If the quadratic trinomial 4x2 + ax + 9 is a complete square, then a=______ ．

If the quadratic trinomial 4x2 + ax + 9 is a complete square, then a=______ ．

A = ± 2 × 2 × 3 = ± 12

Let the left and right focus discrimination of the ellipse C1: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) be F1 and F2, the lower vertex be a, and the midpoint of the line OA be B (o is the coordinate origin). If the intersection of the parabola C2: y = x ^ 2-1 and the Y axis is B and passes through F1 and F2, let m (0, - 4 / 5), n be a moving point on the parabola C2, and n be the tangent intersection of the parabola C2. The ellipse C1 is located at P and Q, and the maximum area of the triangle MPQ is obtained

If an integer has the following three properties: 1. The difference between the number and 1 is prime; 2. The quotient of the number divided by 2 is also prime;
If an integer has the following three properties at the same time:
1. The difference between this number and 1 is prime;
2. The quotient of this number divided by 2 is also prime;
3. The remainder of this number divided by 9 is 5;
Then we call this integer a lucky number and find out all the two - digit lucky numbers

According to the meaning of the title,
The difference between this number and 1 is prime,
So this number must be even,
And the remainder of 9 is 5,
So it can only be the following number
14、14+18=32、32+18=50、50+18=68、68+18=86
The results show that only the second condition is satisfied
16 and 86

It is proved that the function f (x) = x + (1 / x) is a decreasing function on (0,1) and an increasing function on [1, + ∞)

f(x)=x+（1/x）
Let's take x1, X2 in (0, + ∞), and X1 < x2
Then f (x2) - f (x1) = x2-x1 + 1 / x2-1 / x1
=(x2－x1)(1-1/x2x1)
If x 2-x 1 > 0, then f (x 2) - f (x 1) < 0 is a decreasing function when x 1, x 2 ∈ (0,1)
When x1, X2 ∈ [1, + ∞), f (x2) - f (x1) ＞ = 0, it is an increasing function

If f (x) = 2-lg (x-3), what is f (x) equal to?
If f (x) = 2-lg (x-3), what is f - & sup1; (x) equal to?

The analytic formula is: y = 2-lg (x-3),
lg（x－3）=2-y
x-3=10^(2-y)
x=10^(2-y),
That is f - 1 (x) = 10 ^ (2-x)

Fill in with prime numbers. 22 = () + () = () + ()

22＝（ 3）＋（19 ）＝（ 5）＋（ 17）

Let the distribution density function of random variable be, try to find the density function, mathematical expectation and variance of X
Let the distribution density function of random variable be, and try to find the density function, mathematical expectation and variance of X. f (x) = 0, X ＜ - 2,
x／4,-2≤x≤2,
1,x＞2

Firstly, the probability density function f (x) of random variable x is obtained by deriving the distribution function f (x), then E (x) and E (x ^ 2) are obtained by using the definition of expectation and second moment, and then the variance is obtained
Take a good look at the textbook of probability theory

If the image of the function y = a (x + m) ^ is translated to the left along the X axis by 4 unit lengths, the image of the function y = - 2 / 3x ^ can be obtained, then a=______ ,m=_______

a=-2/3,m=-4
Y = a (x + m) ^ 2 shift 4 units to the left to get y = - 2x ^ 2 / 3
Then a = - 2 / 3
-m-4=0
M = - 4 (equivalent to the left horizontal displacement of the symmetry axis of the original quadratic function - M image by 4 units, the symmetry axis of the new function is 0)

The greatest common factor of 30 and 35

Don't put your mouth on me,
The greatest common factor of 30 and 35 is 5

In the original operation method of rational number, we define the new operation "@" as follows: when a is greater than or equal to B, a @ b = the square of B; when a is greater than or equal to B, a @ b = the square of B

I try to be clear:
first 1@x ,1