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ra1l [238]
3 years ago
5

At a movie theater tickets for children cost 6.5 dollars each and adult tickets cost $8.75 each if tickets sales for a group of

35 people totaled $259 how many children were in this group
Mathematics
1 answer:
Masteriza [31]3 years ago
3 0

Answer:

21 children

Step-by-step explanation: 6.50x+8.75y=259

This equation came from the cost of the tickets for the children and adults.

x+y=35

This comes from the group of 35 people that consists of children and adults.

We can use substitution to solve for x and y.

x=35-y

6.50(35-y)+8.75y=259

227.5-6.50y+8.75y=259

227.5+2.25y=259

2.25y=31.5

y=14

Now that we have found y, we can plug it into any of the equations to find x.

x+14=35

x=21

Therefore, there are 21 children and 14 adults in the group.

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a river flows due south at 1.2 miles per hour. A swimmer attempting to cross the river heads due east swiming at 3 miles per hou
kotegsom [21]

Answer:

The swimmer must move in the direction 338.2°

Step-by-step explanation:

Since the river flows due south at 1.2 miles per hour and the swimmer swims 3 miles per hour due east of the river, since their directions are perpendicular,  the resultant speed is the hypotenuse of the triangle formed by the two perpendicular directions.

The direction of the resultant speed is thus θ = tan⁻¹( vertical component/horizontal component) where vertical component = 1.2 mph due south = -1.2 mph and horizontal component = 3 mph due east = + 3 mph

So, θ = tan⁻¹(-1.2 mph/+ 3mph)

θ = tan⁻¹(-1.2/3)

θ = tan⁻¹(-0.4)

θ = -21.8°

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4 0
3 years ago
Simplify cotø(tanø+cotø)​
Sladkaya [172]

Answer:

\large\boxed{\cot\theta(\tan\theta+\cot\theta)=1+\cot^2\theta=\dfrac{1}{\sin^2\theta}=\csc^2\theta}

Step-by-step explanation:

\text{Use}\\\\\text{distributive property:}\ a(b+c)=ab+ac\\\cot\alpha\tan\alpha=1.\\\\======================\\\\\cot\theta(\tan\theta+\cot\theta)=(\cot\theta)(\tan\theta)+(\cot\theta)(\cot\theta)\\\\=1+\cot^2\theta\\\\\text{If you want next transformation, then use:}\\\\\cot\alpha=\dfrac{\cos\alpha}{\sin\alpha}\\\\\sin^2\alpha+\cos^2\alpha=1\\\\=======================

=1+\left(\dfrac{\cos\theta}{\sin\theta}\right)^2=1+\dfrac{\cos^2\theta}{\sin^2\theta}=\dfrac{\sin^2\theta}{\sin^2\theta}+\dfrac{\cos^2\theta}{\sin^2\theta}=\dfrac{\sin^2\theta+\cos^2\theta}{\sin^2\theta}\\\\=\dfrac{1}{\sin^2\theta}\\\\\text{If you want next transformation, then use:}\\\\\csc\alpha=\dfrac{1}{\sin\alpha}\\\\=\left(\dfrac{1}{\sin\theta}\right)^2=(\csc\theta)^2=\csc^2\theta

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3 years ago
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