The canteen bought some flour. On the first day, they ate half of the whole flour, which was less than 28 kg. On the second day, they ate the remaining half, which was less than 8 kg. Finally, they had 122 kg. How many kg of flour are there?

400kg
If the total amount of flour is x kg, there are:
The first day: X / 2-28 more than: X / 2 + 28
The next day: (x / 2 + 28) / 2-8, that is, X / 4 + 14-8
The rest: 122 kg
So there's Flour: X / 2-28 + X / 4 + 14-8 + 122
So there is an equation: x = x / 2-28 + X / 4 + 14-8 + 122
Or: X - (x / 2-28) - (x / 4 + 14-8) = 122
The solution of the equation is x = 400
The tests are as follows:
On the first day, he ate 172 kg and the rest 228 kg;
The next day, I ate 106 kg and the rest 122 kg
The test results are correct

If the sum of three natural numbers is 99 and the number in the middle is x, can you list the equation to find the value of X? What are the other two numbers?
If the five continuous techniques are suitable, the middle comfortable n will be calculated by equations.

Let the other two numbers be x + 1 and X-1
3x+1-1=99
3x=99
x=33
33+1=34
33-1=32
5n+1+2-1-2=55
5n=55
n=11

Given that the inequality (x + y) * (1 / x + A / y) is greater than or equal to 9 pairs of arbitrary real numbers x and y, what is the minimum value of positive real number a?

（x+y)*(1/x+a/y)
=1+a+y/x+ax/y
>=1+a+2√a
>=9
That is (√ a + 1) ^ 2 > = 9
a>=4
So the minimum value of positive real number a is 4

As shown in the figure, in rectangular ABCD, ab = m (M is a constant greater than 0), BC = 8, e is the moving point on the line BC (not coincident with B and C). Connect De, make ef ⊥ De, let EF and ray Ba intersect at point F, let CE = x, BF = y. (1) find the functional relationship between Y and X; (2) if M = 8, what is the value of X, and what is the maximum value of Y? (3) If y = 12M, what is the value of m to make △ def an isosceles triangle?

(1) ∧ EF ⊥ De, ∧ bef = 90 ° - ∧ CED = ∧ CDE, ∧ bfce = BEDC, that is, YX = 8 − XM, the solution is y = 8x − x2m; (2) y = 8x − x2m is obtained from (1), and y = - 18x2 + x = - 18 (x2-8x) = - 18 (x-4) 2 + 2 is obtained by substituting M = 8, so when x = 4, the maximum value of Y is 2; (3) ∧ def = 90 °, only when de = EF, ∧ DEF is isosceles triangle If we solve the equation 12m = 8x − x2m, we can get x = 6, or x = 2, when x = 2, M = 6, when x = 6, M = 2

Similar figure
1. It is known that the parallelogram ABCD, e is a point on the extension line of Ba, CE intersects AD and BD at g and F, and the square of CF = GF * EF is proved

Analysis: the square of CF is required to be GF × EF, i.e. CF / GF = EF / cf. the two ratios are in two pairs of similar triangles, so we need to find a bridge between the two pairs of similar triangles to make them equal
In ABCD
∵ ad ∥ BC (parallelogram opposite side parallel)
The two lines are parallel and the internal stagger angle is equal
∧ GDF ∧ CBF (two angles corresponding to equal triangles are similar)
Ψ CF / GF = BF / DF (the ratio of the corresponding sides of similar triangles is equal)
In ABCD
∵ ad ∥ BC (parallelogram opposite side parallel)
The two lines are parallel and the internal stagger angles are equal
∧ EBF ∧ CDF (two angles corresponding to equal triangles are similar)
Ψ EF / CF = BF / DF (the ratio of the corresponding sides of similar triangles is equal)
Ψ CF / GF = EF / CF (equivalent substitution)
That is, the square of CF = GF × EF

Similar figure
Help me to see if I do this problem wrong, just look at the choice and fill in the blanks
The answer I did was:
1： 1 a 2 C 3A 4D 5C 6C 7a 8A 9C 10A
2： 11. - 1 / 4 12. Radical 5 13.3/4 14. Angle ade = angle B
15.1 vs. 3

B (assuming x = 1, y = 2) 2. C 3. A 4. C (△ ADF and △ CFE, △ ADF and △ Abe, △ CFE and △ ABE) 5. C 6. C 7. A 8. A 9. C 10. A 2. 11. - 1 / 4 12. Radical 5 13.3 / 4 14. ∠ ade = ∠ C or ∠ AED = ∠ B or / BC = AE / AB = ad / AC 15.1

As shown in the figure, in the isosceles trapezoid ABCD, ad ∥ BC, ad = 3, BC = 7, ∠ B = 60 °, P is a point on the bottom BC (not coincident with B and C), and PE intersects DC at e through P, so that ∥ ape = ∠ B. (1) calculate the waist length of the isosceles trapezoid; (2) prove: △ ABP ∥ PCE; (3) whether there is a point P on the bottom BC, so that de: EC = 5:3? If it exists, find the length of BP; if not, explain the reason

(1) In the isosceles trapezoid ABCD, ad ∥ BC, ∥ quadrilateral ADHF is rectangle, ∥ AF = DH, FH = ad, ∥ AB = DC, ≌ RT △ Abf ≌ RT △ DCH, ∥ BF = ch, ∥ BF = BC − ad2 = 7 − 32 = 2 In RT △ ABF, the waist length of isosceles trapezoid is 4 (4 points) (2) prove that: from the outer angle of ∠ APC as △ ABP, we can get ∠ APC = ∠ B + ∠ BAP, and ∵ ∠ APC = ∠ APE + ∠ CPE, ∠ B = ∠ ape, ∵ BAP = ∠ CPE (6 points) from the isosceles trapezoid property, we get ∠ B = ∠ C, ∧ △ ABP ∧ PCE (if the two angles of a triangle correspond to the two angles of another triangle, then the two triangles are similar) & nbsp; & nbsp (8 points) (3) there is such a point P The reason is as follows: from de: EC = 5:3, de + CE = DC = 4, CE = 32 (10 points) let BP = x, then PC = 7-x. from △ ABP ∽ PCE, ABPC = pbce, that is 47 − x = X32 & nbsp (12 points) the solution is X1 = 1, X2 = 6, which are consistent with the meaning of the question, so BP = 1 or BP = 6 (13 points) scoring instructions: there are many solutions to some of the problems. Only one solution is given to the above problems. Students can refer to other solutions for scoring

In the plane rectangular coordinate system, the coordinates of vertex a of △ ABC are (2,3). If the origin o is taken as the position similar center, draw the position similar figure △ a ′ B ′ C ′ of △ ABC, so that the similarity ratio of △ ABC and △ a ′ B ′ C ′ is equal to 12, then the coordinates of point a ′ are___ ．

∵ in △ a ′ B ′ C ', the coordinates of its corresponding point are (KX, KY) or (- KX, - KY) ∵ a' and (4,6) or (- 4, - 6)

On the similar figures in mathematics of grade eight
If the area ratio of two similar polygons is 25:16, then their similarity ratio is If the perimeter of one of the similar polygons is 36cm, the perimeter of the other polygon is 36cm Or__ .
Please explain the answer and solution, as well as the analysis process of this kind of problem

According to the theorem, the area ratio of similar figures is the square of the similar ratio, and the ratio of their perimeter is equal to the similar ratio. The first space is 5:4. It can be seen that the perimeter of another similar polygon is 36: x = 5:4 or X: 36 = 5:4, and the perimeter is 144 / 5 or 180 / 4 = 45

If the equation 2x (kx-4) - x2 + 6 = 0 has no real root, then the minimum integer value of K is ()
A. 2B. 1C. - 1D. Does not exist

The original equation can be reduced to: (2k-1) x2-8x + 6 = 0, when 2k-1 = 0, i.e. k = 12, the original equation can be reduced to: - 8x + 6 = 0, at this time, the equation has real number roots, so it is not meaningful; when 2k-1 ≠ 0, i.e. K ≠ 12, the equation has no real number roots, and the solution is k ＞ 116, and the minimum integer value of K is 2

The canteen bought some flour. On the first day, they ate half of the whole flour, which was less than 28 kg. On the second day, they ate the remaining half, which was less than 8 kg. Finally, they had 122 kg. How many kg of flour are there?