If the quadratic function f (x) has f (2 + x) = f (- x) for any real number x, then the equation of symmetry axis of F (x) is?

If the quadratic function f (x) has f (2 + x) = f (- x) for any real number x, then the equation of symmetry axis of F (x) is?

Let a = - 1-x
Then x = - 1-A
-x=1+a
2+x=1-a
So f (1 + a) = f (1-A)
So the axis of symmetry is x = 1

The function f (x) = ax ^ 2 + BX + C, the axis of symmetry is x = 7 / 4, and the equation f (x) = 7x + A has two equal real roots

The function f (x) = ax ^ 2 + BX + C, the axis of symmetry is x = 7 / 4,
x=-b/2a=7/4,
f(x)=7x+a=ax^2+bx+c
ax^2+(b-7)x+c-a=0
There are two equal real roots, that is, there is only one with,
A is not equal to 0, so the discriminant B ^ 2-4ac = 0, and C = 0,
(b-7)^2-4a(c-a)=0;
c-a=0;
b=7,a=-2,c=-2
f(x)=-2x^2+7x-2

It took 6 hours for a worker to process a machine part. After the technical reform, it took 5 hours, and the work efficiency increased by ()%

It took 6 hours for a worker to process a machine part. After the technical reform, it took 5 hours, and the work efficiency increased by (16.67)%
（6-5）÷6×100％=16.67％
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x+y=84 5/8x+3/4y=58

x+y=84 ①
5/8x+3/4y=58 ②
② Multiply 8 to get 5x + 6y = 464 ③
① Multiply by 5 to get 5x + 5Y = 420
③ (4) y = 44
Because x + y = 84
So x is 84-y, 84-44, 40
So, x = 40, y = 44

The grain stored in warehouse A is 20 tons, and that in warehouse B is 16.4 tons. After warehouse B delivers part of the grain to warehouse A, the grain stored in warehouse A is three times as much as that in warehouse B. how many tons of grain does warehouse B deliver to warehouse a?

(20 + 16.4) △ 3 + 1) = 36.4 △ 4 = 9.1 (tons) 16.4-9.1 = 7.3 (tons) a: warehouse B delivers 7.3 tons of grain to warehouse a

0.8x-2 = 0.4x + 2 (solution equation)
You can't just write one answer

0.8X－2＝0.4X＋2
0.8X-0.4X=2+2
0.4X=4
X=10

My friend gave me a math problem, nine squares, fill in 1-9, let it each line is 1-9, nine numbers without repetition!
My friend gave me a math problem. Fill in 1-9 in nine horizontal and vertical boxes, and let it be 1-9 in each horizontal and vertical line. Nine numbers are not repeated! And some of the numbers are fixed
1.（7）（ ）（1）（ ）（ ）（ ）（ ）（4）（ ）
2.（ ）（8）（9）（3）（ ）（ ）（6）（ ）（ ）
3.（ ）（ ）（ ）（6）（ ）（7）（1）（ ）（8）
4.（ ）（2）（ ）（ ）（3）（ ）（8）（ ）（ ）
5.（ ）（ ）（8）（ ）（6）（ ）（9）（ ）（ ）
6.（ ）（ ）（5）（ ）（7）（ ）（ ）（2）（ ）
7.（8）（ ）（7）（9）（ ）（6）（ ）（ ）（ ）
8.（ ）（ ）（3）（ ）（ ）（5）（7）（9）（ ）
9.（ ）（1）（ ）（ ）（ ）（ ）（5）（ ）（4）

1.（7）（6）（1）（2）（5）（8）（3）（4）（9） 2.（5）（8）（9）（3）（1）（4）（6）（7）（2） 3.（4）（3）（2）（6）（9）（7）（1）（5）（8） 4.（1）（2）（4）（5）（3）（9）（8）（6）（7） 5.（3）...

It is known that {an} is an arithmetic sequence with non-zero tolerance, and its second, third and sixth terms are three consecutive terms of an arithmetic sequence

Let the tolerance of arithmetic sequence be D, and let D ≠ 0
Then A2 = a1 + D, A3 = a1 + 2D, A6 = a1 + 5D
A2, A3 and A6 are three consecutive terms of the equal ratio sequence, then
a2*a6=a3^2
(a1+d)(a1+5d)=(a1+2d)^2
D (2A1 + D) = 0
And D ≠ 0
Then d = - 2A1
Then A2 = - A1, A3 = - 3A1
Then the common ratio of the equal ratio sequence is A3 / A2 = 3

Fill in the rules (1). 2.9.23.37.2.1.16.49

Fill in the rules
(1) 9. (16) 23. (30) 37. (44) 7
(2) 1. (4) 9.16. (25). (36). 49

As shown in the figure, given AB = AC, Pb = PC, the following conclusions are: ① be = CE; ② AP ⊥ BC; ③ AE bisection ⊥ BEC; ④ ⊥ PEC = ⊥ PCE, in which the number of correct conclusions is ()
A. 1 B. 2 C. 3 d. 4

∵ AB = AC, Pb = PC, ∵ AP ⊥ BC, AE bisection ∠ bec (three lines in one), so ② and ③ are correct, ∵ BP = PC, ∵ BPE = ∠ CPE = 90 °, PE = PE, ≌ BPE ≌ CPE, ≌ be = EC, so ① and ④ cannot be proved, so C is selected