This relationship leads to the conclusion that there is no Pythagorean triple of this form that contains the integer 2. Why?
Answers
Answer:
suppose 2^2 + b^2 = c^2 with 2 < b < c (it should be clear that this assumption is fine, 12 + 22 = 5 and sqrt(5) is not an integer; 22 + 22 = 8 and sqrt(8) is not an integer). Then c^2 - 4 = b^2 so (c+2)(c-2) = b^2. As b is prime, this means c-2=b or c-2=1 (since c+2 > 1). So either c=b+2 or c=3. The c=3 case can't happen since that would make b^2 = 5 so we are left with c=b+2. Then we have 4 + b^2 = (b+2)2 = b2 + 4b + 4 meaning that b=0. So there are no triples involving 2.
Step-by-step explanation:
A Pythagorean triple of this form cannot contain integer 2 if we add extra 2x²y² because it will increase the value of the coefficient of xy to 4.
The given function:
[tex](x^2-y^2) + (2xy)^2 = (x^2 + y^2)^2[/tex]
This function is expanded as follows;
[tex](x^2-y^2)^2 + (2xy)^2 = (x^2 + y^2)^2\\\\x^4 + y^4 -2x^2y^2 + 4x^2y^2 = x^4 +y^4 + 2x^2y^2\\\\add \ \ (+2x^2y^2) \ to \ both \ sides \\\\x^4 +y^4 +4x^2y^2 = x^4 +y^4 +4x^2y^2[/tex]
In this expanded form of the given function, it is clear that non of the coefficients of x and y contains integer 2 and the supposed coefficient value of xy increase to 4 because of the extra 2x²y² added to the function.
Thus, we can conclude that a Pythagorean triple of this form cannot contain integer 2 if we add extra 2x²y² because it will increase the value of the coefficient of xy to 4.
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Related Questions
Please help me! Correct answer will get brainliest
Answers
Answer:
[tex]4(\sqrt{\frac{147}{3} }+3)=40[/tex]
Step-by-step explanation:
Given: [tex]4(\sqrt{\frac{147}{3} }+3)[/tex]
Evaluate radical: [tex]4(\sqrt{49}+3)[/tex]
Evaluate radical: [tex]4(7+3)[/tex]
Evaluate parentheses: [tex]4(10)[/tex]
Distribute 4: [tex]40[/tex]
What is the probability that you will randomly land on a BLUE section?
Write your answer in a simplified fraction, using a "/" to separate the numerator and denominator.
Answers
Answer:
2/8. or simplified= 1/4
Step-by-step explanation:
Every 20 seconds a sprinkler passes across a garden will it take more than an hour for the sprinkler to cross the garden 150 times
Answers
Answer:
No
Step-by-step explanation:
If the sprinkler takes 20 seconds to cross the garden, and it crosses the garden 150 times, the total number of seconds it took can be calculated by multiplying 20 and 150. You get 3000 seconds, but you need to convert that to minutes to tell if it will take more or less than an hour. So divide 3000 by 60 (the number of seconds in 1 minute). Your answer is 50 minutes. And since 1 hour is 60 minutes, it doesn't take more than an hour to cross the garden 150 times.
The required, 50 minutes is less than 1 hour, so we can conclude that it does not take more than an hour for the sprinkler to cross the garden 150 times.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
If a sprinkler passes across a garden every 20 seconds, then it makes 60/20 = 3 passes per minute.
To find out how many minutes it takes for the sprinkler to cross the garden 150 times, we can divide the total number of passes by the number of passes per minute:
150 passes / 3 passes per minute = 50 minutes
So it takes 50 minutes for the sprinkler to cross the garden 150 times.
To see if this is more than an hour, we can convert 50 minutes to hours:
50 minutes / 60 minutes per hour = 0.83 hours
Since 0.83 hours is less than 1 hour, we can conclude that it does not take more than an hour for the sprinkler to cross the garden 150 times.
Learn more about simplification here:
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The price of an item has been reduced by 35%. The original price was $17.
Find the price now
Answers
Then just solve the equation
Hope it does help
help me get it right no links
Answers
Answer:
kjhgfdfgbjuyt hope it helps
Step-by-step explanation:
A DVD player manufacturer shipped 960 DVD players last month. According to the manufacturers records, 5 out of every 24 players were repaired during the first year of ownership. How many of the 960 DVD players were repaired in the first year?
a: 40
b: 120
C: 192
D: 200
Answers
Answer:
D: 200
Step-by-step explanation:
Given that
The DVD player shipped 960 players last month
There is a record that out of every 24 players, the 5 would be the repaired
So we need to find the number of DVD players were repaired in this 960 players
So
= 960 × 5 ÷ 24
= 200 players
Hence, the option is d.
How many solutions does the following linear equation have?
3(x – 5) = 1 (62 - 12)
O no solution
O one solution
O infinitely many solutions
Answers
Answer:
no solution
Step-by-step explanation:
3(x – 5) = 1/2 (6х- 12)
3х-15= 6/2х-12/2
3х-6/2х=15-12/2
3х-3х=15-6
0х=9 no solution
Answer:
no solution
Step-by-step explanation:
3(x – 5) = 1/2 (6х- 12)
3х-15= 6/2х-12/2
3х-6/2х=15-12/2
3х-3х=15-6
0х=9 no solution
Sora was given two data sets, one without an outlier and one with an outlier.
Data without an outlier: 108, 113, 105, 118, 124, 121, 109
Data with an outlier: 108, 113, 105, 118, 124, 121, 109, 41
How is the mean affected by an outlier?
The outlier did not affect the mean at all.
The outlier made the mean higher than all the other values.
The outlier made the mean lower than all the other values.
The mean is centered around all the other numbers in both sets of data.
Answers
Answer:
The outlier made the mean lower than all the other values.
Step-by-step explanation:
Mean is a measure of central tendency. It is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
Mean of numbers without the outlier = (108 + 113 +105 + 118 + 124 + 121 +109) / 7 = 114
Mean of numbers with the outlier = (108 + 113 +105 + 118 + 124 + 121 +109 + 41) / 8 = 104.9
the mean with the outlier is lower than any of the numbers
Answer:
C
Step-by-step explanation:
Three candy bars are being shared equally between four friends.
How much does each friend get?
Answers
Answer:
[tex] \frac{3}{4} [/tex]
When n = 4, which of the expressions below will be greater than 20? Select all that apply.
A) n2+6n÷3
B) 12n –(6n+3)
C) n2–6
D) 4(n+6) –3n
Answers
D. 4(n+6) - 3n = 28
help help help help ill like five y’all brian list or something just pls help
Answers
Answer: 0.086x
Step-by-step explanation:
Since the trend line starts at the origin, there is no y-intercept. To calculate the slope, divide the change in y over change in x. Since one of our points is the origin, we can just divide the y value by the x value, or 1.38 by 16, to get 0.08625. Rounded to the nearest thousandth, we get a slope of 0.086.
NEED HELP! The wind-speed, in miles per hour (mph), was measured every six hours during a day on the Isles od Scilly.
Answers
Answer:
Mean=
36/5=7.2
Median=8
Step-by-step explanation:
mean=add all the numbers/divide by how many
13+12+8+2+1=36
5 numbers altogether hence,
36/5=7.2
median=arrange all numbers and middle term is the median(for odd numbers only)
13,12,8,2,1
Hence,8 is the middle term
Hope this helped xx
An equation is shown below.
−45(9x−20)−3x=45x−6
Enter the value of x that makes this equation true.
Answers
X=2
6+5·(8÷2)2
PLSS help i will mark brainliest
Answers
answer:
46
step-by-step explanation:
use PEMDAS in order to solve this6 + 5 · (8 ÷ 2)2
6 + 5 · (4)2
6 + 40
= 46
The price of a book that originally cost c dollars was decreased by $10 and then increased by 25% select all the expressions that represent the new price of the book.
A. (c-10) + (0.25)c
B. (c-10) + 0.25
C. (c-10) + 25
D. (c-10) + (c-10)(0.25)
E. (c-10)(1.25)
Answers
Answer:
Step-by-step explanation:
B. (c- 10)+ 0.25
what is the correct answer?
Answers
Answer:
Step-by-step explanation:
The missing height is 5 units
Recall that (area of a parallelogram) = (length)(height) and that
(height) = (area) / length.
Here,
(height) = (35 units^2) / (7 units) = 5 units
The missing height is 5 units
A box plot is shown below what is the median and q3 of the data set represented on the plot median=30;q3=44
Answers
The required boxplot isn't attached, an hypothetical solution is given which could be applied to solve your actual task.
Answer:
Kindly check explanation
Step-by-step explanation:
The median of a dataset plotted on a box and whisker plot can be obtained directly from the plot as the point where a vertical line splits the box. The line inside the box gives the median of the data. The Q3 value which is the upper quartile is depicted on the box and whisker plot as the endpoint of the box. The endpoint of the box gives the upper quartile value for the dataset.
In the scenario above, the median = 29
The upper quartile = 38
Solve the equation: 7(x + 8) = 49
Answers
Answer:
-1
Step-by-step explanation:
1.)Reorder the terms:
7(8 + x) = 49
(8 * 7 + x * 7) = 49
(56 + 7x) = 49
2.)Solving
56 + 7x = 49
3.)Solving for variable 'x'.
4.)Move all terms containing x to the left, all other terms to the right.
5.)Add '-56' to each side of the equation.
56 + -56 + 7x = 49 + -56
6.)Combine like terms: 56 + -56 = 0
0 + 7x = 49 + -56
7x = 49 + -56
7.)Combine like terms: 49 + -56 = -7
7x = -7
8.)Divide each side by '7'.
x = -1
9.)Simplifying
x = -1
Hope this helps
plz like and brainy
I nEED HELP HIRRY WITH EXPLANATION PLS PLS
find the missing angle,k, in the diagram below
1) 90°
2) 145°
3) 55°
4)35°
Answers
what is a2+b2=c2 what formula is this
Amos trevor_frost
Answers
Answer:
[tex]\huge{\boxed{\boxed{\tt { ⎆ \ Pythagorean \ Theorem :-}}}} \ [/tex]
[tex]a {}^{2} + b {}^{2} = c {}^{2} [/tex]
This is the formula for the pythagorean theorem i.e, one leg of a triangle squared plus another leg of a triangle squared equals the hypotenuse squared.
Answer:
[tex]a^2+b^2=c^2[/tex] is the formula for the Pythagorean Theorem
Step-by-step explanation:.
The Pythagorean Theorem, also referred to as the ‘Pythagoras theorem,’ is arguably the most famous formula in mathematics that defines the relationships between the sides of a right triangle. This mathematical law states that the sum of squares of the lengths of the two short sides of the right triangle is equal to the square of the length of the hypotenuse.
How many terms are in the expression below?
5x +3 - 3x – 1 + 2x + 5
Answers
Answer:
2
Step-by-step explanation:
5x + 3 - 3x - 1 + 2x + 5
you can combine the like terms
5x - 3x + 2x = 4x
3 - 1 + 5 = 7
4x + 7
there are 2 terms in the expression
Find tan(a) in the triangle.
Choose 1 answer:
A. 7/25
B. 24/25
C. 7/24
D. 24/7
Answers
Tan(a)= Toa
Toa =opposite/adjacent
Toa=7/25
final answer is 7/25
Answer: 24/7
this is the answer enjoy
what is the distance between (3,2) and (1,6)
Answers
Answer:
The answer is 2√5 or 4.47213595...
Step-by-step explanation: use the distance formula
A sociedade brasileira de pediatria recomenda limitar o tempo máximo de telas e jogos de videogames a três horas por dia, para adolescentes com idades entrar 11 e 18 anos Este tempo máximo, se usado todos os dias, representa, dos 11 aos 18 anos, um total de horas que equivale a A) 1 ano B) 3 anos C) 6 anos D) 7 anos E) 8 anos
Answers
Responder:
A) 1 ano
Explicação passo a passo:
Tempo máximo de tela = 3 horas / dia
Número de anos entre 11 e 18 anos = 8 anos
Vamos calcular o número de tempo de tela em um ano:
Número de dias em um ano = 365
Horas de uso em um ano:
3 horas / dia * 365 dias = 1.095 horas
Horas de uso em 8 anos:
1.095 horas * 8 = 8.760 horas
Convertendo o número de horas em anos:
Número de horas em um ano:
24 horas * 365 dias = 8760 horas por ano
Anos de tempo na tela:
Número de horas em 8 anos / número de horas em um ano
8760/8760 = 1 ano
u get brainlyist if quick
Find the value of y that makes the equation 3y = x + 2 true, when x = 1.
A. 1
B. 3
C. 1/3
D. 2
Answers
Answer:
A. 1
Step-by-step explanation:
just plug it in here
3y = 1 + 2
3y = 3
y = 1
Find the area of a circle with a circumference of 31.4 units
Answers
Answer:
Step-by-step explanation:
hope it helps you
A lap around Natalie's neighbourhood is 20 kilometres. Natalie ran 2 laps before
walking the rest. How many kilometres did Natalie run?
Answers
Denesh is creating a triangular flower bed using three pieces of wood. The two shorter pieces of wood have lengths of 7 feet and 24 feet. How long, in feet, should the third piece of wood be for Denesh to create a right triangle?
Answers
Answer:
The answer is 25
Step-by-step explanation:
Answer:
The third piece of wood that for denesh need to create to form a right triangle is: 25 feet.
Step-by-step explanation:
We are given two shorter legs of a wood of lengths as: 7 feet and 24 feet. We know that in a right angled triangle with two shorter sides as a and b the longer length or the hypotenuse of the triangle of length c is given by Pythagorean Theorem as: We have: a=7 and b=24 Hence,
PLEASE HELP ASAP WILL MARK BRAINLIEST
Part A
Which line best fits the data, l, m, or n? Why?
Part B
In the equation of a line, y = mx + b, what does b stand for? What is the value of b for the line of best fit?
Part C
In the equation of a line, y = mx + b , what does m stand for? What is the value of m for the line of best fit?
Part D
Now that you know m and b, what is the equation of the line of best fit?
Answers
Answer:
Part A:
Most of the data points are above line m. All of the data points are below line n. The data points are evenly distributed on either side of line l. Therefore, line l is the line of best fit for the data.
Part B:
For the line of best fit, the y-intercept is approximately 10 and the slope is approximately 2 .
Part C:
Y= 2x+10
Step-by-step explanation:
Part A:
Most of the data points are above line m. All of the data points are below line n. The data points are evenly distributed on either side of line l. Therefore, line l is the line of best fit for the data.
Part B:
To find the y-intercept of a line, identify where the line intersects the y-axis. Because the line of best fit is line l, the y-intercept is 10.
To find the slope, choose two points on line l, such as (10,30) and (30,70):
Part C:
To get the equation of the line, substitute the y-intercept, 10, for b and the slope, 2, for m.
Please give me the brainlliest crown Pls
14523 round to nearest 10
Answers
Answer:
14520
Step-by-step explanation: