Mathematics Middle School

Show that if x, y, z are integers such that x^3+5y^3 = 25z^3, then x = y = 0.

Answers

Answer 1

Answer:

3125*k^9 + y^3 is an integer my closure property.

 but 5^(1/3) is not an integer, which forces z to be irrational.

Note that there is no way an integer value can rationalize 5^(1/3)

Step-by-step explanation:

x^3 = 25z^3 - 5y^3

x^3 = 5 ( 5z^3 - y^3)

x  =  (5 ( 5z^3 - y^3) )^(1/3) must be an integer

  = 5^(1/3) * (5z^3 - y^3)^(1/3)

Then  (5z^3 - y^3)^(1/3) = 25*k^3 for some integer k

 5z^3 - y^3 = 15625*k^9

 5z^3 = 15625*k^9 + y^3

  z^3 = 3125*k^9 + (1/5)*y^3

z =  ( 3125*k^9 + (1/5)*y^3 )^ ( 1/3)

Related Questions

A stadium has seats that are arranged into sections. In each section, the seats

are arranged into rows. There are 11

sections, 7 rows in each section, and 10

seats in each row. As a baseball game

in the stadium, all of the seats are

occupied. A seat will be chosen at

random and a price will be awarded to

the person sitting in that seat. If Hoda is

sitting in one of the seats, what is the

probability that she will win the price?

Answers

Answer:

1/770

Step-by-step explanation:

7x10x11=770 he is sitting in one seat so 1/770 she will win.

the answer is 770 so 1/770

yall help me again please!

yall help me again please!

Answers

Answer:

T F F T

Step-by-step explanation:

T - there are no green marbles

F - the majority of the marbles are yellow

F - nothing is for certain there's possibilities to pick the other 2 colours

T - there are few red marbles compared to the total of the others

Answer:

T, F, F, T

Step-by-step explanation:

1. There are no green marbles

2. more than half the marbles are yellow there is a high chance

3. Blue have quite a lot as well

4. there are only 2 red marbles very low chance

i need help please and ty

i need help please and ty

Answers

Answer:

Down below ↓

Step-by-step explanation:

2 sqaure inch is the answer! I hope you enjoy!

Answer:

✔️ 42

Step-by-step explanation:

Area= length x width

first we have to find entire area
12 x 6 = 74

Now find the picture’s area

8 x 4 = 32

Then subtract the area of the whole and the area of the picture to find the are of the frame

74 - 32= 42

Therefore the area of the fame is 42

Please help please show steps

Please help please show steps

Answers

Answer: D

Step-by-step explanation: it’s going down by 4 in the pattern

ill give a
brainliest

ill give a brainliest

Answers

9/20 and 0.45 hope this helps

ASAP PLS I NEED IT AND TY

ASAP PLS I NEED IT AND TY

Answers

Dilations and Scale Factors

When we're solving with scale factors, we either divide or multiply.

If the shape becomes larger, we multiply to get the new length.

If the shape becomes smaller, we divide to get the new length.

Solving the Question

We're given:

Original side length is 2.5 unitsScale factor = 6

Because the shape becomes larger, we have to multiply the original side length by the scale factor, 6, to get the new side length.

2.5 x 6 = 15

Therefore, the missing side length is 15 units.

Answer

15 units

Answer:

6

Step-by-step explanation:

Bjorn is making aush, and he does not have enough of all the ingredients. He decides to make 5/6 of a whole recipe, which means he uses 1 1/4 L of water.
How much water is in a whole recipe?
____?

Answers

Answer:

1\(\frac{1}{2}\)

If Bjorn used 5/6 of the whole recipe to make 1 1/4 L of water, we can find out how much water is in the whole recipe by using a proportion:

5/6 of the whole recipe = 1 1/4 L of water
1 whole recipe = (1 1/4 L of water) / (5/6)
To divide a fraction by another fraction, we can multiply by the reciprocal of the divisor. Therefore, we can simplify the above expression as follows:

1 whole recipe = (1 1/4 L of water) * (6/5)
Multiplying 1 1/4 L by 6/5, we get:

1 whole recipe = (5/4 L) * (6/5) = 30/20 L = 1 1/2 L
Therefore, a whole recipe of aush requires 1 1/2 L of water.

Answer: 1 1/2 L

what is the value of x in the figure

what is the value of x in the figure

Answers

90 - 63 = 27

Answer: 27

please help me on this :DD

please help me on this :DD

Answers

So all you do is the first number goes on the bottom and the second number on the coordinates goes on the top.

So if you had 5,4 you would move it over to 5 on the bottom and 4 on the top. It’s actually super easy!

Answer:

parallelogram

Step-by-step explanation:

As you can see in the pic the shape is a parallelogram.

:)

please help me on this :DD

if there are 28 centimeters and 2 centimeters = 3 meters, how many meters do you have

Answers

Answer:

42 meters

Step-by-step explanation:

28/2 = 14, 3*14 = 42

Which of these is the best estimate for ​275% of 40 ​?
greater than 0 but less than 1
greater than 1 but less than 2
greater than 2 but less than 3
greater than 3
Use pencil and paper. Explain the reasoning behind your choice.
Question content area bottom
Part 1
​275% of 40 is :

Answers

Answer: 110

Step-by-step explanation: Write 275% as

275

100

Since, finding the fraction of a number is same as multiplying the fraction with the number, we have

275

100

of 40 =

275

100

× 40

Therefore, the answer is 110

If you are using a calculator, simply enter 275÷100×40 which will give you 110 as the answer.

275 of 40 = 110.


275/100 x 40/1 = 11,000/100.

11,000/100 = 110.

Is this right? I chose 15.

Is this right? I chose 15.

Answers

Answer:

Correct, it is 15

Step-by-step explanation:

Because 3 turns into 9, you also want to multiply the other by 3, so you’d do 5x3 to get 15

Answer:yes you are correct. The answer is 15

Step-by-step explanation:

You would have to do 9/3=x/5. If you simplify that it would be 3x=45. If you simply further, you would get x=15 so yes you are correct.

A group of friends was working on a student film. They spent $650 on equipment, which was 65% of their total budget. What was the total budget for their student film?

Answers

Answer:

1,072.5

work to prove:

650 x .65 = 422.5

650 + 422.5 = 1,072.5

1,072.5
650x.65=422.5
650+422.5=1,072.5

Which list orders the numbers from least to greatest?

Negative 2.4, negative 1.5, negative 2 and one-fourth, negative 3, negative 1 and one-eighth

A number line going from negative 4 to positive 4.
Negative 1 and one-eighth, negative 1.5, negative 2 and one-fourth, negative 2.4, negative 3
Negative 3, negative 2.4, negative 2 and one-fourth, negative 1.5, negative 1 and one-eighth
Negative 3, negative 2 and one-fourth, negative 2.4, negative 1 and one-eighth, negative 1.5
Negative 1.5, negative 1 and one-eighth, negative 2.4, negative 2 and one-fourth, negative 3

Answers

Negative 3, negative 2.4, negative 1.5, negative 2 and one-fourth, negative 1 and one-eighth


Hope my answer helps you✌️

Negative 3, negative 2 and one-fourth, negative 2.4, negative 1 and one-eighth, negative 1.5 is the list that orders the numbers from least to greatest.

Greg invests $500 in a savings account that earns 4% simple interest annually. If he does not make any additional deposits or withdrawals, how much money will be in the savings account after 3 years?

Answers

Answer:

562.430

Step-by-step explanation:

Using a directrix of y = −2 and a focus of (2, 6), what quadratic function is created?
here are the answers given
\/
f(x) = −one eighth (x − 2)2 − 2
f(x) = one sixteenth (x − 2)2 + 2
f(x) = one eighth (x − 2)2 − 2
f(x) = −one sixteenth (x + 2)2 − 2

Answers

Answer:

f(x)=1/16(x-2)^2+2

Step-by-step explanation:

The Equation can be written like this:

f(x) = 1/(4p)(x -h)^2 +(k-p)

where (h, k) is the focus, and p is half the distance between focus and directrix. Here, (h, k) = (2, 6) and p=(6-(-2))/2 = 4. So the equation is ...

 f(x) = 1/16(x -2)^2 +2

I need help for my question please

Find the exact solution of x.

4x3 = 500
a. 3√5
b. ±5
c. -5
d. 5

Answers

A because I do not know what the problem is

Answer:

Step-by-step explanation: hope that helps

Find the exact solution of x.4x3 = 500a. 35b. 5c. -5d. 5

Please help me with this question

Please help me with this question

Answers

Answer:

56 and 7 its going by 5

Step-by-step explanation:

it is what it is yes ma’am

Arnold is testing a new train locomotive on circular rail track with a radius of 0.9 kilometers. How many times around the track does Arnold need to run the train to cover a distance of at least 50 kilometers?

Answers

Answer:

At least 9 times

Step-by-step explanation:

switch radius to circumference

0.9 —> 5.65487

Divide 50 by circumference

50/5.65487

Answer:

8.84193624257 times

So at least 9 times

Answer:

But what did i telly you

Step-by-step explanation:

anyone know this need asap

anyone know this need asap

Answers

Answer: y=x-20

Step-by-step explanation:

(90,70) will be x1,y2. (30,10) will be x1,y1. Put these values into the slope formula, which is y2-y1/x2-x1. 70-10/90-30. 60/60=1. The slope is 1. Now to find the slope-intercept equation, use point slope form which is y-y1=m(x-x1). y-10=1(x-30). Distribute the 1 to the terms in the parenthesis. y-10=x-30. Add 10 to both sides to eliminate 10. y-10+10=x-30+10. y=x-20.

person up top is correct

A container has a capacity of 3 L. It contains 1L of water.
How much more water is needed to fill the container completely?

Answers

Answer:

2L

Step-by-step explanation:

3-1 lol

Consider the two functions shown here. Which function has the greater rate of change? Explain your answer. Responses A Function 1, because its rate of change is ½ .Function 1, because its rate of change is ½ . B Function 1, because its rate of change is 2.Function 1, because its rate of change is 2. C Function 2, because its rate of change is ½.Function 2, because its rate of change is ½. D Function 2, because its rate of change is 7.

Consider the two functions shown here. Which function has the greater rate of change? Explain your answer.

Answers

Answer:

Function 1 has the greater rate of change because it is 2.  Function 2's rate is 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

The rate of change of a function is its slope, which is the ratio of the change in the y-coordinate to the change in the x-coordinate. The slope is also known as the "rise over run" or "change in y over change in x".From the given information, the first function is y=x+2 and the second function is y=7x-2.The rate of change of the first function is 1, because the y-coordinate changes by 1 unit for every 1 unit change in the x-coordinate. The rate of change of the second function is 7, because the y-coordinate changes by 7 units for every 1 unit change in the x-coordinate.Therefore the correct answer is D) Function 2, because its rate of change is 7.

HELP ASAP
Classify each pair of numbered angles as corresponding, alternate interior, alternate exterior, or none of these.



Drag and drop the choices into the boxes to correctly complete the table.

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
corresponding alternate interior alternate exterior none of these

HELP ASAPClassify each pair of numbered angles as corresponding, alternate interior, alternate exterior,
HELP ASAPClassify each pair of numbered angles as corresponding, alternate interior, alternate exterior,
HELP ASAPClassify each pair of numbered angles as corresponding, alternate interior, alternate exterior,
HELP ASAPClassify each pair of numbered angles as corresponding, alternate interior, alternate exterior,
HELP ASAPClassify each pair of numbered angles as corresponding, alternate interior, alternate exterior,

Answers

Answer:

1. Alternate Exterior
2. None of these
3. Corresponding
4. Alternate Interior
5. Corresponding

Step-by-step explanation:

Alternate Exterior angles are when the two angles are on opposite sides on the outside.
Corresponding angles are when two angles are on the same side and "correspond" meaning they both have the same amount of degrees.
Alternate Interior angles are when two angles are on opposite sides on the inside.

simplify 5^3 x 5^2
A.25^7 '=
B.5^12
C.5^7
D.5^9

Answers

Answer:

Answer: None of the choices.

Step-by-step explanation:

• Consindering the law of indices:

\( \hookrightarrow \: { \rm{ {a}^{n} \times {a}^{m} = {a}^{(n + m)} }} \\ \)

• Then, let's take;

a to be 5n to be 3m to be 2

\({ \rm{ {5}^{3} \times {5}^{2} = {5}^{(3 + 2)} }} \\ \\ = { \rm{ {5}^{5} }}\)

Answer:C

Step-by-step explanation:

I belive

1 point

The equation of the line of best fit relating age (in years, x) and the median height (in cm, y) of boys is given.

y = 6.5x + 75.5y=6.5x+75.5
Predict the median height of boys age 13.



123 cm

140 cm

160 cm

82 cm

Answers

Answer:

140cm

Step-by-step explanation:

140 is the right answer

Type a digit that makes this statement true.
153,80(number here) is divisible by 5.

Answers

Answer:

5Hope it helps!

Step-by-step explanation:

153805 is divisible by 5

The answer would be 5!
I hope this help!

Please help and you get a cake

Please help and you get a cake

Answers

Answer:

Mean = 33.7

Median = 34.5

Mode = 34

Range = 33

After adding 26....


mean decreases by 0.7

median decreases by 0.5

mode is 34

range is 33

Step-by-step explanation:

mean = sum of all the data values/number of data values

= (18 + 19 + 20  + 34 + 34 + 35 + 37 + 42 + 47 + 51)/10
= 337/10
= 33.7

To find median arrange the values in increasing order, find the mid value

If the number of data points is even, find the average of the mid 2 data values

Arranging data values we get:
18, 19, 20, 34, 34, 35, 37, 42, 47, 51

Since there are 10 data values, take the average of the middle two:
(34 + 35)/2 = 34.5

The mode is the value that occurs most often. We see that there are two instances of 34 whereas the other values appear only once

Mode = 34

The range is highest - lowest = 51 - 18 = 33

After we add 26, we get the following data set arranged

18, 19, 20, 26, 34, 34, 35, 37, 42, 47, 51

we can calculate the stats using the same technique as above

We get the following values

mean = )(18 + 19 + 20 + 26 + 34 + 34 + 35 + 37 + 42 + 47 + 51)/11
= 33  

median = 34

mode = 34

range = 51-18 = 33

To find the decrease in mean and median subtract from the first set of values

im pretty sure the answer is 56 because i said so

you have to do all of the questions and add the answers together

Answers

Answer: Where is the question?

Step-by-step explanation:

I'm sorry, I'm not sure what you mean. Could you please clarify which questions you are referring to and what you would like me to add together?

Please Help ASAP!!!
What is the correct expanded form and value of (One-fifth) Superscript 4?
One-fifth + one-fifth + one-fifth + one-fifth = StartFraction 4 Over 5 EndFraction
One-fifth times one-fifth times one-fifth times one-fifth = StartFraction 1 Over 625 EndFraction
StartFraction 1 + 1 + 1 + 1 Over 5 times 4 EndFraction = StartFraction 4 Over 20 EndFraction
One-fifth times 4 = StartFraction 4 Over 5 EndFraction

Answers

Answer:

One-fifth times one-fifth times one-fifth times one-fifth = StartFraction 1 Over 625 EndFraction

Step-by-step explanation:

1/5^4 = 1/5 * 1/5 * 1/5 *1/5 = 1/625

The expanded form of (One-fifth)⁴ is "StartFraction 1 Over 5 EndFraction times StartFraction 1 Over 5 EndFraction times StartFraction 1 Over 5 EndFraction times StartFraction 1 Over 5 EndFraction," and its value is "StartFraction 1 Over 625 EndFraction."

              The expanded form of (One-fifth)⁴ can be derived by multiplying (1/5) four times. Each multiplication represents multiplying by one-fifth, resulting in "StartFraction 1 Over 5 EndFraction times StartFraction 1 Over 5 EndFraction times StartFraction 1 Over 5 EndFraction times StartFraction 1 Over 5 EndFraction." This can be further simplified as "StartFraction 1 Over 625 EndFraction" by multiplying the numerators and the denominators separately.

              In mathematical terms, when we raise one-fifth to the power of 4, we are essentially multiplying one-fifth by itself four times. Thus, (One-fifth)⁴ is equal to "StartFraction 1 Over 5 EndFraction times StartFraction 1 Over 5 EndFraction times StartFraction 1 Over 5 EndFraction times StartFraction 1 Over 5 EndFraction."

            Evaluating this expression yields the value "StartFraction 1 Over 625 EndFraction" since multiplying the numerators (1 * 1 * 1 * 1) and the denominators (5 * 5 * 5 * 5) results in 1 and 625, respectively.

           Mathematical representation:  \(\frac{1}{5}^4= \frac{1}{5} * \frac{1}{5} * \frac{1}{5} * \frac{1}{5}\)

To learn more about expanded form,

https://brainly.com/question/102887

Help pls. I'll mark as brainlist.

Help pls. I'll mark as brainlist.

Answers

Answer:1. height in feet and height in Inches

1 feet = 12 inches

So, it's proportional2. The number of cookies baked and the minutes in the ovenSo, it's not proportional3. One bread needs a fixed grams of flourSo, it's proportional4. Since s = vtSo, it's proportional5. One gallon of gasoline cost's a fixed prince.So, it's proportional

Note : We just need to judge whether it accords with "y = kx"

{Proportional relationship}

It is a consistent raise on the price for every number of gallons. For example, so it is proportional.
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