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Reika [66]
1 year ago
9

Use mathematical induction to prove that, for n ≥ 1, n³ – n is divisible by 3.

Mathematics
1 answer:
ICE Princess25 [194]1 year ago
5 0

Answer:

Step-by-step explanation:

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Y=10x+100 what is the independent and dependent variable in this equation
valentina_108 [34]

Answer:

In this equation X is independent variable while Y is dependent variable.

Step-by-step explanation:

Equation:

Y=10x+100

Independent variable in math:

A variable in an equation that may have its value freely chosen without considering values of any other variable.

Dependent variable in math:

A dependent variable is a variable in an expression, equation, or function that has its value determined by the choice of value of other variable.

<u>According to above definitions Y is dependent of x. As we changes the value of x the value of Y changes.</u>

For example if x = 1, Y will be 110.

And if x = 10, Y will be 200.


6 0
3 years ago
What is the value of x = ?
jeka57 [31]

I think it is 174. I could be wrong.

6 0
3 years ago
What are decimals?<br> ??????????????????
lora16 [44]

Answer:

The decimal numeral system is the standard system for denoting integer and non-integer numbers.

Step-by-step explanation:

Its Just There...

3 0
3 years ago
Lee las situaciones y realiza lo siguiente con cada una:
Julli [10]

Answer:

Part 1) see the explanation

Part 2) see the explanation

Part 3) see the explanation

Part 4) see the explanation

Step-by-step explanation:

<u><em>The question in English is</em></u>

Read the situations and do the following with each one:

Write down the magnitudes involved

Write which magnitude is the independent variable and which is the dependent variable

It represents the function that describes the situation

SITUATIONS:

1) A machine prints 840 pages every 30 minutes.

2) An elevator takes 6 seconds to go up two floors.

3) A company rents a car at S/ 480 for 12 days.

4) 10 kilograms of papaya cost S/ 35

Part 1) we have

A machine prints 840 pages every 30 minutes

Let

x ----> the time in minutes (represent the variable independent or input value)

y ---> the number of pages that the machine print (represent the dependent variable or output value)

Remember that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form k=\frac{y}{x} or y=kx

In this problem

we have a a proportional variation

so

The value of the constant of proportionality is equal to

 k=\frac{y}{x}

we have

y=840\ pages\\x=30\ minutes

substitute

 k=\frac{840}{30}=28\ pages/minute

The linear equation is

y=28x

Part 2) we have

An elevator takes 6 seconds to go up two floors.

Let

x ----> the time in seconds (represent the variable independent or input value)

y ---> the number of floors (represent the dependent variable or output value)

Remember that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form k=\frac{y}{x} or y=kx

In this problem

we have a a proportional variation

so

The value of the constant of proportionality is equal to

 k=\frac{y}{x}

we have

y=2\ floors\\x=6\ seconds

substitute

 k=\frac{2}{6}=\frac{1}{3}\ floors/second

The linear equation is

y=\frac{1}{3}x

Part 3) we have

A company rents a car at S/ 480 for 12 days.

Let

x ----> the number of days (represent the variable independent or input value)

y ---> the cost of rent a car (represent the dependent variable or output value)

Remember that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form k=\frac{y}{x} or y=kx

In this problem

we have a a proportional variation

so

The value of the constant of proportionality is equal to

 k=\frac{y}{x}

we have

y=\$480\\x=12\ days

substitute

 k=\frac{480}{12}=\$40\ per\ day

The linear equation is

y=40x

Part 4) we have

10 kilograms of papaya cost S/ 35

Let

x ----> the kilograms of papaya (represent the variable independent or input value)

y ---> the cost  (represent the dependent variable or output value)

Remember that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form k=\frac{y}{x} or y=kx

In this problem

we have a a proportional variation

so

The value of the constant of proportionality is equal to

 k=\frac{y}{x}

we have

y=\$35\\x=10\ kg

substitute

 k=\frac{35}{10}=\$3.5\ per\ kg

The linear equation is

y=3.5x

6 0
2 years ago
Shane, Cheryl, and Isaac went to the store to buy school supplies. Shane bought 4 pens, 3 folders, and 2 notebooks for a total o
vladimir1956 [14]

Answer: 3.00

Step-by-step explanation:

8 0
2 years ago
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