Given a = 5, find (A-4) / (A & sup2-9) △ 1 / (A-3) * (A & sup2 + 6A + 9) / (A & sup2-8a + 16)

Given a = 5, find (A-4) / (A & sup2-9) △ 1 / (A-3) * (A & sup2 + 6A + 9) / (A & sup2-8a + 16)

（a-4）/（a²-9）÷1/（a-3）*（a²+6a+9）/（a²-8a+16）
=(a-4)/[(a+3)(a-3)]×(a-3)×(a+3)²/(a-4)²
=(a+3)/(a-4)
=8

"The bottom of a triangle is enlarged by two times, the height of the bottom is reduced by two times, and the area remains unchanged." is that right?

Yes
The area of the triangle = (base x height) / 2. If the base is enlarged by two times and the height of the bottom side is reduced by two times, the area will remain unchanged. "

It is known that the opposite sides of the three inner angles a, B and C of △ ABC are a, B and C respectively. If a, B and C form an arithmetic sequence and 2cos2b-8cosb + 5 = 0, the size of angle B is calculated and the shape of △ ABC is judged

From 2cos2b-8cosb + 5 = 0, we can get 4cos2b-8cosb + 3 = 0, that is, (2cosb-1) (2cosb-3) = 0. The solution is CoSb = 12 or CoSb = 32 (rounding off). ∵ 0 ＜ B ＜ π, ∵ B = π 3 and ∵ a, B, C form an arithmetic sequence, that is, a + C = 2B. ∵ CoSb = A2 + C2 − b22ac = A2 + C2 − (a + C2) 22ac = 12. The simplification is A2 + c2-2ac = 0, the solution is a = C, ∵ B = π 3 ∵ ABC is an equilateral triangle

A cuboid water tank with a square bottom is 4 decimeters high and a side area of 40 square decimeters. What is the volume of the tank?

Is the side area the area of one side?
If yes:
40 / 4 = 10 decimeters
10 * 10 * 4 = 400 liters
If it is the sum of the area of four faces, it becomes:
40 / 4 / 4 = 2.5 decimeters
2.5 * 2.5 * 4 = 25 liters

It is known that: as shown in the figure, in △ ABC, D is the midpoint of AC, e is a point on the extension line of line BC, the parallel line passing through point a as be intersects with the extension line of line ed at point F, connecting AE and cf. (1) verification: AF = CE; (2) if AC = EF, try to judge what kind of quadrilateral afce is, and prove your conclusion

(1) It is proved that in △ ADF and △ CDE, ∵ AF ‖ be, ∵ fad = ∠ ECD. And ∵ D is the midpoint of AC, ∵ ad = CD. ∵ ADF = ∠ CDE, ≌ ADF ≌ CDE. ≌ AF = CE

It is known that a (4,0) and B (2,2) are the points in the ellipse X225 + Y29 = 1, and M is the moving point on the ellipse, then the maximum value of | Ma | + | MB | is______ ; the minimum value is______ ．

A is the right focus of the ellipse, and the left focus is f (- 4,0), B is in the ellipse, then the definition of the ellipse is defined by the ellipse definition | | +