PLEASE HELP I WILL GIVE 100 POINTS!!!!!!!!Given rectangle ABCD ~ HGFE , what is the length of HG ?
2 answers:
Since rectangle ABCD is similar to HGFE, the ratios of the lengths of their corresponding sides are equal. We can infer form our picture that AD is corresponding to EH and DC is corresponding to HG, so lets find the ratios of those corresponding sides and establish a proportion to find the length of HG:
We know that
, 
, and 
, so lets replace those values in our proportion:
We can conclude that the length of the segment HG is 9.
We know that
We can conclude that the length of the segment HG is 9.
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To model and solve our situation we are going to use the equation: 
where
is speed
is distance
is time
1. We know that the distance between the cities is 2400 miles, so
. We also know that the speed of the plane is 450 mi/h. Since we don't know the speed of the air, 
. We don't know how much the westward trip takes, so 
, and we also don't know how much the eastward trip takes, so 
.
Going westward. Here the plane is flying against the air, so we need to subtract the speed of the air from the speed of the plane:
Going eastward. Here the plane is flying with the the air, so we need to add the speed of the air to the speed of the plane:
2. We know for our problem that the round trip takes 11 hours; so the total time of the trip is 11,
. Notice that we also know that the total time of the trip equals time of the tip going westward plus time of the trip going eastward, so 
. Since we know that the total trip takes 11 hours, we can replace that value in our total time equation and solve for 
:
Now we can replace in our going westward equation to model our round trip with a system of equations:
equation (1)
equation (2)
3. To solve our system of equations, we are going to solve for
in equations (1) (2):
From equation (1)
equation (3)
From equation (2):
equation (4)
Replacing (4) in (3)
Now, we can solve for
to find the speed of the wind:
Since speed cannot be negative, the solution of our equation is:
We can conclude that the speed of the wind is 78 mph.
where
1. We know that the distance between the cities is 2400 miles, so
Going westward. Here the plane is flying against the air, so we need to subtract the speed of the air from the speed of the plane:
Going eastward. Here the plane is flying with the the air, so we need to add the speed of the air to the speed of the plane:
2. We know for our problem that the round trip takes 11 hours; so the total time of the trip is 11,
Now we can replace
3. To solve our system of equations, we are going to solve for
From equation (1)
From equation (2):
Replacing (4) in (3)
Now, we can solve for
Since speed cannot be negative, the solution of our equation is:
We can conclude that the speed of the wind is 78 mph.