It is known that a and B are two points on the line Mn, Mn = 4, Ma = 1, MB > 1. Take a as the center, rotate clockwise to point m, and take B as the center, rotate anticlockwise to point n, so that two points m and N are combined into a point C again to form a triangle ABC (1) Find the value range of X (2) If △ ABC is a right triangle, find the value of X (3) Explore: the largest area of △ ABC Don’t copy

1. Because the length of the three sides of the triangle is 1,3-x, X
So x + 1 > 3-x gets x > 1
3-x + 1 > x gets X

Two triangles of equal area can be combined into a parallelogram. () right / wrong? If wrong, please state the reason for the mistake:------------------

Wrong! Equal area can only be equal to the product of the bottom multiplied by the height. To form a parallelogram, the two triangles must be congruent

What does PM am mean

a. M. in the morning
p. M. afternoon

[(-3n)^2-(m^2-3n)^2]/(2m)^2

Original formula = (9N ^ 2-m ^ 4 + 6m ^ 2n-9n ^ 2) / 4m ^ 2
=(6m^2n-m^4)/4m^2
=3n/2-m^2/4

Through the point m (- 1,4) to the circle (X-2) ^ 2 + (Y-3) ^ 2 = 1, lead the tangent, find the tangent equation and tangent length

First, it is judged that m (- 1,4) is outside the circle
Let y-4 = K (x + 1)
According to the geometric properties of a circle, the distance from the center of the circle to the tangent is the radius of the circle
|3-4-k(2+1)|/√1+k²=1
The solution is as follows
K = 0 or - 3 / 4
The distance from the center of the circle to m is √ (- 1-2) &# 178; + (4-3) &# 178; = √ 10
So the tangent length is √ (√ 10) &# 178; - 1 = 3
Tangent equation: y = 4 or 4Y + 3x-13 = 0
The tangent length is 3

The tolerance of arithmetic sequence is 5
2 7 12 17 is represented by N or - 23 - 18 - 13 - 5 is represented by n

2 7 12 17.
Because the tolerance d = 5, the general term is an = a1 + (n-1) * d = 2 + (n-1) * 5 = 5n-3 (n ≥ 1)
Similarly, for - 23 - 18 - 13 - 5, the general term is an = 5N - 28 (n ≥ 1)

In the pyramid P ABCD, the bottom quadrilateral ABCD is a diamond, O is the intersection of AC, Po is perpendicular to ABCD, e is the midpoint of Pb
2 Q, PBD vertical plane ace

Note: O should be the intersection of AC and BD, or the midpoint of AC
ABCD is a diamond and O is the intersection of AC and BD
The midpoint of BD is o
Connect EO
E is the midpoint of Pb and O is the midpoint of BD
The EO parallel PD
Ψ PD parallel plane ace

It is known that the quadratic function f (x) = AX2 + BX (a, B are constants, and a ≠ 0) satisfies the condition f (2) = 0, and the equation f (x) = x has two equal real numbers
It is known that the quadratic function f (x) = AX2 + BX (a, B are constants, and a ≠ 0) satisfies the following conditions: F (2) = 0, and the equation f (x) = x has two equal real roots;

(1) If f (2) = 0, 4A + 2B = 0,
That is 2A + B = 0
If f (x) = x has equal roots,
The discriminant △ = 0 of the equation AX & # 178; + bx-x = 0
That is, (B-1) ² = 0,
b=1.
A = - 1 / 2
Then the analytic expression of quadratic function is
f(x)=-0.5x²+x.

Solve the plane equation which passes through the point P (- 1.2. - 3) and is perpendicular to the line x = 3 + T.Y = t.z = 1-t

According to the linear equation, the direction vector s = (1,1, - 1) is the normal vector of the surface
The surface equation is: x + 1 + Y-2 - (Z + 3) = 0
Namely:
x+y-z-5=0

How to prove: if P is an odd prime, then p | (p-1)! A?

If P is an odd prime, then p | (p-1)! A)
Certificate:
Just prove a ^ P + (p-1)! A = = 0 mod P
According to Fermat's theorem, a ^ P = = a mod P
According to Wilson's theorem, (p-1)! = = - 1 mod p
therefore:
a^p+（p-1）!a==a+(-1)a==0 mod p
The proof is complete
For the proof of Fermat's small theorem, see:
Or Baidu Encyclopedia - Fermat theorem:
For the proof of Wilson theorem, please refer to:
or
Baidu Encyclopedia - Wilson theorem:
The generalization of Wilson theorem
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