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:
m = 10/3
<em>(as a decimal: m = 3.333...)</em>
<em />
Step-by-step explanation:
5m - 8 = 2m + 2
5m - 8 = 2m + 2
- 2m - 2m <em>(make all "m" on one side to isolate variable)</em>
3m - 8 = 2
+ 8 + 8 <em>(get m entirely on 1 side)</em>
3m = 10
÷3 ÷3 <em>(divide by 3 to get 1m)</em>
m = 10/3
<em>(as a decimal: m = 3.333...)</em>
<em />
<em />
hope this helps!! have a lovely day :)
Answer:
Mr.Smith paid $29.4.
Step-by-step explanation:
Mr.Smith paid $24.5 plus additional 20% of $24.5, and to figure out the total amount that he paid, we need to know what is 20% of $24.50.
20% of $24.50 is:
.
Mr.Smith paid additional $4.9; therefore, the total amount he paid was
$24.5 + $4.9 = $29.4.
Mr. smith paid $29.4.
Answer:
What ever you have learned
Step-by-step explanation:
Its like a working machine like for ex any vending machine
Answer: A,C
Step-by-step explanation: They are facing each other making them interior angles