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Luden [163]
3 years ago
8

Sharon is making 100 liters of punch for a party. The punch contains ginger ale (g) and fruit juice (f). The cost of the ginger

ale is $1 per liter and the fruit juice is $1.50 per liter. If Sharon spent a total of $130, how many liters of each did she put in the punch?
Which solution is reasonable?
A) 30 liters of ginger ale and 45 liters of fruit juice
B) 40 liters of ginger ale and 60 liters of fruit juice
C) 40 liters of ginger ale and 30 liters of fruit juice
Eliminate
D) 50 liters of ginger ale and 70 liters of fruit juice
Mathematics
1 answer:
Flura [38]3 years ago
5 0
B) 40 liters of ginger ale and 60 liters of fruit juice.
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let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b)
statuscvo [17]

In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement

\sin (\theta)=\frac{3}{5}

Describes the following triangle

To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation

x^2+3^2=5^2

Solving for x, we have

\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}

The missing length of the first triangle is equal to 4.

For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression

\tan (y)=\frac{12}{5}

Describes the following triangle

Using the Pythagorean Theorem again, we have

5^2+12^2=h^2

Solving for h, we have

\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}

The missing side measure is equal to 13.

Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.

The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles

\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}

To calculate the sine and cosine of the sum

\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}

We can use the following identities

\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}

Using those identities in our problem, we're going to have

\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}

4 0
1 year ago
A bakery sells pie slices that are 1/6 of a pie. If they made 18 pies today.How many slices of pie will they have?
Lera25 [3.4K]

Answer:

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Step-by-step explanation:

One pie is 6 slices so 6*18 is equal to 108

4 0
2 years ago
Which inequality represents the statement below?
patriot [66]

Answer:

B. X+6.4<9.9

Step-by-step explanation:

The sum of a number is represented by X. So X and 6.4 is X+6.4. Is less than 9.9, so <9.9. You get X+6.4<9.9.

4 0
3 years ago
Read 2 more answers
HELPPP
kiruha [24]

Answer:

90

Step-by-step explanation:

You would get 36 dollars from 90 liters.

The answer is in the photo.

6 0
3 years ago
A swimming pool can be filled in 18 hours if water enters through a pipe​ alone, or in 25 hours if water enters through a hose a
pychu [463]
I am not sure, but this is what I got:
 <span>Pipe ALONE = 18 hours 

Pipe ALONE in 1 hour = 1/18 of the pool 

Hose ALONE in 1 hour = 1/25 of the pool 

TOGETHER in 1 HOUR = 1/18 +1/25 = 43/450 

TOGETHER they will fill the pool in 450/43 hours 

So 5/6 of the pool will take 5/6 X 450/43 = 2250/ 258 = 8.7209302 hours OR 

8 hours AND 43.26 minutes ANSWER
</span>
Hope this helps!


6 0
3 years ago
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