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Marat540 [252]
3 years ago
10

The math club sells candy bars and drinks during football games.

Mathematics
1 answer:
Vinvika [58]3 years ago
5 0

Answer:

The price of candy bar is 75 cents

Step-by-step explanation:

Let c be the price of candy bar and d be the price of drinks

Then according to given statements

60c+110d = 265\ \ \ \ Eqn\ 1\\120c+90d = 270\ \ \ \ Eqn\ 2

Multiplying equation 1 by 2

120c+220d = 530\ \ \ \ Eqn\ 3

Subtracting equation 2 from equation 3

120c+220d - (120c+90d) = 530 - 270\\120c+220d-120-90d = 260\\130d=260

Dividing both sides by 130

\frac{130d}{130} = \frac{260}{130}\\d = 2

Putting d=2 in equation 1

60c+110(2) = 265\\60c + 220 = 265\\60c+220-220 = 265-220\\60c=45\\c = \frac{45}{60}\\c = 0.75

Price of candy bar is $0.75 or 75 cents

Hence,

The price of candy bar is 75 cents

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Dividing each part of the inequality by 2 tells us that 45° < <em>θ</em>/2 < 90°, so the half-angle falls in the first quadrant, which means both cos(<em>θ</em>/2) > 0 and sin(<em>θ</em>/2) > 0.

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Plug in tan(<em>θ</em>) = - 12/5 and solve for cos(<em>θ</em>) :

cos(<em>θ</em>) = - 1/√[1 + (-12/5)²] = - 5/13

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tan(<em>θ</em>/2) = √[(1 - (- 5/13)) / (1 + (- 5/13))] = 3/2

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