(6m³n)²(-4m⁵n) must be simplified
1 answer:
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Answer:
The dimensions of the driveway are 21 ft x 47 ft, which is option "D" in your list of possible answers
Step-by-step explanation:
Notice that the length "L" of the driveway can be written in terms of its width as:
L = 2 w + 5
based on the given information.
Please see the attached diagram to understand the geometry of the problem, and what the area of the brick walkway involves (depicted in brick color) as the addition of the area of two rectangles:
1) one of length L= 2 w + 5 (w being the width of the driveway - depicted in grey) times 3 feet (the width of the brick walkway
and the other one:
2) w + 3 times 3
Therefore the total area of the brick walkway is given by the formula:
(2 w + 5) * 3 +(w + 3) * 3 = 213 square feet
Now we can solve for "w" in the above equation:
6 w + 15 + 3 w + 9 = 213
9 w + 24 = 213
9 w = 213 - 24
9 w = 189
w = 189/9
w = 21 feet
We can now solve for the L of the driveway, using the first formula we created:
L = 2 w + 5
L = 2 (21) + 5
L = 42 + 5
L = 47 feet
Therefore the driveway's width is w = 21 feet
and its length is L = 47 feet
Answer:
about 2.81 km/h
Step-by-step explanation:
It can be useful to draw a diagram.
The lines pointing to due north from points B and P are parallel, so the angle BCP and the bearing of point C from P are the same, 30°. The angle BPC will be the difference of bearings of B and C at P, so is 47-30=17°. This is enough information to solve the triangle using the Law of Sines:
PB/sin(C) = CB/sin(P)
CB = PB·sin(P)/sin(C) = (1200 m)·sin(17°)/sin(30°) ≈ 701.7 m
The speed of the boat is then ...
x = distance/time = (0.7017 km)/(1/4 h) = 2.8068 km/h
