294 / 14 = 21 miles per gallon
21 * (5280 ft per mile / 3 yards per foot) =
36,960 yards per gallon
If you were to make your own measurements, your significant digits should include all of the measurable digits (the digits that correspond to the marks on the ruler) as well as one estimated position beyond the smallest measureable digit (the 5 in 3.5 cm, and the 2 in 3.52 cm).
Speed of the plane: 250 mph
Speed of the wind: 50 mph
Explanation:
Let p = the speed of the plane
and w = the speed of the wind
It takes the plane 3 hours to go 600 miles when against the headwind and 2 hours to go 600 miles with the headwind. So we set up a system of equations.
600
m
i
3
h
r
=
p
−
w
600
m
i
2
h
r
=
p
+
w
Solving for the left sides we get:
200mph = p - w
300mph = p + w
Now solve for one variable in either equation. I'll solve for x in the first equation:
200mph = p - w
Add w to both sides:
p = 200mph + w
Now we can substitute the x that we found in the first equation into the second equation so we can solve for w:
300mph = (200mph + w) + w
Combine like terms:
300mph = 200mph + 2w
Subtract 200mph on both sides:
100mph = 2w
Divide by 2:
50mph = w
So the speed of the wind is 50mph.
Now plug the value we just found back in to either equation to find the speed of the plane, I'll plug it into the first equation:
200mph = p - 50mph
Add 50mph on both sides:
250mph = p
So the speed of the plane in still air is 250mph.
I believe that A and D would be the correct answer. Because both are 30,60,90 triangles and would be congruent. The other 2 triangles only have 1 angle and their side measures are at two different places meaning they cannot be congruent.
