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Evgesh-ka [11]
1 year ago
7

What are the perfect squares

Mathematics
1 answer:
V125BC [204]1 year ago
3 0

Answer: A perfect square is a positive integer that is obtained by multiplying an integer by itself.

They are 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900 and 961

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PLEASE HELP I WILL PICK BRAINLIEST
Mnenie [13.5K]

Answer:

A more complex question has rarely been asked.

Principia Mathematica took nearly a thousand pages to prove that 1+1=2. It does meander a bit, but had they wanted to prove 1+1=2 alone, it could have done so in 500 pages.

Mathematically speaking, the definition of 1 is:

There exists a number such that when multiplied upon an element of a specified set, yields the element of the specified set.

It is also defined as:

1.0000000000000000000000…

.9999999999999999999999999…

as the set of all singletons.

a singleton is a set with exactly 1 element.

These 4 definitions work in tandem with one another.

For example:

1=1

Divide both sides by 3.

1/3=1/3

Rewrite.

1/3=.33333333333333333...

Multiply both sides by 3.

1=.9999999999999999999...

Similarly:

If    =.9999999999999999999...

10=9.99999999999999999...

10=9+.99999999999999...

10=9+

Simplify by subtracting x from both sides.

9=9

=1

.99999999999999999999...=1

As the set of all singletons, 1 is also THE element that represents the set of all single entities.

That is to say: if you have 7 erasers. What you really have is a set of 7 single entities. The definition of 7 becomes: 1 + 1 + 1 + 1 + 1 + 1 + 1; and not as is commonly believed as: 6 + 1.

There is an argument for 7 to be defined as 6 + 1, but this argument is a corollary of the Peano Axioms which in turn argues that there exists a set with absolutely nothing in it {} and a set with exactly something in it {x}. More on this later.

The Principia Mathematica uses Peano's (from the Peano Axioms mentioned earlier) work and notation to expertly slice through the many nuances pertaining to this question.

This is something we will not do; but hopefully, we will also be able to effectively demonstrate why 1 + 1 = 2 in less than 1000 pages.

We will assume these basic principles of number theory:

There exists a number such that when multiplied to an element of a specific set, yields that element of the specific set.

There exists a number such that when added to an element of a specific set, yields that element of the specific set.

If we again assume to have only two sets, a set that is empty: {} containing no elements, and a set that is not empty {x} containing an element. We realize that Consequently, we went from nothing {}, to something {x}. This means that {x} is the successor to {}, as the next step up from nothing, is something.

As such we now have two elements:

Nothing, {}, and something that comes after {}, this something is called the successor, and it is the Successor of nothing.

in written notation we have:

{} and { the Successor of nothing }

Rewritten:

{0, the thing that comes after 0}

Further reworded:

{0, Successor (0) }

Reduced further:

0,(0)

Where S(0) stands in place of ‘the successor’. Further, we know there are an infinite number of possible Natural numbers, and we get:

{0, Successor of 0, the successor of the successor of 0, the successor of the successor of the successor of 0,…}

Further reduced:

0,(0),((0)),(((0))),((((0)))),(((((0)))),…

Further explained:

We know that we had nothing, and added something to it, and got something:

Nothing + Something = Successor of nothing.

0+__=(0)

We also know that there is nothing closer to 0, than the thing that comes after 0.

0+(0)=(0)

This implies that S(0) is the smallest increment possible from natural number to next natural number.

As a consequence, we now have two discovered entities: Something, and Nothing.

Let’s give them names.

We have decided that

Nothing = 0 .

0 = Nothing.

S(0) is the something that comes after nothing.

We define a new symbol: 1, to be: 1 = S(0)

This is to say that 1 IS the symbol that succeeds 0;

We could have drawn any shape to define the number that succeeds 0; we chose to draw a 1.

0+(0)=(0)

0+1=(0)

0+1=1

0,1,((0)),(((0))),((((0)))),(((((0)))),…

We now have definitions for 0, and 1. What about a definition for the thing that comes after one? The successor of 1?

As we know S(0) is the smallest increment available, and we are interested in finding S(0)’s successor we investigate:

The successor to the successor of Nothing:

0+(0)=1;1+(0)=(1)

This reads:

The successor of the successor of nothing IS the successor of one

And now… we need a new symbol.

We define the

(1)=2

The successor of 1 IS 2.

Thus:

0+(0)=1;1+(0)=(1)=2

Simplify:

0+1=1;1+1=(1);(1)=2.

Further:

0+1=1;1+1=2;2=2.

1 has many different properties; but all of the properties and their resulting definitions have little to do with why 1 + 1 = 2. And that 1 + 1 = 2 is a byproduct of properties inherent to Natural numbers.

Step-by-step explanation:

6 0
3 years ago
(6x + 3) + (3 + x^4)
olganol [36]

The answer is: x^4+6x+6

3 0
3 years ago
Read 2 more answers
A student earned grades of​ B, B,​ A, C, and D. Those courses had these corresponding numbers of credit​ hours: 4,​ 5, 1,​ 5, 4.
antiseptic1488 [7]

Answer:

<h2> 1.69</h2>

Step-by-step explanation:

Let the five courses with their corresponding credit hours be represented as shown;

FST 201 = 4

FST 203 = 5

FST 112 = 1

FST 219 = 5

FST 223 = 4

If a student earned grades of​ B, B,​ A, C, and D respectively in those courses with the following grading system  A =​4, B =​3, C =​2, D =​1, and F =0, before we can get the student GPA, we need to know the total credit point for the five courses.

Credit point for each course = Number of credit hour * point for each grade

FST 201 = 4 * 4 = 16points (A)

FST 203 = 5 * 4 = 20points (A)

FST 112 = 1 * 4  = 4points (A)

FST 219 = 5 * 4 = 20points (A)

FST 223 = 4 * 4 = 16points (A)

Total credit point = 16+20+4+20+16 = 76points

Total credit point gotten by the student is calculated as thus;

FST 201 = 4 * 3 = 12points (B)

FST 203 = 5 * 3 = 15points (B)

FST 112 = 1 * 4  = 4points (A)

FST 219 = 5 * 2 = 10points (C)

FST 223 = 4 * 1 = 4points (D)

Total credit point gotten by the student = 45points.

student's Grade Point Average​ (GPA) = Total credit point/Total credit point gotten by the student = 76/45 = 1.69 (to 2dp)

5 0
3 years ago
Write x2 - 12x + 8 in vertex form.
Marysya12 [62]

Answer:

The answer to this is: y = (x - 6)² - 28

Step-by-step explanation:

The first step is to make sure the coefficient in front of x² is 1. If it isn't, just divide the whole equation by the coefficient. In this case, you don't need to do any division because you just have x²

Group the first two terms involving x² and x:

(x² - 12x) + 8

Now complete the square as follows:

a. Take the coefficient in front of x --> -12

b. Halve it --> -6

c. Square it --> (-6)² = 36

d. Add this and subtract it

(x² - 12x + 36 - 36) + 8

Take the negative number outside the parentheses:

(x² - 12x + 36) - 36 + 8

(x² - 12x + 36) - 28

The part in parentheses is a perfect square so rewrite it as such. If you need help refer back to step b.

(x - 6)(x - 6) - 28

(x - 6)² - 28

P.S. Vertex form is:

(x - h)² + k

In that form, the vertex is (h, k). In your case, the vertex of the parabola would be (6, -28).

Answer:

y = (x - 6)² - 28

6 0
3 years ago
In Ellen’s sixth grade class there are 14 boys and 11 girls write each ratio using numbers in two ways
r-ruslan [8.4K]

Answer:

h

Step-by-step explanation:

7 0
3 years ago
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