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Leviafan [203]
2 years ago
11

Find the height of the building below by using your knowledge of trigonometry.

Mathematics
1 answer:
Lilit [14]2 years ago
5 0

Answer:

50\sqrt{3}

Step-by-step explanation:

The figure represents a 30-60-90 special triangle

in this special right triangle the measure of sides lengths is represented by

a, a\sqrt{3}, and 2a

The side length that sees angle measure 30 is represented by a and here we see a = 50m

The height of the building, which sees angle measure 60, is equal to

50\sqrt{3}

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What is the inverse of the function y=3x+4
almond37 [142]
f^{-1} (x)=- \frac{4}{3} + \frac{x}{3}
6 0
3 years ago
There are some goats, cows, and sheep on a farm. 2/5 of the animals were goats. There are 3 times as many sheep as cows. If ther
svetlana [45]

Answer:

180

Step-by-step explanation:

First thing to do is to get all the animals in terms of cows, since that is our main unknown.  All the other animals' numbers are based on cows.  So let's call cows "x".  Then sheep is 3 times the number of cows, so sheep is 3x.  The number of goats is 45 more than the number of cows, so goats is x + 45.  Let's say, for the sake of ease, that the number of animals is "a".

Here's what we have so far:

# of animals: a

# of cows: x

# of sheep: 3x

# of goats: x + 45

We are told that 2/5 of the animals are goats.  In an equation, that is:

2/5 (animals) = goats, where the word "of" means to multiply, and the word "are" is the equals sign.  Filling in from our key above:

\frac{2}{5}a=x+45

That says that 2/5 of the animals are goats when goats is x + 45.

If 2/5 of the animals are goats, then 3/5 of the animals have to be cows and sheep.  In an algebraic equation:

\frac{3}{5}a=x + 3x.  

Let's go back to the first equation and get rid of the fraction by multiplying everything by 5.  When we do that we get

2a = 5(x + 45) so

2a = 5x + 225

Now let's get rid of the fraction in the second equation by multiplying everything by 5.  When we do that we get

3a = 5(x + 3x) or

3a = 5(4x) so

3a = 20x.  Solve that equation for a.

a=\frac{20}{3}x

Now that we have a in terms of x, we can sub that value in for a in the first equation to solve for x, the number of cows:

2(\frac{20}{3}x)=5x+225 and, simplifying:

\frac{40}{3}x=5x+225 and

\frac{40}{3}x-5x=225.  Get rid of the fraction here by multiplying everything by 3:

40x - 15x = 675 and

25x = 675 so

x = 27

That means that there are 27 cows.

Sheep is 3 times that, so there are 81 sheep.

Goats is 45 more than that, so there are 72 goats.

The total number of animals then is 27 + 81 + 72 which is 180.  Let's check that to see if the number of goats, 72, is 2/5 of 180.

\frac{2}{5}(180) = 72

So we got it!  Yay!  That was hard!!

7 0
3 years ago
Kellan’s lemonade recipe uses 4 scoops of lemonade powder for every 2.5 cups of water. Kellan uses 10 scoops of lemonade powder
3241004551 [841]
6.25 because 2.5+2.5= 5 and then half of 2.5 is 1.25 so 6.25

3 0
3 years ago
Consider a sequence given by the formula f(n)=3n-1 starting with n=1. Generate the first 5 terms of the sequence
Rufina [12.5K]

Answer:

The first 5 terms are 2, 5, 8, 11, 14.

Step-by-step explanation:

  1. You use the formula to find out each term.
  2. f(n)=3n-1 starting with n=1. If n=1 that is the 1st term, if n=2 that is the 2nd term, and so on. n means what number term it is.
  3. Now to find each term:
  • n=1: f(1)= 3(1)-1= 3-1= 2 The 1st term is 2
  • n=2: f(2)= 3(2)-1= 6-1= 5 The 2nd term is 5
  • n=3: f(3)= 3(3)-1= 9-1=8 The 3rd term is 8
  • n=4: f(4)= 4(3)-1= 12-1= 11 The 4th term is 11
  • n=5: f(5)= 5(3)-1= 15-1= 14 The 5th term is 14

So the first 5 terms are 2,5,8,11,14

5 0
3 years ago
I need help with one more of these.
nataly862011 [7]
I think it is yz but I and not completely sure
6 0
3 years ago
Read 2 more answers
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