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masha68 [24]
3 years ago
6

Aaron bought 8 red flags for the parade. Large flags cost $20 each. Medium flags cost $12 each. Aaron spent $112 in all. How man

y large flags (L) and how many medium flags (M) did he buy?
Mathematics
1 answer:
andrew11 [14]3 years ago
6 0

Answer:

Step-by-step explanation:

Price assuming he bought all large flags: 20*8=160

Amount of money more: 160-112=48

Difference of price in both flags: 20-12=8

Medium Flags: 48\div8=6

Large Flags: 8-6=2

----------------------------------

The reason why this works, is because the amount of money more comes from the difference between both flags.

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Angle α lies in quadrant II , and tan α = <img src="https://tex.z-dn.net/?f=-%5Cfrac%7B12%7D%7B5%7D" id="TexFormula1" title="-\f
Hunter-Best [27]

Since \alpha lies in quadrant II and \beta lies in quadrant IV, we expect \sin\alpha>0, \cos\alpha, and \sin\beta.

Recall the Pythagorean identities,

\sin^2x+\cos^2x=1\iff1+\cot^2x=\csc^2x\iff\tan^2x+1=\sec^2x

It follows that

\sec\alpha=\dfrac1{\cos\alpha}=-\sqrt{\tan^2\alpha+1}=-\dfrac{13}5\implies\cos\alpha=-\dfrac5{13}

\sin\alpha=\sqrt{1-\cos^2\alpha}=\dfrac{12}{13}

\sin\beta=-\sqrt{1-\cos^2\beta}=-\dfrac45

Recall the angle sum identity for sine:

\sin(\alpha+\beta)=\sin\alpha\cos\beta+\sin\beta\cos\alpha

So we have

\sin(\alpha+\beta)=\dfrac{12}{13}\dfrac35+\left(-\dfrac45\right)\left(-\dfrac5{13}\right)=\boxed{\dfrac{56}{65}}

4 0
3 years ago
In 2013, the population of the state of New York was approximately 19.65 million, and the population of New York City was 8,406,
maks197457 [2]
Population of the state of New York is 19.65 million. 
Million is equal to 1*10^6
So 19.65*10^6

Population of New York city is 8,406,000.
It is equal to 8.406*10^6

Therefore people in New York state did not in New York city is,
19.65*10^6 - 8.406*10^6
11.244*10^6
1.1244*10^7
7 0
3 years ago
2 procedimientos por favor
IceJOKER [234]

Answer:

184.8

Step-by-step explanation:

385/25×12

385÷25=15.4

15.4×12=184.8

8 0
3 years ago
Help me find m and n please
nekit [7.7K]

Answer:

n is 68 and m is 44

Step-by-step explanation:

5 0
3 years ago
Width of a rectangle if the area is 60 cm2 and the length is 15 cm
Sedaia [141]

Width is 4

60 divide by 15 is 4.

6 0
3 years ago
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