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serg [7]
3 years ago
6

Does a triangle with side lengths 7, StartRoot 80 EndRoot, and StartRoot 31 EndRoot from a right triangle?

Mathematics
2 answers:
g100num [7]3 years ago
7 0

Answer:

Square of the longest side: 80

Sum of squares of two shorter sides: 80

Yes

Step-by-step explanation:

7, sqrt(80) , sqrt(31)

(sqrt80)² = 7² + (sqrt31)²

80 = 49 + 31

80 = 80

Satisfies pythagoras theorem,

Hence forms a right angle triangle.

Square of the longest side: 80

Sum of squares of two shorter sides: 80

AlladinOne [14]3 years ago
4 0

Answer and Step-by-step explanation:

The sides we have are 7, \sqrt{80} , and \sqrt{31} .

The square root of 80 is less than 9 but greater than 8 (because 8^2 is 64, 9^2 is 81, and 80 is in between those two values), and the square root of 31 is definitely less than the square root of 80.

So, \sqrt{80} is the longest side.

1) The square of \sqrt{80} is: (\sqrt{80} )^2=80

2) The sum of the squares of the two shorter sides is:

7^2+(\sqrt{31} )^2=49+31=80

3) Since the square of the longest side is equal to the sum of the squares of the two shorter sides, by the Pythagorean Theorem, the triangle is a right triangles.

Hope this helps!

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ivann1987 [24]

Given :

  • A = {x: 2x² + 3x - 2 = 0 }
  • B = {x : x² + 3x - 4 = 0 }

To find :

  • (A U B ) × (A Π B )

Solution :-

<u>The </u><u>first </u><u>set </u><u>is </u><u>,</u>

  • A ={x : 2x² + 3x - 2 = 0}

<u>Solving</u><u> </u><u>the </u><u>Quadratic</u><u> equation</u><u> </u><u>,</u>

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  • 2x² + 4x - x - 2 = 0
  • 2x( x + 2) -1( x + 2 ) = 0
  • (2x -1) ( x + 2) = 0
  • x = 0.5 , -2

<u>Hence</u><u> </u><u>,</u>

  • A ={0.5, -2}

<u>The </u><u>second</u><u> </u><u>set </u><u>is </u><u>,</u>

  • B ={ x :x² + 3x - 4 = 0 }

<u>Solving</u><u> the</u><u> Quadratic</u><u> equation</u><u> </u><u>,</u>

  • x² + 3x - 4 = 0
  • x² + 4x - x - 4 = 0
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<u>Hence</u><u> </u><u>,</u>

  • B ={1,4}

<u>Now </u><u>,</u>

  • A U B = { 0.5 , 1 , 4 , -2}
  • A Π B = {∅ }

Since AΠ B is a null set , hence ,

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer to the second question: Daniel read three (3/10) more books

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