Mathematics High School

The Pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the
hypotenuse by the formula a? + b2 = -2
If a is a rational number and b is a rational number, why could c be an irrational number?

The Pythagorean Theorem States That The Sum Of The Squares Of The Legs Of A Right Triangle Is Equal To

Answers

Answer 1

Answer:

For the value of hypotenuse can be irrational, sum of squares of other two legs might be imperfect square number.

Step-by-step explanation:

We all know, the Pythagorean theorem can be stated as follows:

The sum of squares of two legs of a right angled triangle is equal to the square of the hypotenuse.

i.e.

[tex]a^2+b^2=c^2[/tex]

Where, [tex]c[/tex] is the hypotenuse and [tex]a, b[/tex] are the two other legs of the right angled triangle.

Given that:

[tex]a[/tex] and [tex]b[/tex] are rational numbers.

To find:

Situation for which [tex]c[/tex] is irrational.

Square of a rational number is always rational.

So, [tex]a^{2} , b^{2}[/tex] both will be rational.

And sum of squares of two rational numbers will also be rational.

Therefore, [tex]a^2+b^2[/tex] will also be rational.

and

[tex]c = \sqrt{a^2+b^2}[/tex]

For the value of [tex]c[/tex] can be irrational, sum of squares of other two legs might be imperfect square number.

Related Questions

Mike deli just sold 328 ham sandwiches this week around how many ham sandwiches did mike sell every eat this week (round to the nearest number)

Answers

Answer:

To the nearest number = 47 ham sandwiches

Step-by-step explanation:

Mike deli just sold 328 ham sandwiches this week around how many ham sandwiches did mike sell every day this week (round to the nearest number )

Total ham sandwiches Mike sold this week = 328

Total number of days in a week = 7

how many ham sandwiches did mike sell every day this week

Number of ham sandwiches mike sell every day this week = Total ham sandwiches Mike sold this week / Total number of days in a week

= 328 / 7

= 46.9

To the nearest number = 47 ham sandwiches

I really need some help.

Answers

I got you , it’s option 4 .

Which expression represents Add the product of 7 and 5 to the quotient of 288 and 18

Answers

Answer:

51

Step-by-step explanation:

7×5=35

288÷18=16

35+16=51

Expresion- 7×5+288÷18

Zoe paid 18.60 in sales tax and tips for dinner. The sales tax is 11% and she tipped 20%. What was the price of Zoe’s dinner before sales tax and tip?

Answers

Answer:

$60 was the price of Zoe's dinner, before sales tax and tip.

Step-by-step explanation:

Sales tax = 11% * original price = 0.11 * x= 0.11xTips for dinner = 20% * original price = 0.20 * x = 0.2x0.11x + 0.2x = 18.600.31x = 18.60x = 60$60 was the price of Zoe's dinner, before sales tax and tip.

Answer:

$60 was the price of Zoe's dinner, before sales tax and tip.

Step-by-step explanation:

1. Sales tax = 11% times original price = 0.11 times x= 0.11x

2. Tips for dinner = 20% times original price = 0.20 times x = 0.2x

3. 0.11x + 0.2x = 18.60

4. 0.31x = 18.60

5. x = 60

6. $60 was the price of Zoe's dinner, before everything else

a bag of potatoes and a bag of onions combined weigh 11 kilograms 15 grams. if the bag of potatoes weighs 7 kilograms 300 grams. how much does the bag of onions weigh?

Answers

Answer:

4. 715

Step-by-step explanation:

11.015 - 7.300= 4.715

factor this out:
7y³ + 21y² + 14y

Answers

Factor out 7y
7y(y^2 + 3y + 2)
7y(y + 1)(y + 2)

PLEASE HELPP
STOP TELLING ME WEBSITES TO GO TO PLEASE ITS WASTING MY POINTSSS

Answers

Can you take a brighter picture I may be able to solve and also turn it the other way

Answer:

lollll

Step-by-step explanation:

b) Simplify fully V8 x V18​

Answers

Answer:

v8 x v18 = v²144

Step-by-step explanation:

v x v = v²

18 × 8 = 144

so the answer is v²144

Answer:

V8 x V18

=V144

HOPE IT HELPED U,

MARK AS THE BRAINLIEST

^_^

I’ll give the Brainliest to who answers this question with a reasonable explanation.

Thank you.

Answers

Answer:

B: 10

Step-by-step explanation:

The angle measures are all multiplied by 2.

I believe the answer should the 10.

Looking at the two given triangles, the singular line in the bottom left triangles means that the angles are the same. As to the corner seen in cornerF and cornerC, and cornerD with cornerA. Knowing that all of the angles in the triangle are the same, means that the side lengths should all be generally on the same scale.

With triangle DEF, this triangle got scaled up by 2. This can be seen from line AB and line DE. AB was multiplied by two, in order to get line DE, which is 8. Apply the x2 rule to lines DF and EF, and the unknown "e" turns into 10. Unkown "d" turns into 12.

I need help please.....

Answers

Answer:

9.42

Step-by-step explanation:

pretend the missing piece is still there.  Find the area of the piece first.

90/360(3.14*2^2)=

90/360(12.56)=

3.14

the whole circle's area would be 3.14(4)=12.56, since it is a 90 degree angle.

then subtract the area of the piece  12.56-3.14=9.42

Answer:

so a good strategy might be to solve for the entire area of a circle.. then cut that up into quarters and add 3 of those together to get the correct answer

Step-by-step explanation:

area of a circle formula = pi * [tex]r^{2}[/tex]

we are given r =2  ( nice and easy to work with )

and we get to use an easy approximation of pi of 3.14

so the whole circle's area is  pi * [tex]2^{2}[/tex]

3.14 * 4 = 12.56

that's the entire circle.. divide by 4 the multiply by 3   like this

3/4 * 12.56 = 9.42

you could also think of this as multiplying the entire circle by 3/4 (0.75) if you prefer but it's good to recognize that you can divide it up into 4 parts .. then multiply by 3...

What is the equation of the line perpendicular to the
line shown in the diagram that passes through the point
(-2,-4)?

Answers

Answer: x + 3y = -14

Step-by-step explanation:

Plug in the coordinates

-2+3(-4) = - 14

Sam measured the height of a window frame as 5.23 feet, but the actual height was 6 feet. What is the percentage of error in Sam's measurement?

Answers

Answer:

Sam is 13% wrong.

Step-by-step explanation:

The answer is 13% because 5.23 is 87% of 6 and 100% minus 87% is 13%.

P.S Can I have brainliest?

Answer:

12.83%

Step-by-step explanation:

Hope I helped! pls give brainliest if you can.

Can somebody tell me the answer??

Answers

Answer:

The answer is B

Step-by-step explanation:

Divided 422 by 6 and you will get 70.33 which is rounded to 70 mph

I hope you find this useful :) Long division btw

Answer:

70mph

Step-by-step explanation:

422mi/6hr

=70.33333333333333

70mph

A bus makes a stop at 2:30, letting off 11 people and letting on 5. The bus makes another stop ten minutes later to let off 3 more people. How does the number of people on the bus after the second stop compare to the number of people on the bus before the 2:30 stop?

Answers

Answer:

Answer down below Branliest Please

Step-by-step explanation:

What is the greatest common factor of 24,36, and 50?

Answers

Answer:

12

Step-by-step explanation:

Answer:

The biggest common factor number is the GCF number. So the greatest common factor 24 and 36 is 12.

Step-by-step explanation:

two square are congruent ,if they have same ______​

Answers

Two squares are congruent if they have the same side length.

Answer:

If they have the same sides.

Step-by-step explanation:

The method of comparing these two figures is also known as the method of superstition.

Zander wants to find out what the most popular sporting event is in the district’s high schools. He surveys a sample of the population. Under which condition is surveying a sample valid?
The population is small.
The population contains a large diverse group of people.
There are many different possible answers to the question.
There are some people in the population that do not like sports.

Answers

Answer:

The answer would be B.

Step-by-step explanation:

I hope you all are doing great and staying positive. It will get better.

Answer:

b

Step-by-step explanation:

i just did the test

Write the equation of the line with a slope of -5 and y-intercept of 12.

Answers

Answer:

y=-5x+12

Step-by-step explanation:

Since slope-intercept form is y=mx+b, m is the slope, and b is the y-intercept. We substitute m for -5, since it is the slope, and we substitute 12 for b, since it is the y-intercept. I hope this helps!

Sam and Janet are mountain biking. Sam rides his bike down into a valley, 8 feet below sea level. Janet rides her bike to the top of a hill, 437 feet above sea level. What is the vertical distance between Sam and Janet?

Answers

The answer is 429. May not be right. But I am positive it is

Pls help due soon will give brainilist

Answers

Answer:

B. 6 teaspoons

Step-by-step explanation:

..................

Answer: it 6 teaspoons

Step-by-step explanation:

if the waffle calls for 2 cup the answer  will be 6 because 2*2 equals the 4 so 3*2 equal 6

the price p of a pizza is 6.95 plus 95. for each topping t on the pizza

Answers

There isn’t a question, that’s a statement, please provide a more informative question in the comments of this for me to answer. Thank you!
-Chicken Nugget

Productivity: My candy bar company made 100 million bars last year, sold for $1 each. I also paid [L] people last year, with an average salary of $100K last year. I have overhead cost of $10M. What was my TOTAL productivity (no units, rounded to 2 decimal places)?

Answers

Answer:

5

Step-by-step explanation:

Productivity: My candy bar company made 100 million bars last year, sold for $1 each. I also paid [L] people last year, with an average salary of $100K last year. I have overhead cost of $10M. What was my TOTAL productivity (no units, rounded to 2 decimal places)?

Solution:

Total productivity is the average of labour and capital productivity weighted and adjusted to price fluctuations. It is the ratio of total output to the total input. The total productivity is given by the formula:

Total productivity = total output / total input

Total output = Revenue = number of bars sold * price per bar

Total output = 100 million * $1 = $100 million

Total input = Total salary + overhead cost

Total salary = number of people * average salary = 100 *$100000 = $10 million

overhead cost = $10 million

Total input = $10 million + $10 million = $20 million

Total productivity = total output / total input = $100 million / $20 million

Total productivity = 5

What is the body of water that was constructed the great lakes to atlantic ocean?

Answers

Answer:

The Saint Lawrence Seaway (French: la Voie Maritime du Saint-Laurent) is a system of locks, canals, and channels in Canada and the United States that permits oceangoing vessels to travel from the Atlantic Ocean to the Great Lakes of North America, as far inland as Duluth, Minnesota, at the western end of Lake Superior.

Step-by-step explanation:

HELP ! i’ll give brainliest!!!

Answers

Answer:

$30.15

Step-by-step explanation:

i think sorry if im wrong

10 percent increase of $29000 over 5 years,will give brainly is urgent

Answers

Answer:

$43,500

Step-by-step explanation:

10 percent increase of $29,000

10% = 0.10

29,000*0.10 = 2,900

So 2,900 a year

so 2,900*5 = 14,500

Then add

29,000+14,500 = 43,500

The distance between towns A and B is 300 km. One train departs from town A and another train departs from town B, both leaving at the same moment of time and heading towards each other. We know that one of them is 10 km/hr faster than the other. Find the speeds of both trains if 2 hours after their departure the distance between them is 40 km.

Answers

Answer:

The speed of the slower train is 60km/hr or 80km/hr and the speed of the faster train is 70km/hr or 90km/hr.

pls help me with this question..... if right I will follow u.... and give u brainliest ......pls it's urgent......​

Answers

Answer:

Step-by-step explanation:

3). Naomi walked 4560 m to the nearest 10 m. Peta walked 4600 m to the nearest 100 m.

a). 4555 m ≤ n ≤ 4564 m

    4550 m ≤ p ≤ 4649 m

b). If n = 4555 m and p = 4550 m

   Then Naomi walked more than Peta

   If n = 4555 m and p = 4555 m

   Then Both Naomi and Peta walked exactly the same.

   If n = 4555 m and p = 4649 m

   Then Peta walked further than Naomi.

  Therefore, all three statements could be true.

4). (a). x = 120 to nearest 10 → 115 ≤ x ≤ 124

(b). y = 1.24 to 2 decimal places → 1.24

    (Already given in 2 decimal places)

(c). z = 0.0124 to 3 significant numbers → 0.0124

2. Find the slope, or rate of change, represented in the table below. x -1 0 1 2 3 У -8 3 14 25 36​

Answers

Answer:

11

Step-by-step explanation:

slope is change in y over change in x. so, if x is increasing by one every time and y is increasing by 11, then the slope is 11/1, which we write as 11.

A two-digit numner is four times the sum and three times the product of its digits. Find the number.​

Answers

Answer:

24 i thik?

Step-by-step explanation:

help please .........

Answers

The answer should be option 3 because they’re congruent to each other.
Hope this helped have a good day :)
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