The first one. Segment NO is proportional to segment QR, and angles M and P are congruent.
In similar triangles, their angles are congruent but their sides are only proportional. That is why the last three are not true.
Using the diameter, we can find the circumference of the wheel.
Circumference = 2 * pi * radius
To find the radius, divide the diameter by 2. 6/2 = 3; your radius is 3.
2 * pi * 3 = 6 pi.
The circumference is 6pi. Leave it like this for an accurate answer in the next step.
If the rope can wrap around the wheel 3 times, then it can do 3 times the circumference.
3 * 6pi = 18pi
18pi ≈ 56.549 meters (round to whatever decimal you deem fit for 18pi).
The length of the rope is 18pi or approximately 56.549 meters long.
Realistically though, the answer would be more than 18pi meters long because the problem does not say it wraps around exactly 3 times. It just says it can completely wrap around the wheel. That's not what you should go with though; that's just me being nit-picky.
∠CAB = m∠DAB - <span>m∠DAC
</span>∠CAB = 64 - 53
∠CAB = 11
answer
<span>A) 11°</span>
Based on how the triangle looks and the directions given, you know that this is a right triangle.
You can use the Pythagorean Theorem, which is a^2 + b^2 = c^2, with c being the hypotenuse. If you plug in the values, you get
6^2 + 8^2 = c^2
36 + 64 = c^2
100 = c^2
√100 = √c^2
c = 10
This means that Robert traveled 10 kilometers on the way back home, HOWEVER, it asks for the round trip distance. He traveled 14 km on the way there and 10 km on the way back, which means the round trip distance is 24 km.
I hope this makes sense!
Answer:
680
Step-by-step explanation:
680 ÷ 5 = 136
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