It is known that there is a point P (- 2,1) on the inverse scale function image, and the intersection coordinates of the image and the line y = 2x-5 are obtained Come on!

Let the analytic expression of inverse scale function y = KX and substitute it into the coordinates of P point to get k = - 1 / 2, so the analytic expression is
y=-1/2x
And y = 2x-5 simultaneous equations, the intersection coordinates are obtained
x=2
y=-1

As shown in the figure, the image of inverse scale function y = m / X (x > 0) and the image of primary function y = - 1 / 2x + 5 / 2 intersect at two points a and B, and the coordinates of point C are (1,1 / 2), connecting AC, AC / / Y axis
1. There is a right triangle plate. Let its right vertex P slide between a and B (not coincident with a and b) on the inverse scale function image. The two right angles are always parallel to the x-axis and y-axis, and intersect with the line AB at two points m and N. when point P passes through point (2,1) in the sliding process, calculate the perimeter of triangle PMN

P(2,1)
Let m (2, a), n (B, 1)
When y = - 1 / 2x + 5 / 2
So a = - 1 + 5 / 2 = 3 / 2
1=-1/2b+5/2
b=3
So PM = | A-1 | = 1 / 2
PN=|2-b|=1
So by Pythagorean theorem
MN=√5/2
So perimeter = (√ 5 + 3) / 2

Let the plane region represented by the inequality system x + Y-11 ≥ 03x-y + 3 ≥ 05x-3y + 9 ≤ 0 be d. if there are points on region D on the image of exponential function y = ax, then the value range of a is ()
A. （1，3]B. [2，3]C. （1，2]D. [3，+∞]

Make the image of region D, connect the image of exponential function y = ax, and get the point C (2,9) from x + Y-11 = 03x-y + 3 = 0. When the image passes through the boundary point C (2,9), a can take the maximum value 3. Obviously, as long as a is greater than 1, the image must pass through the points in the region

It is known that a vector = (SiNx, 2cosx) B vector = (cosx, cosx) function FX = a vector · (a vector - B vector), X ∈ R
① Finding the minimum positive period of FX
② Monotone increasing interval of FX
③ The value range of X when FX is greater than or equal to 3 / 2

I'm really limited in terms of symbols, but I'll try my best. You first express FX as a vector
FX = a vector (SiNx cosx, cosx) = the square of SiNx (SiNx cosx) + 2cosx. Now you have to use your own formula, which is the formula of trigonometric function,

Write the negative integer of equation 3x + 4Y = - 20
Express y with algebraic expression containing x

From 3x + 4Y = - 20, the following results are obtained
4y＝－3x－20
Divide both sides by 4 to get:
y＝－3x/4－5
Because y < 0
So - 3x / 4-5 < 0
So x ＞ - 20 / 3 = - 6 and 2 / 3
So x can only take integers between - 6 and - 1
But x has to be divisible by four
So x can only be equal to - 4
Then y = - 2
So the negative integer solution of equation 3x + 4Y = - 20 is only x = - 4, y = - 2

Write the non positive integer solution of equation 3x + 4Y = - 20
Write down the process, thank you

It can be seen from the meaning of the title
4y+20=-3x≥0
Then x is divisible by 4
And 3x ≥ - 20
0≥x≥-20/3
Then x = 0, - 4
Here y = - 5, - 2

Find 3x + 4Y = 23 natural number solution!

Substitute: x = 1, y = 5; X = 5, y = 2

Solution of natural number 3x + 4Y = 6
3X+4Y=6

X=2,Y=0.
From 3x + 4Y = 6, x = (6-4y) / 3 = 2-y-y / 3 = 2-y-k,
In fact, k = Y / 3, so y = 3k, x = 2-y-k = 2-3k-k = 2-4k
The general solution of the equation is x = 2 - 4K, y = 3k, K is an integer
10. Y is a natural number, x = 2-4k ≥ 0, 3K ≥ 0, k = 0
K=0,X=2,Y=0

Given that X and y are natural numbers and satisfy the equation 9x2-4y2 = 5, find the value of X and y

∵ 9x2-4y2 = 5, ∵ 3x + 2Y) (3x-2y) = 5, ∵ X and y are natural numbers, ∵ 3x + 2Y = 13X − 2Y = 5 or 3x + 2Y = 53x − 2Y = 1, ∵ x = 1y = − 1 or x = 1y = 1, the values of ∵ x and y are 1 and 1, respectively

It is known that the solution of the equation 3x + a = 1 about X is 1 larger than that of the equation 4x-a = 0 about X

The solution of the equation 3x + a = 1 of X is x = (1-A) / 3
The solution of the equation 4x-a = 0 about X is x = A / 4
It is known that: (1-A) / 3-A / 4 = 1
The solution is a = - 8 / 7

It is known that there is a point P (- 2,1) on the inverse scale function image, and the intersection coordinates of the image and the line y = 2x-5 are obtained Come on!