Eighteenth middle school participatory classroom ninth grade math tutorial case answers

Mathematical propositions are an important class of propositions, generally speaking, they refer to judgments in mathematics. It is generally divided into three forms, first, for two propositions, if the conditions and conclusions of one proposition are the conclusions and conditions of the other proposition, respectively, then the two propositions are called reciprocal propositions; Second, if the conditions and conclusions of a proposition are the negation of the conditions and the negation of the conclusion of another proposition, respectively, then these two propositions are called mutually negative propositions, one of which is called the original proposition, and the other is called the negative proposition of the original proposition; The third type of p>

Of course, it depends on what branch of mathematics you're in.

If it's in elementary math.

The similarity of triangles in geometry can be represented by .

i.e. triangle abc triangle a'b'c'

In higher mathematics, if the elementary transformation of linear algebra can be written as a b, in fact, for the nth order square matrix a and b, if there is an invertible matrix p, such that p (-1)ap=b

then A and B are similar, that is, A B

1. & means "and" in mathematics, which is equivalent to the English word and character & The earliest history can be traced back to the 1st century AD, and the earliest is a conjunctional of the Latin et (meaning and). The earliest & very similar.

The combination of E and T, with the development of printing technology, this symbol gradually formed its own style and broke away from its original shadow. In this character, the shadow of e can still be seen, but t has disappeared.

In mathematics, it generally represents the meaning of numbers, and in many places it means the meaning of numbers.

For example, the document record is represented by document number 1, number 2, etc. in the form of 2. There are 101 building representations, which means 1 building, 1 room, etc.

！In mathematics, it is a factorial notation. The factorial of a positive integer is the product of all positive integers that are less than or equal to that number, and the factorial of 0 is 1.

That is, n!=1×2×3×..n。The factorial can also be defined recursively: 0!=1，n!=(n-1)!×n。

The factorial can also be defined for the whole real number (except for negative integers), and its relation to the gamma function is:

n!The mass factor is broken down into, e.g., 6!=24×32×51。

Simplification generally refers to the process of simplifying complex formulas into simple formulas in science and engineering disciplines such as physics, chemistry, mathematics and so on.

Cycles are all about repeating themselves.

For example, f(0)=f(10) and in this way, every 10 added to the independent variable is still equal to them.

Periodic function. For the function y=f(x), if there is a constant t that is not zero, such that f(x+t)=f(x) holds when x takes every value in the defined domain, then the function y=f(x) is called the periodic function, and the non-zero constant t is called the period of the function.

!It means factorial, an arithmetic invented by Christian KRAMP (1760 1826) in 1808. Factorial is also a term in mathematics.

The method of calculating the factorial of this segment.

Factorial is multiplication from 1 times 2 times 3 times 4 all the way up to the required number. For example, if the required number is 4, then the factorial is 1 2 3 4, and the resulting product is 24, and 24 is the factorial of 4. For example, if the required number is 6, then the factorial is 1 2 3 ......6, the product obtained is 720, and 720 is the factorial of 6.

For example, if the required number is n, then the factorial is 1 2 3 ......n, let the product be x, and x is the factorial of n.

The representation of the factorial of this segment.

Any natural number greater than 1 n factorial representation: n!=1×2×3×……n or n!=n×(n-1)!

The factorial of 4 is 4*3*2*1=24

You're talking a bit general.

Triangles in plane geometry are similar to use this symbol.

The meaning of the cycle.

For example, f(0)=f(10) and in this way, every 10 added to the independent variable is still equal to them.

Periodic function. For the function y=f(x), if there is a constant t that is not zero, such that f(x+t)=f(x) holds when x takes every value in the defined domain, then the function y=f(x) is called the periodic function, and the non-zero constant t is called the period of the function.

* It doesn't mean much in mathematics, it's just an asterisk.

However, the multiplication sign is represented in computer programming and some application software.

For example, 4*5 means 4 5, and 4*5 cannot be represented in mathematics.

In mathematics, "meaningful" refers to compliance with a regulation, requirement, or restriction within the limits of the definition.

For example: (1) The denominator and divisor of fractions or fractions cannot be "0". If the denominator and divisor of a fraction or fraction are "0", it violates the rules of the fraction or fraction and is "meaningless"; Conversely, the denominator and divisor of fractions or fractions are either "0" or "meaningful";

2) In the range of real numbers, quadratic radicals require that the number of squares to be opened cannot be negative (i.e., it can only be non-negative numbers - positive numbers and 0s). If the square of the quadratic radical is negative, it violates the rule of the square of the quadratic radical within the range of real numbers, and it is "meaningless"; Conversely, the number of open squares of a quadratic radical formula is either negative, or it is in accordance with the regulations, that is, it is "meaningful".

The mathematical meaning of the ratio: the division of two numbers, also known as the ratio of these two numbers.

The ratio is a division formula consisting of a preceding term and a posting term, except that the " "division sign" is changed to ":" ratio sign), but the division equation represents an operation, and the ratio represents the relationship between two numbers. It is similar to the cut-off score for fractions.

It is generally denoted by Greek letters.

is the Greek alphabet, i.e. the capital form of , in mathematics.

Quadratic or direct product operation, similar in form to , is sometimes used to represent the value of pi Pi (pi) is the ratio of the circumference of a circle to its diameter, generally represented by Greek letters, and is a mathematical constant that is common in mathematics and physics.

Mathematics means the discriminant expression of the root.

The discriminant formula of roots is a formula for judging the number of real roots of an equation, which is widely used in solving problems, involving the value range of the solution coefficients, the number and distribution of the roots of the equation, etc. The discriminant formula for the root of the unary quadratic equation ax 2+bx+c=0(a≠0) is b 2-4ac, denoted by " " (pronounced "delta").

δ is discriminant, δ> 0, with two unequal real roots.

0, there are two equal real roots.

0, there is no real root.

The discriminant expression of the quadratic function, read him.

is a discriminant test when =0 has two equal real roots.

There is no real follow-up at 0.

At 0, there are two real roots that do not =.

mathematical"*"Yes: the meaning of multiplication, e.g. 3*4=3 times 4=12

mathematical"^"Yes: the meaning of power, e.g. 2 3 = 2 to the 3rd power = 8

Dear, please [adopt the answer], your adoption is the motivation for me to answer the question, thank you.

Division. Because there is no handwritten division in the keyboard.

If a and b are substituted into the calculation definition of "", then a b means a divided by b, which can also be called action b to divide a

Parallel meaning.

A type of positional relationship between two people.

Just a math fit.

Translated into Chinese.

It's parallelism.

It means "divide", and sometimes it is a few "fractions". But it can be classified as dividing by the meaning. Such as 1 5=

Or "one in five", but it mainly depends on what the problem itself needs it to do, whether it allows you to calculate or gives you a data to analyze someone else's problem.

It means "divide", and it can be used during the exam, but pay attention to the specification, for example, (1+2) (2+4) is not the same as 1+2 2+4.

When I went to high school, I rarely used " " to mean division.

It is generally expressed in the form of fractions

Generally, because the keyboard is inconvenient, this is used on the computer to represent the score line, that is, the division sign.

Try to write the score or form during the exam, it is not recommended to write it like this, otherwise it depends on the teacher's mood ......

No. ( ) is a printed version ofand a fraction of how to write.

The definition of mathematics is deeper than in the past! For example, the definition of ancient mathematics in China, number, stays in counting. Reaction in Heluo book!

Later numbers are divided into inner numbers and outer numbers. Now mathematics refers to outer numbers. The Pythagorean theorem, one of which is the relationship between the number and the shape!

Mathematics is the study of concepts such as quantity, structure, change, and spatial models. Through the use of abstraction and logical reasoning, it is produced from counting, computation, measuring, and observation of the shape and motion of objects. Mathematicians expand these concepts, in order to formulate new conjectures as well as designate from suitability.

Mathematics is the study of quantitative relations and spatial forms in the real world, and in short, the study of numbers and shapes.

Mathematics (or maths) is a discipline that studies concepts such as quantity, structure, change, space, and information, and belongs to a kind of formal science from a certain point of view.

Mathematics also plays an irreplaceable role in the historical development and social life of mankind, and is also an indispensable basic tool for learning and researching modern science and technology.

Hello! Mathematics (mathematics), abbreviated as maths (British English) or math (American English), is an ancient discipline that studies concepts such as quantity, structure, change, space and information, and belongs to a kind of formal science from a certain point of view It is divided into advanced mathematics and elementary mathematics, and there are also complex sets, functions, algebra, and geometry in high school called intermediate mathematics It plays an irreplaceable role in the historical development of human beings and social life. It is also an indispensable basic tool for learning and researching modern science and technology.

!!In mathematics it is denoted a double factorial product.

Double factorial is a mathematical concept that uses n!!Denote. The double factorial of a positive integer represents the product of all positive integers that do not exceed this positive integer and have the same parity as it.

The double factorial of the first 6 positive integers is: 1!!=1，2!!

15 and 6!!=48。As.

"*" means multiplication sign in mathematics.

Sometimes the computer doesn't have the symbol "x", so "*" is used instead of the multiplication sign, so you see "*" in mathematics", which means multiplication.

"In your question here is a definition of an operator notation, depending on your formulation there are two possible scenarios:

1) p*q=(p+q) 2 indicates the provision"*"The operation is to find the average of the two numbers p and q;

2) p*q=(p 2)+q"*"The operation is the sum of half of p and q.

Occasionally. You can give the formulas that appear.

One of the more common is skip factorial, or double factorial. English double factorial.

For example, ordinary factorials are 5! = 1*2*3*4*!!= 1*3*5。It's to jump a number and multiply a number. Skip factorial is often used in series theory.

For example, ordinary factorials are 5! = 1*2*3*4*!!= 1*3*5。It's to jump a number and multiply a number.

is a double factorial and is defined as follows:

2n+1)!!=1*3*…*2n+1)

2n)!!=2*4*…*2n)

In mathematics, "meaningful" refers to compliance with a regulation, requirement, or restriction within the limits of the definition.

For example: (1) The denominator and divisor of fractions or fractions cannot be "0". If the denominator and divisor of a fraction or fraction are "0", it violates the rules of the fraction or fraction and is "meaningless"; Conversely, the denominator and divisor of fractions or fractions are either "0" or "meaningful";

2) In the range of real numbers, quadratic radicals require that the number of squares to be opened cannot be negative (i.e., it can only be non-negative numbers - positive numbers and 0s). If the square of the quadratic radical is negative, it violates the rule of the square of the quadratic radical within the range of real numbers, and it is "meaningless"; Conversely, the number of open squares of a quadratic radical formula is either negative, or it is in accordance with the regulations, that is, it is "meaningful".