1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
A square garden is 50 inches long on each side.What is the length of the perimeter in feet?
leva [86]

Answer:

50/3 feet

Step-by-step explanation:

A square has 4 equal sides, so the perimeter is 4*50, or 200 inches.

But we want the answer in feet. There are 12 inches in a foot, so the perimeter in feet is 200/12 or 50/3 feet.

5 0
3 years ago
B. (4,-7)
zvonat [6]

Answer:

b)-3

c)17

d)-11

Step-by-step explanation:

4,-7)

-3

5 0
3 years ago
A sample of students at a university took a test that diagnosed their learning styles as active or reflective and also as visual
anastassius [24]

Answer:

Kindly check explanation

Step-by-step explanation:

Given that :

Sample size, n = 39

Correlation Coefficient, r = 0.273

The hypothesis test to examine if there is a positive correlation :

H0 : ρ = 0

If there is a positive correlation, then ρ greater than 1

H0 : ρ > 1

The test statistic :

T = r / √(1 - r²)/(n - 2)

T = 0.273 / √(1 - 0.273²)/(39 - 2)

T = 0.273 / 0.1581541

T = 1.726

The Pvalue using a Pvalue calculator can be be obtained using df = n - 2, df = 39 - 2 = 37

The Pvalue = 0.0463

α= .10 and α= .05

At α= .10

Pvalue < α ; Hence, we reject H0 and conclude that a positive correlation exists

At α= 0.05 ;

Pvalue < α ; Hence, we reject H0 and conclude that a positive correlation exists

3 0
2 years ago
A box contains 18 yellow, 24 green and 28 red jelly beans. If 12 jelly beans are selected at random, what is the probability tha
Nana76 [90]

Yellow: 25.71% chance of you grabbing a yellow jelly bean

Green:34.29% chance of you grabbing a green jelly bean

Red: 40% chance of you grabbing a red  jelly bean

4 0
2 years ago
An English professor assigns letter grades on a test according to the following scheme. A: Top 15% of scores B: Scores below the
lisabon 2012 [21]

Answer:

59 to 66

Step-by-step explanation:

Mean test scores = u = 74.2

Standard Deviation = \sigma = 9.6

According to the given data, following is the range of grades:

Grade A: 85% to 100%

Grade B: 55% to 85%

Grade C: 19% to 55%

Grade D: 6% to 19%

Grade F: 0% to 6%

So, the grade D will be given to the students from 6% to 19% scores. We can convert these percentages to numerical limits using the z scores. First we need to to identify the corresponding z scores of these limits.

6% to 19% in decimal form would be 0.06 to 0.19. Corresponding z score for  0.06 is -1.56 and that for 0.19 is -0.88 (From the z table)

The formula for z score is:

z=\frac{x-u}{\sigma}

For z = -1.56, we get:

-1.56=\frac{x-74.2}{9.6}\\\\ x = 59

For z = -0.88, we get:

-0.88=\frac{x-74.2}{9.6}\\\\ x = 66

Therefore, a numerical limits for a D grade would be from 59 to 66 (rounded to nearest whole numbers)

7 0
3 years ago
Other questions:
  • 12÷478<br> find two estimates <br> plz help thank you<br> ill give you 12 points
    7·1 answer
  • All I need to know is if I picked the right one!
    5·2 answers
  • Solve the equation after making an appropriate substitution. X^6-98x^3=3375
    8·1 answer
  • Find the inverse function of <img src="https://tex.z-dn.net/?f=y%3D3%5E%7Bx-2%7D" id="TexFormula1" title="y=3^{x-2}" alt="y=3^{x
    8·1 answer
  • A regular hexagon is to be cut out of a circular sheet of metal that has a radius of 6 inches.
    12·1 answer
  • Which proportion is true?
    11·1 answer
  • Oliver spot frustrated sometimes with his somewhat limited set of red We, and green building bricks. Part way through project, h
    13·2 answers
  • I will give you brainlist. But only if your answer is valid
    15·2 answers
  • Which is not a binomial in the following expressions? *
    7·1 answer
  • Given f of x is equal to the quantity 8x plus 1 end quantity divided by the quantity 2x minus 9 end quantity, what is the end be
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!