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dangina [55]
2 years ago
7

If x and y are positive numbers with x>y, show that a triangle with sides of lengths 2xy, x^2-y^2, and x^2+y^2 and is always

a right triangle?
Mathematics
1 answer:
Marianna [84]2 years ago
5 0

Answer: 2xy

Step-by-step explanation: We know that x%5E2+%2B+y%5E2 must be the longest side of the triangle (it cannot be 2xy, I will demonstrate why afterwards). By the Pythagorean theorem,

. Therefore this is a right triangle.

The only "assumption" we had to make was that x%5E2+%2B+y%5E2+%3E+2xy, but this is easy to prove. By the AM-GM inequality, %28x%5E2+%2B+y%5E2%29%2F2+%3E=+sqrt%28x%5E2y%5E2%29+=+xy. Multiplying both sides by 2, x%5E2+%2B+y%5E2+%3E=+2xy. Equality occurs only when x+=+y, but this cannot be true, so x%5E2+%2B+y%5E2 is strictly greater than 2xy.

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Use a model to divide. 45 by 6
Savatey [412]

Answer:

45 / 6

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
The area of the parallelogram shown is (35x2 + 46x +15) square meters. If its base is (5x + 3) meters, find
attashe74 [19]

Answer:

(7x + 5)m

Step-by-step explanation:

area = base  * height = (35x2 + 46x +15) m²

base = (5x + 3)

Using algebraic division, find the height. SEE ATTACHMENT

height = (7x + 5)

7 0
3 years ago
Please give the answer
sweet [91]

The function can be solved as follows:

  • f(6 + 4) = 25
  • f(6) - f(4) = 20
  • f(6 - 4) = 1
  • f(6) - f(4) = 6
  • f(6) . f(4) = 91

<h3>How to solve function?</h3>

f(x) = 3x - 5

Therefore, the function can be solved as follows:

f(6 + 4) = f(10) = 3(10) - 5 = 25

f(6) + f(4) = 3(6) - 5 + (3(4) - 5)

f(6) - f(4) = 13 + 7

f(6) - f(4) = 20

f(6 - 4) = f(2) = 3(2) - 5 = 6 - 5 = 1

f(6) - f(4) = 3(6) - 5 - (3(4) - 5)

f(6) - f(4) = 18 - 5  - (12 - 5)

f(6) - f(4) = 13 - 7

f(6) - f(4) = 6

f(6.4) = f(24) = 3(24) - 5 = 72 - 5 = 67

f(6) . f(4) = (3(6) - 5 ) (3(4) - 5)

f(6) . f(4) = (18 - 5)(12 - 5)

f(6) . f(4) = (13)(7) = 91

learn more on function here: brainly.com/question/9390144

#SPJ1

5 0
1 year ago
pretty sad and pathetic when half the answers on here are wrong and marked verified or brainliest. even more sad when 18/20 ques
tekilochka [14]

Answer:

Well im sure that it wasn't a persons intention it must be a mistake i have found this very useful and i have the basic

Step-by-step explanation:

5 0
3 years ago
Match the following figure<br><br><br> ​
grigory [225]

Answer:

#4 Would be rectangular prism

#5 would form into a cone

#3. A cylinder

I could be wrong but I hope this helps for a start , it's hard to see the picture  but it's what i could make out. I suggest you look up pics of a cylinder, cone, etc on google images to help more.

Step-by-step explanation:

5 0
3 years ago
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