Answer: 292
Step-by-step explanation:
Recall that the diagonals of a rectangle bisect each other and are congruent, therefore:
![\begin{gathered} FH=2EI, \\ GI=EI. \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20FH%3D2EI%2C%20%5C%5C%20GI%3DEI.%20%5Cend%7Bgathered%7D)
Substituting the given expression for each segment in the first equation, we get:
![3x+6=2(2x-2).](https://tex.z-dn.net/?f=3x%2B6%3D2%282x-2%29.)
Solving the above equation for x, we get:
![\begin{gathered} 3x+6=4x-4, \\ 3x+6+4=4x, \\ 3x+10=4x, \\ 4x-3x=10, \\ x=10. \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%203x%2B6%3D4x-4%2C%20%5C%5C%203x%2B6%2B4%3D4x%2C%20%5C%5C%203x%2B10%3D4x%2C%20%5C%5C%204x-3x%3D10%2C%20%5C%5C%20x%3D10.%20%5Cend%7Bgathered%7D)
Substituting x=10 in the equation for segment EI, we get:
![EI=2*10-2=20-2=18.](https://tex.z-dn.net/?f=EI%3D2%2A10-2%3D20-2%3D18.)
Therefore:
![GI=18.](https://tex.z-dn.net/?f=GI%3D18.)
Now, to determine the measure of angle IEH, we notice that:
![\Delta HFG\cong\Delta GEH,](https://tex.z-dn.net/?f=%5CDelta%20HFG%5Ccong%5CDelta%20GEH%2C)
therefore,
![\measuredangle GHF\cong\measuredangle HGE.](https://tex.z-dn.net/?f=%5Cmeasuredangle%20GHF%5Ccong%5Cmeasuredangle%20HGE.)
Using the facts that the triangles are right triangles and that the interior angles of a triangle add up to 180° we get:
![m\measuredangle IEH=90^{\circ}-35^{\circ}=55^{\circ}.](https://tex.z-dn.net/?f=m%5Cmeasuredangle%20IEH%3D90%5E%7B%5Ccirc%7D-35%5E%7B%5Ccirc%7D%3D55%5E%7B%5Ccirc%7D.)
<h2>Answer: </h2>
Answer:
f(x)=12x
Step-by-step explanation
We know that f(x) is our y-coordinate and x is the x-coordinate
Next we should insert x-6 as x in the equation
This is f(x)=12(x-6)-72
But if you look at this that leads to 12x-72 (ignore y-intercept)
That is our first equation
This means that if you take out -6 from the x
You will get f(x)=12x
(Also do you go to RSM?)