If M + 2n + 6 + 2m + M-3 = 0, then M + n=

Because the root sign m + 2n + 6 + root sign 2m + M-3 = 0,
So m + 2n + 6 = 0, 2m + M-3 = 0
So m = 1, n = - 3.5
So m + n = - 2.5

It is known that the line L of two points a (- 2,3), B (3,1), passing through P (2, - 1) has a common point with the line segment ab. the slope k of the line L and the value range of the inclination angle a are obtained

∵A(-2,3),B(3,1)
The line L passing through point P (2, - 1) has a common point with line ab
When the line L has a slope:
① When k ＞ 0, at least the line L intersects with point B. from the two-point formula (x-3) / (2-3) = (Y-1) / (Y - (- 1)), the slope of BP line is 2,
When the line L is closer to the line x = 2, K → + ∞ K ≥ 2;
② When k ＜ 0, at least line L intersects point a, and the slope of AP line is - 1 according to the two-point formula (x - (- 2)) / (2 - (- 2)) = (Y-3) / (- 1-3),
When the line L is closer to the line x = 2, K → - ∞ K ≤ - 1
When the line L has no slope, the line L: x2 = and ab still have a common point, but K has no slope;
∪ [2, + ∞) ∪ k = Tan α (0 °≤ α < 180 °)
The image shows that when Tan α ≤ - 1, π / 2 ＜ α ≤ 3 π / 4;
When Tan α ≥ 2, arctan2 ≤ α < π / 2;
∵ when α = 90 °, the line L and ab also have a common point ∵ α = π / 2
The α belongs to [arctan2,3 π / 4]

It is known that there is always a common point between the line L passing through the point P (- 1,2) and the line segment AB at two points a (2, - 3), B (3,0). The value range of the slope k of the line L is obtained

The slope of ∵ line PA is 2 + 3 − 1 − 2 = − 53, and the slope of line Pb is 2 − 0 − 1 − 3 = − 12. As shown in the figure, ∵ line L and line AB always have a common point, and the value range of ∵ slope k is [− 53, − 12]

It is known that the line L passes through P (1,1) and intersects the line segment AB with a (2, - 3), B (- 3, - 2) as the endpoint. The range of the slope k of the line is obtained
If it intersects with line AB, it must be two special points!
Then: slope AP = [1 - (- 3)] / [1-2] = - 4
Slope BP = [1 - (- 2)] / [1 - (- 3)] = 3 / 4
So the range of slope k is k > = 3 / 4 or K

It's a little complicated to explain. I'll tell you the rules and think for yourself
Two critical values are obtained,
In the process of change, if it passes through a vertical straight line, then the range of K is beyond the two critical values;
If it does not pass through a vertical line, then the range of K is between two critical values
Note: because both sides of the vertical line, the slope has positive infinity and jumps directly to negative infinity
If you don't understand, please hi me,

Given that the lengths of two sides of a triangle are 3cm and 5cm, and the length of the third side is an even number, what is the perimeter of the triangle?

5-3=2
5+3=8
two

If the lengths of two sides of a triangle are 9 and 4, and the circumference is even, then the third side may be ()
A. 5B. 7C. 8D. 13

Let the length of the third side X. according to the trilateral relationship of the triangle, we can get 5 ＜ x ＜ 13. The value range of the perimeter l of the triangle is: 18 ＜ L ＜ 26. Also ∵ the perimeter of the triangle is even, so the number that satisfies the condition is 20, 22, 24. The length of the third side is 20-9-4 = 7, 22-9-4 = 9, 24-9-4 = 11

The perimeter of a triangle is odd, and the lengths of its two sides are 4 and 2013___ One

Let the length of the third side be X. according to the trilateral relationship of the triangle, there is 2013-4 < x < 2013 + 4, that is, 2009 < x < 2017. ∵ the length of the third side is odd, ∵ x = 201120132015. So the answer is: 3

The perimeter of an isosceles triangle is 18cm. (1) if the waist length is twice the length of the ground side, calculate the length of each side. (2) if the length of one side is 8cm, calculate the length of each side
The circumference of isosceles triangle is 18 cm
(1) If the waist length is 2 times of the ground side length, seek the side length!
(2) If the length of one side is known to be 8cm, find the length of the other sides!

(1) Set waist length x and bottom edge X / 2
18-2x=X/2
x=7.2
Bottom edge = 7.2 divided by 2 = 3.6
(2) When the waist is 8, the bottom edge is 18-2 * 8 = 2
come on.
When the base is 8, waist = (18-8) divided by 2 = 5

It is known that in △ ABC, ab = AC, BD is the middle line. BD divides the perimeter of △ ABC into two parts, 18cm and 21cm, and calculates the three sides

Let AB = AC = xcm, BC = YCM, according to the meaning of the question, we get x + 12x = 18y + 12x = 21 or x + 12x = 21y + 12x = 18, and the solution is x = 12Y = 15 or x = 14y = 11, so the three sides of the triangle are 12, 12, 15 or 14, 14, 11

It is known that in △ ABC, ab = AC, BD is the middle line. BD divides the perimeter of △ ABC into two parts, 18cm and 21cm, and calculates the three sides

If M + 2n + 6 + 2m + M-3 = 0, then M + n=