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Sedbober [7]
3 years ago
11

An ancient culture had a solar calendar with a 365 day cycle and a religious calendar with a 292 day cycle. If the calendars bot

h start today, in how many days will they next coincide?
Mathematics
1 answer:
Scrat [10]3 years ago
3 0
Make the Least common multiple (LCM) of 365 and 292:

365, 292 | 5
73, 292 | 2
73, 146 | 2
73, 73 | 73
1, 1 |\underline{5*2*2*73 = 1460}

Answer:
\underline{1460\:days\:will\:they\:next\:coincide}
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If Bruce observes that the number of pitches a batter hits varies and is given by the function f(x)=x-11, and the batters get {4, 12, 14, 27, 42}, then Bruce threw {15, 23, 25, 38, 53} pitches. We get this solution set by adding 11 to each element in the set {4, 12, 14, 27, 42}. 
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Answer:  A) 126.6

<u>Step-by-step explanation:</u>

Since we know ∠B = 85° and ∠C = 53°, we can use the Triangle Sum Theorem (angles of a triangle = 180°) to calculate ∠A.

∠A + ∠B + ∠C = 180

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∠A = 42

Now we have:

                       A = 42          B = 85       C = 53

                       a = 85          b = ???       c = ???

We have all of the information for ∠A and side a so we can use the Law of Sines to find b (AC).

\dfrac{\sin 42}{85}=\dfrac{\sin 85}{b}\\\\\\b(\sin 42)=85(\sin 85)\\\\\\b=\dfrac{85\sin 85}{\sin 42}\\\\\\b=\large\boxed{126.547}

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