Answer is BF...hope this helps
Answer:
The first one is a reflection of the figure shown over the given line reflection.
<h3>
Answer: A. 18*sqrt(3)</h3>
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Explanation:
We'll need the tangent rule
tan(angle) = opposite/adjacent
tan(R) = TH/HR
tan(30) = TH/54
sqrt(3)/3 = TH/54 ... use the unit circle
54*sqrt(3)/3 = TH .... multiply both sides by 54
(54/3)*sqrt(3) = TH
18*sqrt(3) = TH
TH = 18*sqrt(3) which points to <u>choice A</u> as the final answer
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An alternative method:
Triangle THR is a 30-60-90 triangle.
Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.
The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.
Now use the pythagorean theorem
a^2 + b^2 = c^2
(TH)^2 + (HR)^2 = (TR)^2
(x)^2 + (54)^2 = (2x)^2
x^2 + 2916 = 4x^2
2916 = 4x^2 - x^2
3x^2 = 2916
x^2 = 2916/3
x^2 = 972
x = sqrt(972)
x = sqrt(324*3)
x = sqrt(324)*sqrt(3)
x = 18*sqrt(3) which is the length of TH.
A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.
<h3>
Answer: 35</h3>
A prime number is one where the only factors are one and itself. A composite number has other factors.
You'll have to look at the list of numbers from 1 to 50
In that list, 47 is the largest prime less than 50, and 12 is the smallest composite number greater than 10.
So 47-12 = 35
Answer:
Zero, based on the information provided.
Step-by-step explanation:
The output rate of the teller machine is (1 transaction/6 minutes). The input rate is (1 customer/10 minutes). This means that the machine completes a cycle faster than the customers arrive, on the average. I don't know how an average can be calculated without more information. If we assume customers arrive every 10 minutes, and no one screws up the machine, that there should be no waiting line. Is there more information about when the customers arrive? E.g., 50 arrive in the first hour the machine is open.
