approximately 71.835 g/mol, and so the mass of 42.4 mol of FeO is
(42.4 mol) × (71.835 g/mol) ≈ 3050 g
Answer:
sure?
Step-by-step explanation: