21 = multiplication of several prime numbers

21 = multiplication of several prime numbers

21=3×7

There are three primes whose least common multiple is 105______ And______ ．

105 = 3 × 5 × 7, so the three prime numbers are 3, 5 and 7 respectively

Association of composition after listening to music

With the melodious trumpet, this group of orchestral music began her colorful movement. The first is the soft violin. The beautiful notes seem to drift on the just melting river. Where they pass, the grass bursts out new life, and the willows pull out new branches. With the sunshine, the notes rise into the sky, and the darkness of winter becomes spring

Junior 1 mathematics (national standard Jiangsu version) exercises, will be into
1. For a city to carry out engineering transformation, it takes three months for engineering team a to complete this task alone, with a monthly cost of 120000 yuan; for engineering team B to complete this task alone, it takes six months, with a monthly cost of 50000 yuan
How many months will it take to complete the cooperation between a and B engineering teams? How much will it cost?
B due to other reasons, the leaders concerned require that the project be completed within 4 months at the latest. Please design a plan to ensure the project to be completed on time and save money as much as possible
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2. There are 2280t coal in the three warehouses a, B and C. if the ratio of coal quantity of a and B is 2:7, and the ratio of coal quantity of B and C is 3:7, then a has tons of coal (fill in the blank)
We need to solve the first-order equation with one variable!

1. A: suppose the workload is 1
The working speed of a is 1 / 3, and that of B is 1 / 6
Then the cooperation time between the two teams is 1 △ 1 / 3 + 1 / 6
2 months
Then a needs 2 * 12 = 240000 yuan, B needs 2 * 5 = 100000 yuan, and the total cost is 340000 yuan
B: If Party A works for x months and Party B works for y months, and the total cost is z0000 yuan, then z = x * 12 + y * 5
X*(1/3)+Y*(1/6)=1 ②
Condition x

Solution equation: 0.3 (3x + 2) = 8.7
Right now,

0.3(3x+2)=8.7
3(3X+2)=87
9X+6=87
9X=81
X=9

What is 720 △ 90 △ 125?

720÷(90÷125)
=720÷90×125
=8×125
=1000

Solve the following equation, find out the law and prove it: (1) the root of equation x2 + 2x + 1 = 0 is: X1 = 0___ ，x2= ___ ，x1+x2= ___ ，x1x2= ___ (2) the root of equation x2-3x-1 = 0 is: X1 = 0___ ，x2= ___ ，x1+x2= ___ ，x1x2= ___ (3) the root of equation 3x2 + 4x-7 = 0 is: X1 = 0___ ，x2= ___ ，x1+x2= ___ ，x1x2= ___ What conjecture can you draw from (1) (2) (3)? Can you prove your conjecture?

(1) This is the (x + 1) 2 = 0 (x + 1) 2 = 0, and (x + 1 + 1) 2 = 0 \\\\\\ (x + 1) 2 + 2x2x + 1 = 0, namely (x + 1) 2 (x + 1) 2 = 2 (x + 1) 2 = 2 = 2 = 2 = 0 \\ + 1 = 0 \\\\\\\\\\\\\\ (x + 1) 2 + BX + BX + C = 0 (a = 0 (a, a, a, a, a, a, a, a, B, B, B, C, a, a, a, a, a, a, a, a, a, a, if x has two roots X1 and X2, then X1 + x2 =-ba，x1•x2=ca．

The price of a commodity is reduced by 35% first, and then by 20% according to the price after the reduction. What percentage of the price before the reduction is the current price?

Now = (1-35%) × (1-20%) = 52%

It is known that the domain of definition of function y = f (x) is r, and for any a, B ∈ R, f (a + b) = f (a) + F (b). When x > 0, f (x) < 0 holds, f (3) = - 3
(1) It is proved that the function y = f (x) is a decreasing function on R;
(2) Try to find the range of function y = f (x) on [M, n] (m, n ∈ z)
Let f (3) = f (3) + F (0) get f (0) = 0, f (3) - f (0) < 0, so it is a decreasing function
Then there is the second question. I don't understand the answer. The answer is f (n) = 2F (1) + F (n-2) = n * f (1). I don't understand why 2F (1) + F (n-2) = n * f (1)

It is equivalent to the sum of N F (1), f (n-2) = f (1) + F (n-3) ‖ f (n) = 2F (1) + F (n-2) = 3f (1) + F (n-3) = =NF (1) (1) prove that let x1, X2 ∈ R, and x1 ＜ X2, f (x2) = f [X1 + (x2-x1)] = f (x1) + F (x2-x1). ∵ x2-x1 ＞ 0, ∵ f (x2-x1) ＜ 0. ∵ f (x2) = f (x1) + F (x2-x1) ＜ f (x1). So f (x) is a decreasing function on R. (2) prove that ∵ f (a + b) = f (a) + F (b) is constant, and ∵ let a = - B = x, then f (x) + F (- x) = f (0), and let a = b = 0, Since y = f (x) is a monotone decreasing function on R, y = f (x) is also a decreasing function on [M, n], the maximum value f (x) max of F (x) on [M, n] is f (m), and the minimum value f (x) min is f (n) =NF (1), the same as f (m) = MF (1). Also f (3) = 3f (1) = - 3, х f (1) = - 1, х f (m) = - m, f (n) = - N. the value range of х function y = f (x) on [M, n] is [- N, - M]

A high school mathematics compulsory three probability problem
A, B and C answer a question at the same time. It is known that the probability of a answering the right question is 3 / 4, the probability of a and C answering wrong is 1 / 12, and the probability of B and C answering right is 1 / 4,
(1) Ask for the probability that B and C will answer this question respectively
(2) Find out the probability of two out of three people answering the question

Let B answer correctly and C answer correctly
(1) It is known that, (1-y) * 1 / 4 = 1 / 12
xy=1/4
The solution is x = 3 / 8, y = 2 / 3
（2）P=3/4 * 3/8 *(1-2/3)+3/4 * (1-3/8) * 2/3+(1-3/4) * 3/8 * 2/3=7/16