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2 years ago

Using elimination.

Mathematics

1 answer:

Svet_ta [14]2 years ago

8 0

Answer: x=2 y=1

Step-by-step explanation:

11x = 22

x = 2

5*2-2y=8

10-2y=8

10-8=2y

y=1

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Sin α = 21/29, α lies in quadrant II, and cos β = 15/17, β lies in quadrant I Find sin (α - β).

Sever21 [200]

$\sin(\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta$

$\sin\alpha=\dfrac{21}{29}\implies \cos^2\alpha=1-\sin^2\alpha=\dfrac{400}{841}$

Since $\alpha$ lies in quadrant II, we have $\cos\alpha$ , so

$\cos\alpha=-\sqrt{\dfrac{400}{841}}=-\dfrac{20}{29}$

$\cos\beta=\dfrac{15}{17}\implies\sin^2\beta=1-\cos^2\beta=\dfrac{64}{289}$

$\beta$ lies in quadrant I, so $\sin\beta>0$ and

$\sin\beta=\sqrt{\dfrac{64}{289}}=\dfrac8{17}$

So

$\sin(\alpha-\beta)=\dfrac{21}{29}\dfrac{15}{17}-\left(-\dfrac{20}{29}\right)\dfrac8{17}=\dfrac{475}{493}$

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2 years ago

Fifteen students are going hiking on their spring break. They plan to travel in three vehicles—one seating 7, one seating 5, and

andriy [413]

Answer:

The students can group themselves in 360360 ways

Step-by-step explanation:

For this exercise we need to use the following equation:

$\frac{n!}{n1!*n2!*...*nk!}$

This equation give us the number of assignation of n elements in k cell, where n1, n2, ..nk are the element that are in every cell

In this case we have 15 student that need to be assign in three vehicles with an specific capacity. This vehicles would be the equivalent to cells, so we can write the equation as:

$\frac{15!}{7!*5!*3!}$

Because the first vehicle have 7 seating, the second vehicle have 5 seating and the third vehicle have 3 seating.

Solving the equation we get 360360 ways to organized 15 students in three vehicles with capacity of 7, 5 and 3 seating.

5 0

2 years ago

Bob and Caitlyn are playing a trading-card game. Between them, they have 81 cards. Bob has 7 fewer cards than Caitlyn.

Alina [70]

We know that Bob and Caitlyn are playing a trading-card game. Between them, they have 81 cards. <span>Bob has 7 fewer cards than Caitlyn. Since Bob has 7 cards fewer them Caitlyn we have to divide by 2 and subtract 7.

81 / 2 = 40 [rounded]

40 - 7 = cards Bob has

= 33 cards bob has

</span>

3 0

2 years ago

Read 2 more answers

A grocery store sells a bag of 4 oranges for $3.64. How much would it cost for 6

Sergeu [11.5K]

Answer: $6.54

Step-by-step explanation:

The price of one orange is $1.09

The price of 4 oranges is $3.64

The price of 6 oranges is $6.54

6 0

2 years ago