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Mekhanik [1.2K]
2 years ago
10

The sets of numbers 3, 4, 5 and 8, 15, 17 are Pythagorean triples. Use what you know about the Pythagorean Theorem and explain o

r show why they are Pythagorean triples
Mathematics
1 answer:
konstantin123 [22]2 years ago
4 0

Answer:

When we have 3 numbers, like:

a, b and c.

Such that:

a < b < c.

These numbers are a Pythagorean triplet if the sum of the squares of the two smaller numbers, is equal to the square of the larger number:

a^2 + b^2 = c^2

This is equivalent to the Pythagorean Theorem, where the sum of the squares of the cathetus is equal to the hypotenuse squared.

Now that we know this, we can check if the given sets are Pythagorean triples.

1)  3, 4, 5

Here we must have that:

3^2 + 4^2 = 5^2

solving the left side we get:

3^2 + 4^2 = 9 + 16 = 25

and the right side:

5^2 = 25

Then we have the same in both sides, this means that these are Pythagorean triples.

2) 8, 15, 17

We must have that:

8^2 + 15^2 = 17^2

Solving the left side we have:

8^2 + 15^2 = 64 + 225 = 289

And in the right side we have:

17^2 = 17*17 = 289

So again, we have the same result in both sides, which means that these numbers are Pythagorean triples

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Is x = 6 a solution to the equation 5(x – 3) = x + 13?
deff fn [24]

Answer:

x=6 is not a solution

Step-by-step explanation:

We can substitute 6 as x to find out:

5(6-3)=6+13

first, because of PEMDAS we'll do 6-3

5(3)=6+13

multiply 5 by 3 and add 6 and 13

15=19

Since the statement is not true, that means that x=6 is not a solution

Hope this helps!

8 0
3 years ago
The Jones family eats 2/3 of a packet of biscuits every day. How long will 27 packets last the family?
Veseljchak [2.6K]

Answer:

40 1/2 days

Step-by-step explanation:

Quantity of biscuits the Jones eats daily = 2/3 of a packet

Total packets of biscuits = 27 packets

How long will 27 packets last the family?

= Total packets of biscuits / daily intake of biscuits of the Jones

= 27 ÷ 2/3

= 27 × 3/2

= 81 / 2

= 40 1/2 days

6 0
3 years ago
How much is 106 divided by 6?<br> A) 17 R2 <br>B)17 R3 <br>C)17 R4 <br>D)17 R1​
musickatia [10]

Answer:

C, 17 R4.

Step-by-step explanation:

6x17 is equal to 102, and 102+4 gets you to 106, therefor C is the correct answer.

7 0
3 years ago
Nate spent $28 on 2 dvds.at this rate how much would 5 dvds cost him
Anuta_ua [19.1K]
2=28 divide both get 14 . So each cd is 14$. So now 28+28=56 (4 cd's) plus 14 (1 more cd) =5 so 5 is 70.
7 0
3 years ago
Angle r and 92 are supplementary angles. what equation can you use to solve for r?
Oxana [17]

Answer:

88°

Step-by-step explanation:

<h3>supplementary angle are angles that add up to 180°</h3>

r+92= 180

r= 180-92

r = 88°

5 0
1 year ago
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