It is known that in trapezoidal ABCD, ad ∥ BC, median line EF intersects AB with F, intersects AC, BD with m, N, EF = 120, Mn = 80, find the length of AD and BC

Because AD / / BC EF is the median line, EF / / BC / / ad EM is the median line of triangle abd, EM = 1 / 2ad. Similarly, NF = 1 / 2 ad ad = EM + NF = 120-80 = 40, en = 1 / 2BC BC = 2EN = 2 (Mn + EM) = 2 (Mn + 1 / 2ad) = 2 * (80 + 20) = 200

Fill in different natural numbers in the following equation to make the equation hold. 112 = 1 () + 1 ()

Because 112 = 336 = 136 + 236 = 136 + 118, that is 112 = 136 + 118, the answer is: 36, 18

On eigenvalues and eigenvectors of matrices
Does every n-order matrix have eigenvectors? What are the properties of eigenvectors and eigenvalues

For a matrix A of order n, there exists a real number k and a vector a such that AA = Ka. The real number k is called an eigenvalue of matrix A, and the vector a is called the eigenvector corresponding to the eigenvalue K of matrix A
Any matrix of order n has n eigenvalues (i.e. n roots of the characteristic equation | ke-a | = 0, and the multiple roots are counted by multiplicity) and N corresponding eigenvectors

If the positions of the single digit and the ten digit of a two digit number are exchanged, the new two digit number will be 9 larger than the original two digit number. How many two digit numbers are there? What are their characteristics?

Let the original two digits be 10A + B, according to the meaning of the question: 10A + B + 9 = 10B + 1, the solution is: B = a + 1, because it can take 1 to 8 numbers, so the two digits have 8, they are respectively, 12, 23, 34, 45, 56, 67, 78, 89, they are two digits whose one digit is bigger than ten digits

If the rank of a matrix of order n is 1, then the determinant of it is 0

The determinant of a square matrix is not zero if and only if its rank is equal to the order of the matrix
So, when n = 1, the determinant is equal to the element in the matrix
When n > 1, its determinant must be 0

Equation formula of vertical bisector of line segment

A(x1,y1),B(x2,y2),
The midpoint m of AB ((x1 + x2) / 2, (Y1 + Y2) / 2)
The slope of AB: k = (y2-y1) / (x2-x1)
The slope of the vertical bisector of AB is - 1 / K
Therefore, the vertical bisector of AB can be written from the point oblique form: y = - (x2-x1 / (y2-y1) * [x - (x1 + x2) / 2] + (Y1 + Y2) / 2

There is a section of scientific notation in seven mathematics textbooks. A number m can be expressed in the form of a × 10 ^ n, where the value range of a is ≥ 1 < 10,
How does he determine that the value range of a is ≥ 1 < 10?
Why can't a be expressed in other forms, such as ≥ 10 < 100?

Science and technology law no matter how big the number is, just use the first significant number
For example:
forty-four million four hundred and twenty-five thousand six hundred and twenty-seven
The first significant number on the left is 4. OK, then let's show that it's 4.4425627 * 10 octave
【2】 As for why a can't be expressed as other numbers, it's because it's inconvenient to use, and some numbers are difficult to express and read. For example, 0.1 is written to the power of 1 * 10-1, but it's much more troublesome if the requirement is ≥ 10 < 100. Generally, it's convenient to use the range of a ≥ 1 < 10

Xiao Ming read a 270 page story book. On the first day, he read one third of the whole book. On the second day, he read one third of the whole book

If you read all of them, the next day you read six thirds of the first day

If the inequalities x ^ - X-2 > 0 and 2x ^ + (5 + 2a) x + 5A are satisfied at the same time
It seems that the answers are all wrong. Take a = - 3 into the verification. It seems that it is wrong. Here's an answer, which is] - 3, 2) do you see right

The solution set of x ^ 2-x-2 ＞ 0 (x + 1) (X-2) ＞ 0 is: X ＜ - 1, or X ＞ 22x ^ 2 + (5 + 2a) x + 5A ＜ 0 (2x + 5) (x + a) ＜ 0. The solution set is between - 5 / 2 and - A. when - a ＞ - 5 / 2, i.e. a ＜ 5 / 2, the solution set is - 5 / 2 ＜ x ＜ - A. the integer solution only has - 2. Therefore, - 2 ＜ - a ≤ 3-3 ≤ a ＜ 2. When - a ＜ - 5 / 2, i.e. a ＞ 5 / 2, the solution set is - a ＜ - x ＜ -

A passenger car and a freight car leave from a city at the same time. They meet each other in four hours. It is known that they travel 90 kilometers per hour, which is 1.5 times the speed of the freight car. What is the distance between a and B cities?

Speed of freight car 90 △ 1.5 = 60 km / h
Distance (60 + 90) X4 = 150x4 = 600km

It is known that in trapezoidal ABCD, ad ∥ BC, median line EF intersects AB with F, intersects AC, BD with m, N, EF = 120, Mn = 80, find the length of AD and BC