How many numbers are inbetween 20 and 45?

A guy wire 30 ft long supports an antenna at a point that is 24 ft above the base of the antenna.

GalinKa [24]

Use Pythagorean Theorem
c2 = a2 + b2
152 = a2 + 12
a2 = 152 - 122
=225 - 144 = 81
a = 9 ft
Distance from base of antenna = 9ft

4 0

2 years ago

The sum of three consecutive even numbers is 96. What is the smallest of the three numbers

lidiya [134]

The answer is 30.

First off, the numbers are consecutive even numbers. So, the difference between every consecutive number is 2 (numbers go from even to odd to even to odd...). Since the sum of their numbers is 96, I divided that by 3 to get 32. This gives me the median of the three numbers. To find the smallest number, I simply subtracted 2 from the 32.

This may help:

96/3=32

32 + 32 + 32 = 96
(32-2)+(32+0)+(32+2)=96
30+32+34=93

8 0

3 years ago

A shelter in the city house birds and dogs . There are 25% more dogs then birds. If there are 50 birds how many dogs are there?

AfilCa [17]

Answer:

They have 83 dogs and 50 birds.

There are 133 animals in total in the shelter.

Step-by-step explanation:

So let's call the dogs D and the birds B.

D = 25% + B

What ever the amount of animals, the total for D must always be 25% more than B.

To get 100% of the animals, B must equal 37.5% and D must equal 62.5%.

The way I worked this out was:

100% - 25%= 75%

75% divided by 2= 37.5%

37.5% + 25%= 62.5%

And just to check

37.5% + 62.5% = 100%

So to work out 100%:

37.5% = 50

divide both by 37.5 to get 1%

1% = 1.333333

time both by 62.5 to get 62.5%

62.5% = 83.333313

We'll round that answer because I'm pretty sure they don't have a .333313th of a dog.

So D = 62.5% = 83

They have 83 dogs and 50 birds.

Phew! That was the hard part. Now onto something wayyy easier.

To get the total number of animals in the shelter we just do 83 + 50, which is 133.

There are 133 animals in total in the shelter.

Hope this helps you :)

7 0

2 years ago

On a number line, what is the distance between -12 and 20?

bija089 [108]

That would be a total of 32

3 0

3 years ago

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An equilateral triangle has a side length of 6. What is the height of the triangle?

vlabodo [156]

Since the height of an equilateral triangle in terms of its side s is s√3/2, the height of the triangle is 6√3/2 = 3√3 and so the area is (1/2)(6)(3√3) = 9√3.

If we draw a horizontal line a height of h from the base of the triangle, the region is split into two regions: the lower region consisting of a trapezoid of height h and the upper region consisting of a triangle of height 3√3 - h. 

Since the upper triangle and the triangle itself are similar triangles, the base and height are proportional. If we let x denote the base of the length of the upper triangle, we have: 

(S. of small triangle)/(S. of big triangle) = (Ht. of small triangle)/(Ht. of big triangle) 
==> x/6 = (3√3 - h)/(3√3) 
==> x = (6√3 - 2h)/√3 

Thus, the area of the upper triangle is: 

A = (1/2)[(6√3 - 2h)/√3](3√3 - h) = [(6√3 - 2h)(3√3 - h)]/(2√3). 
(Made a dumb mistake about the height here for some reason) 

Since we require that the area of this triangle is to be half of the total area (9√3/2), we need to solve: 

[(6√3 - 2h)(3√3 - h)]/(2√3) = 9√3/2 
==> (6√3 - 2h)(3√3 - h) = 27 
==> 54 - 6h√3 - 6h√3 + 2h^2 = 27 
==> 2h^2 - 12h√3 + 27 = 0. 

Solving with the Quadratic Formula gives: 

h = (6√3 + 3√6)/2 ≈ 8.87 units and h = (6√3 - 3√6)/2 ≈ 1.52 units. 

Since h = (6√3 + 3√6)/2 would place the line outside of the triangle, we pick h = (6√3 - 3√6)/2. 

Therefore, the line should be ==> (6√3 - 3√6)/2 units from the base. 

I hope this helps! ^^ Brainliest Please?

5 0

3 years ago

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