Define an operation of set a and B: a * b = {x | x = X1 + X2, where x1 ∈ a, X2 ∈ B}, if a = {1, 2, 3}, B = {1, 2}, then the sum of all elements in a * B is______ ．

Define an operation of set a and B: a * b = {x | x = X1 + X2, where x1 ∈ a, X2 ∈ B}, if a = {1, 2, 3}, B = {1, 2}, then the sum of all elements in a * B is______ ．

According to the definition, a * b = {2, 3, 4, 5}, so the sum of all the elements in a * B is 14

F (x) is an odd function, G (x) is an even function, f (x) × g (x) = x ^ 2 + 2x-3 find the expression of F (x), G (x)
What the teacher copied is dot product. Maybe I didn't copy it clearly. I made it all zero and didn't feel like it, so let's ask
The confirmation question is wrong
How about f (x) - G (x) = x ^ 2 + 2x-3?

f(-x)-g(-x)=-f(x)-g(x)=x^2-2x-3
So far, I should know how to solve the equations together with the original formula F (x) - G (x) = x ^ 2 + 2x-3

Please read the following process carefully: calculation: 1 + 3 + 3 ^ 2 + 3 ^ 3 + +3^99
Let m = 1 + 3 + 3 ^ 2 + 3 ^ 3 + +3^99 （1）
(1) Multiply by 3:3m = 3 + 3 ^ 2 + 3 ^ 3 + +3^100 （2）
（2）-（1）：2M=3^100-1 ∴M=(3^100-1)/2
Please follow the above method and calculate: 1 + 2 + 2 ^ 2 + 2 ^ 3 + +2^2014

Let s = 1 + 2 + 2 ^ 2 + 2 ^ 4 + +2^2010+2^20122^2*s=2^2+2^3+2^4+2^6+… +2^2012+2^20144s=2^2+2^3+2^4+2^6+… +2 ^ 2012 + 2 ^ 20144s-s = 2 ^ 3 + 2 ^ 2014-1-23s = 2 ^ 2014 + 8-33s = 2 ^ 2014 + 5S = 2 ^ 2014 / 3 + 5 / 3, i.e. 1 + 2 + 2 ^ 2 + 2 ^ 4 + +2^2010+2^2012=2^2014/...

The solution method of 2,1,5,11111 sequence

Solution: multiply the first two numbers, multiply by 2 and add 1 to get the next number
a(1)=2
a(2)=1
[a(i)xa(i+1)]x2+1 = a(i+2) , i=1,2,3,4,.
Examples:
(2×1)×2+1=5
(1×5)×2+1=11
(5×11)×2+1=111
(11×111)×2+1=2443

How many ml is the third power of 75 cm

75 cm to the third power = 75 ml

If you want to use a linear equation of one variable, it's a linear equation of one variable!
In a women's chess competition, Xie Jun, China's female chess master, failed to lose one set after the 11th set of defending the title, thus winning the title successfully and winning the championship. The score is one point more than three times that of Russia's joselaine. How many points are there for each of them?

Because there is no deduction for losing, the total score of China and Russia is 1 point in each game, no matter who wins or loses, so the total score of China and Russia in 11 games is 11 points. If Russia gets x points, then China's score is 3x + 1. If x = 2.5, Russia's score is 2.5, and China's score is 8.5

A series of numbers 1, 1, 2, 3, 5, 8, 13, 21, etc., starting from the third term, the sum of each term, the remainder of the 2011 term of this series divided by 25 is
And how to calculate, not into algorithms

The first 110 items are: 1, 1, 2, 3, 5, 8, 13, 21, 9, 5, 14, 19, 8, 2, 10, 12, 22, 9, 6, 15, 21, 11, 7, 18, 0, 18, 18, 11, 4, 15, 19, 9, 3, 12, 2

8 cubic decimeter 56 cubic decimeter = () cubic meter = () cubic decimeter?

8 cubic meters 56 cubic decimeters = (8.056) cubic meters = (8056) cubic decimeters

In the early July test, I urgently need to review and sort out the knowledge points of the seventh grade English Volume II of the people's education press. Friends, friends' relatives, relatives and friends can help me~
The more detailed the information, the better

I. review of teaching materials
Knowledge review
1 . Could you … You / you The positive answer is OK / all right! / certainly! / of course. The negative answer is sorry, I / we can't
—Could you lend me your dictionary ?
—Of course .
2. One can be used not only as the meaning of "one" in the cardinal vocabulary, but also as a pronoun to replace "one" in the countable nouns mentioned above or to refer to "anyone"
One and two is three
I don't have pens. Please give one to me
3) one must love one's country
That's OK. / that's all right. / not at all
—Thank you very much .
— You’re welcome .
4. The Adverb "too" usually modifies the adjective or adverb (put in front of it) when it is used as "Tai"; when it is used as "Ye", it is usually at the end of the sentence (separated by commas)
1) Your bag is too big
2) Your bag is big, too
5. When there are definite articles, demonstrative pronouns and possessive pronouns before nouns, all is used to precede these determiners. For example: all my books
6. The other usually means "the other (those)" in the two (parts), while the other without definite article is often used to refer to "the other"
The twins are English. One is Lucy, the other is Lily
I have many friends. Some are teachers, others are police men
7. Socks, shoes, trousers, glasses and other nouns used to denote the whole of two parts are usually plural. If they refer to "a pair of", they should be modified by the phrase a pair of
A pair of socks, a pair of glasses, etc
A pair of shoes is under the bed .
8. What's wrong with The interrogative word "what" here can not be influenced by the Chinese language
What's wrong with your kite?
It's broken
9. When it is used as a transitive verb, it is customary to take only the person as the object after it, which means "make "Worry" is used as an intransitive verb and can be followed by a person or thing as an object, but the preposition about must be used, which means "worry..." . example:
These apples worry me
Don't worry about my lessons
10. The material nouns such as tea, milk, bread, water, meat and rice are all uncountable nouns. These nouns have no plural form. They can not be directly modified by indefinite articles, cardinal numbers and demonstrative pronouns. If they indicate their quantity, they must be preceded by the phrase "measure noun + of". For example: a bottle of orange, two cups of tea
Two cups of tea = two teas
11 . It’s time … When a sentence pattern is followed by a noun or pronoun, use for (preposition), and the verb must be followed by to (infinitive). The subject it here can't be replaced by another pronoun, and the article is not used before time
It's time for class
It's time to play games
It is time for sb to do
12. Something to eat (drink) means "something to eat (drink)". To eat (drink) is an infinitive used as a postpositive attributive to modify the infinitive pronoun something
We have something to eat now
II. Appreciation of allusions
Communicative competence and test guidelines
(1) Choose the best answer according to the situation
1 . — ______ ? — It’s eight thirty .
A . How old is your sister B . What class are you in
C . What’s the time , please D . What number is your car
2. When you want to ask someone something, you should first say:______ .
A . Excuse me B . I’m sorry C . Hello D . OK
(2) Complete the dialogue according to the situation
Kate : Hi , Jim . ( 1 ) ?
Jim : Fine , thank you . And you ?
Kate : I’m fine , too . ( 2 ) ?
Jim : Very well , thanks
Kate : ( 3 ) ?
Jim : Class Four .
Kate : ( 4 ) ?
Jim : Room Five .
Kate : Oh , I see .
A . Which is here classroom B . How is your sister
C . How are you today D . What class is she in
In order to solve the problem of "situational communication", we should first know what kind of communication project the situation is; secondly, we should know what to say in which situation and how to express our thoughts; and we should also know the relationship between the context and the situation
In the first question, we must first identify the meaning of a, B, C and D, and then look at the expression form of the answer sentence. Then we can judge that it is C according to the common sense of communication, One to one correspondence with the dialogue
If there are pictures in the test, you should be good at using the information in the pictures to help answer the questions. You should be good at understanding the "secret" from the situation
Communicative English speaking practice
Greetings?
1 . “How are you ? ”“______” ?
A . How do you do ? B . How are you ? ?
C . I‘m fine , thank you . D . What do you do ?
Introduction?
2 . — Li Ping , ______ . ?
— Nice to meet you , Zhang Hong . ?
A . that’s my friend , Zhang Hong B . this is Zhang Hong?
C . she is Zhang Hong D . I introduce Zhang Hong to you
3 . “Nice to meet you . ”“_______” ?
A . Is that so ? B . I‘ve got a cough . ?
C . Yes , do please . D . Nice to meet you , goo .
Making phone calls?
4 . “Hello , 5847552 . ”“Hi ! _____” ?
A . Are you Linda ? B . Who are you ? ?
C . I am David . D . Is that Linda speaking ?
5 . — This is John speaking . Who is that ? ?
— _____ ?
A . This is Bill . B . I am Bill . ?
C . You are Bill . D . Where is bill ?
6 . — Could I speak to headmaster ? ?
— ______ please . ?
A . Hold on for a moment B . Speak loudly?
C . He is at work D . What’s wrong ?
7 . A : Hello ! Could I speak to Miss Grey , please ? ?
B : ______ ?
A . I‘m Miss Grey . B . Yes , you could . ?
C . SPeaking . D . Who are you ?
Answer and analysis:?
1. C. "how are you?" is a common polite greeting between acquaintances. The answers are "fine, thank you." or "very well, thank you." the greetings are "good morning / afternoon / evening. Hello / hi." and so on?
2. B. to introduce someone, the common sentence pattern is "this is...". To introduce yourself, use "my name is..." or "I'm...".? 3. D. "nice to meet you." it is usually used after two people meet for the first time and are introduced to each other. The answers are "nice to meet you, too...", "how do you do?" and "glad to meet you." they are also introductory expressions?
4. D. to ask who the other party is, you should say "who is that (speaking)"?
5. A. to say "I am..." "This is..."?
When answering the phone, if you want to ask the other party not to hang up or wait, you should say "hold on (for a moment), please..."?
7. C. when answering the phone, if you are the person you are looking for, say "speaking." if the person you are looking for is not available, say "he / she isn't here right now. Can I take a message for you?"?
III. grammatical Perspective
Uncountable names