To solve the equation: the difference product of 1,6 and a certain number is 1 to find the number. 2,20 is less than 5 times of a number. 2.5 to find the number. 3,1 / 3 of a number is more than 5 times of a number How much is 40% less than 4

To solve the equation: the difference product of 1,6 and a certain number is 1 to find the number. 2,20 is less than 5 times of a number. 2.5 to find the number. 3,1 / 3 of a number is more than 5 times of a number How much is 40% less than 4

1: 6 * (6-x) = 1 x = 35 / 6
2：5x-2.5=20 x=4.5
3: 1 / 3 x = 40% x-4 1 / 15 x = 4 * 15 x = 60

Two fifths of a number is more than 90% of two and two thirds. What's the number

Let this number be X
2x-2 out of 5 and 2 out of 3 times 9 out of 10 = 2
The solution is x = 11

If you subtract 3 / 4 from a number and 3 / 4 from it, 2 / 3 of the difference is 5 / 6. Find this number (by solving the equation)

Let this number be X
(x-3 / 4x-3 / 4) * 1 and 2 / 3 = 5 / 6
(1/4x-3/4)*5/3=5/6
1/4x-3/4=1/2
1/4x=5/4
x=5

If M = {1,2}, n = {2,3}, then the number of sets P satisfying P (proper subset sign) (MUN) is given

From M = {1,2}, n = {2,3}, we can see that m ∪ n = {1,2,3}
For the convenience of explanation, let a = m ∪ n = {1,2,3}
P is the proper subset of a, so p = Φ, or P = {1}, or P = {2}, or P = {3}, or P = {1,2}, or P = {2,3}, or P = {3,1}
Therefore, the number of sets P satisfying the condition is 7
PS. in fact, there are three elements in set a, so the number of proper subsets is 2 ^ 3-1 = 7
More generally, if there are n elements in the set a, then its subset has 2 ^ n and its proper subset has 2 ^ n-1. Using this conclusion, we can get more rapid and effective solutions to the related problems

Given the line AB = a, extend Ba to point C, so that AC = half ab. point D is the midpoint of line BC
(1) Find the length of CD (2) if ad = 3cm, find the length of ab
Given that point P is a point on line AB, the length ratio of AP to Pb is 2:3. If AP = 4cm, the length of Pb and ab is obtained

(1) AC = AB / 2 = A / 2, then CD = BC / 2 = (AC + AB) / 2 = (A / 2 + a) / 2 = 3A / 4 (2) if ad = 3cm, because ad = cd-ac = 3A / 4-A / 2 = A / 4, then AB = a = 4AD = 4 * 3 = 12cm; if AP = 4cm, AP / Pb = 2 / 3, then Pb = AP * 3 / 2 = 4 * 3 / 2 = 6cm, ab = AP + Pb = 4 + 6 = 10cm

Let a and B be matrices of order n, and a be symmetric. It is proved that B ＾ tab is also symmetric

First of all, you should know the following: 1) if a matrix is symmetric, it is equal to its transpose matrix. Therefore, if a is symmetric, a = a ^ T2. To prove that B ＾ tab is symmetric, it is necessary to prove that this matrix is equal to its transpose matrix, that is, B ＾ tab = (B ＾ tab) ^ t

High school mathematics circle and line position relationship online!
It is known that the circle X & sup2; + Y & sup2; - 6mx-2 (m-1) y + 10m & sup2; - 2m-24 = 0 (m ∈ R)
Verification: no matter what the value of M is, the center of the circle is on the same straight line L
Have a detailed process! Thank you!

The equation in the problem can be reduced to: (x-3m) ^ 2 + [y - (m-1)] ^ 2 = 25. Obviously, the center of the circle is (3m, m-1). The radius is 5. It is easy to know that for any real number m, the point (3m, m-1) is always on the straight line x-3y-3 = 0

How to find the definite integral of xsinx / (1 + cosx ^ 2) from 0 to π,

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Why is the rank of the matrix obtained by multiplying a full rank matrix and an unsatisfied rank matrix less than or equal to the rank of the original unsatisfied rank matrix

rank(AB)

1. It takes 5 hours for a car to go back and forth between a and B. when it comes back, the speed will be increased by one eighth, less than when it goes ()
2. The distance between a and B is 950 meters. A and B start from a at the same time. A walks every 40 meters and B runs every 150 meters. After 40 minutes, they stop exercising. When a and B meet for the first time, they are closest to B? How many meters are they from B?

1. Driving on the same road, the speed is inversely proportional to the time. The return time is 5 / (1 + 1 / 8) = 40 / 9, less 5-40 / 9 = 5 / 9 hours. 2. The first face-to-face meeting time is 2 * 950 / (40 + 150) = 10 minutes, so the face-to-face meeting is once every 10 minutes. There are four times in 40 minutes. The first meeting time is 2 * 950 /