9514 1404 393
Answer:
DE = 86
EF = 84
Step-by-step explanation:
We assume that point E lies on segment DF, so that ...
DE + EF = DF
(3x +20) +(2x +40) = 170
5x = 110 . . . . . . . . . . . . . . . collect terms, subtract 60
x = 22 . . . . . . . . . . . . divide by 5
DE = 3×22 +20 = 66 +20 = 86
EF = 2×22 +40 = 44 +40 = 84
3 - 4z - 4 = 3z - 2 - z
-4z - 1 = 2z - 2
2z + 4z = -1 + 2
6z = 1
z = 1/6
Hope this helps!
Without using the trigonometry ratio, we can find the distance between the ship and the buoy by:
the distance between City and Lemont SUBTRACT the vertical distance between City and the point parallel to the Ship
The distance between the City and Lemont can be worked out using the Sin rule


≈98.3
The vertical distance between the City and the point parallel to the ship can be worked out using the Pythagoras theorem

≈36.8
The distance between the ship and the Buoy is given:

miles
Given
MINING A mine produces 42.5 tons of coal per hour.
Find out the how much coal will the mine produce in 9.5 hours.
To proof
As given in the question
A mine produces 42.5 tons of coal per hour i.e in the 1 hour mine produces the 42.5 tons .
Let us assume that the coal produce in the 9.5 hours be x.
than the equation becomes
x = 9.5 × 42.5
x = 403 . 75 tons
403 . 75 tons coal will the mine produces in the 9.5 hours.
Hence proved