To calculate the perimeter, consider each side separately.
Right side: This is easiest since it's a vertical line - it's 7 units long.
Top side: If you look carefully, this side is really the hypotenuse of a triangle that is 1 unit tall and 6 units long. Using the Pythagorean Theorem, you can calculate the length of the hypotenuse to be 1^2 + 6^2 = c^2 --> c = 6.1
Left side: just like the top side, this side is the hypotenuse of a triangle that is 6 units tall and 6 units long. Pythagoras again: 6^2 + 6^2 = c^2 --> c = 8.5
Add these three numbers to get the perimeter: 7 + 6.1 + 8.5 = 21.6
Answer:
B. m∠B = 118°, a = 17, c = 18
Step-by-step explanation:
The answer choices all agree on the values of ∠B and c, so we only need to compute the value of side a.
We can verify angle B is ...
∠B = 180° -30° -32° = 118°
By the law of sines, ...
a/sin(A) = b/sin(B)
Multiplying by sin(A), we get ...
a = b·sin(A)/sin(B) = 30·sin(30°)/sin(118°) ≈ 16.98855
a ≈ 17.0 . . . units . . . . . matches choice B
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If you like, you can also verify side c:
c = b·sin(C)/sin(B) = 30·sin(32°)/sin(118°) ≈ 18.00512
c ≈ 18.0 . . . units
Answer: A) Producers B) Consumers constitute the upper trophic levels. Unlike producers, they cannot make their own food. To get energy, they eat plants or other animals, while some eat both. c) Through the photosynthesis process, producers, such as grass, absorb the sun's light energy to produce food (stored sugar and starches). Consumers cannot make their own food, so they have to consume other organisms. The food of almost any kind of animal can be traced back to plants and the sun.
Step-by-step explanation:
Let p and w represent the speed of the plane and the speed of the wind, respectively.
.. speed = distance/time
.. p +w = 720/3 = 240
.. p -w = 720/4 = 180
Add the two equations to eliminate w.
.. 2p = 420
.. p = 210
.. w = p -180 = 30
The speed of the wind is 30 mph.
The speed of the plane in still air is 210 mph.
