There are 12 teachers in the first grade of a middle school. There are 8 teachers who teach mathematics, 6 teachers who teach physics, 5 teachers who teach chemistry, 5 teachers who teach both mathematics and physics, 4 teachers who teach both mathematics and chemistry, 3 teachers who teach both physics and chemistry, and 3 teachers who teach all these three courses. How many teachers are there other than mathematics and chemistry? How many teachers teach only one course? How many teachers teach just two courses

There are 12 teachers in the first grade of a middle school. There are 8 teachers who teach mathematics, 6 teachers who teach physics, 5 teachers who teach chemistry, 5 teachers who teach both mathematics and physics, 4 teachers who teach both mathematics and chemistry, 3 teachers who teach both physics and chemistry, and 3 teachers who teach all these three courses. How many teachers are there other than mathematics and chemistry? How many teachers teach only one course? How many teachers teach just two courses

As shown in the figure, & nbsp; from the inside to the outside. The color order is & nbsp; red, green, blue, black and red: first of all, the middle (Trinity.. spoof it) is & nbsp; 3 green: 3 teach both physics and chemistry, minus the red, the remaining 0 teach only chemical physics, 3-3 = 04 teach both mathematics and chemistry, minus the red three

English blessings for teachers' Day
Have a beginning, such as dear teacher Xu

Dear teacher xu your lessons are still the one that helps me.
Your words are still fresh and warm.
You’ve swayed my life so deeply.
You’re still my best teacher.
Far across the miles,sending you wishes of love
and peace on Teacher’s Day.
Dear teacher Xu, I still benefit a lot from your teaching. Your words are still in my ears and deeply affect me. You are my most beloved teacher. I wish you peace and happiness on teacher's day

Teacher's Day blessing how to write, to the language, English three teachers!

Teachers and students love each other like a vast river
Second half

1. Fill the nine numbers - 8 - 6 - 4 - 20 2 4 6 8 into the nine squares, so that the three numbers in each row, column and diagonal angle add up to 0
2. When m is in what range, the equation (M + 2) X-2 = 1-m (4-x) about X is as follows:
(3) solutions not greater than 2?
The speed of the current is 2km / h, and the speed of the motorboat in still water is 18km / h. In order to make the tour time less than 3 hours, how many kilometers can the tourists walk out at most
4 if the solution set of X ＞ (a third) - 1 is x ＞ 0, then a =?
5 given that the solution of equation AX + 12 = 0 is x = 3, then the solution set of inequality (a + 2) x < - 8 is ()
The largest integer in the value of X which makes inequality X-5 ＞ 4x-1 hold is ()
If the solution of the equation 4x-a = 3 about X is negative, then the value range of a is ()
8. Give a basket of oranges to several children. If each child has four oranges, there will be four left. If each child has six oranges, the last child will get less than three oranges. How many children can be deduced from the above conditions? (formula, process)
9, 1 / 2, 1 / 3, 1 / 4, 1 / 5 ··, 1 / 90, 1 / 91, can you pick out 10 of them and add the sign to make their sum equal to 1?
10 100 pieces of sugar are packed in four plates. Add 4 to the number in the first plate, subtract 4 from the number in the second plate, multiply 4 by the number in the third plate, and divide 4 by the number in the fourth plate. Now the number of sugar in each plate is the same. How many pieces of sugar are there in each plate? (formula, process)

1. 2 - 8 640 - 4 - 6 8 - 2 reduce the equation (M + 2) x - 2 = 1 - M (4 - x), and get 2x = 3 - 4 m, x = (3 - 4 m) / 2 (1) x is a positive solution, that is, X > 0, then (3 - 4 m) / 2 > 0, M0, so a / 3 - 1 > 0, then a > 3

Sequence 1, - 3,5, - 7,9, - 11 The general term formula of

If we don't look at the sign, we can easily see that the general term an = 2N-1
But there is a minus sign in front of every even number item,
So we can use (- 1) to represent this minus sign,
So the general term is an = (- 1) ^ n-1 × (2n-1)

1. Sequence 3, 5, 7, 9 What is a general term formula of?

an=a1+(n-1)d
Then an = 3 + 2 (n-1)
That is, an = 2n + 1

General term formula of sequence 3, - 5,7, - 9,11

General term formula: an = (- 1) ^ (n + 1) × (2n + 1)

From the first four terms of the sequence: 32, 1, 58, 38 The general formula an is concluded=______ ．

∵ 32 = 128, 1 = 88 the first four terms of the sequence are equivalent to: 128, 88, 58, 38 Let A1 = 12, A2 = 8, A3 = 5, A4 = 3 Then a2-a1 = 8-12 = - 4, a3-a2 = 5-8 = - 3, a4-a3 = 3-5 = - 2 An-an-1 = n-1-5 = n-6, both sides are added at the same time to get: an-a1 = − 4 + n − 62 × (n − 1) = (n − 10) (n − 1) 2, the nth molecule is an = (n − 10) (n − 1) 2 + 1, that is, an = (n − 10) (n − 1) 2 + 18 = (n − 10) (n − 1) + 1616, so the answer is: (n − 10) (n − 1) + 1616

Sequence - 1, 85, - 157249 A general formula of is______ ．

Sequence - 1, 85, - 157249 It can be written as − 33, 85, - 157249 Furthermore, it can be written as − (1 + 1) 2 − 12 × 1 + 1, (2 + 1) 2 − 12 × 2 + 1, − (3 + 1) 2 − 12 × 3 + 1, (4 + 1) 2 − 12 × 4 + 1 So a general formula is: an = (− 1) n (n + 1) 2 − 12n + 1, so the answer is: an = (− 1) n (n + 1) 2 − 12n + 1

Sequence 1 / 3, - 1 / 8,1 / 15, - 1 / 24 The general term formula an =?

Observation
We can get 3 = 1 & # 178; + 2 × 18 = 2 & # 178; + 2 × 215 = 3 & # 178; + 2 × 324 = 4 & # 178; + 2 × 4
So an = 1 / (- 1) n + 1 times (n & # 178; + 2n)