It is known that the vertex P of parabola y = x? + 4x + C is on the line y = 3x + 5

It is known that the vertex P of parabola y = x? + 4x + C is on the line y = 3x + 5

If y = x + 4x + C = (x + 2) + C-4, vertex coordinates are (- 2, C-4), and y = 3x + 5, then C-4 = - 6 + 5C = 3, P coordinates are (- 2, - 1), then parabolic equation is y = x + 4x + 3, substituting linear equation, there is 3x + 5 = x + 4x + 3x + X-2 = 0 (x + 2) (x-1) = 0, that is, there is an intersection, and x = 1, coordinates are (1,8)

How to explain the congruence of two triangles with two opposite angles and one opposite angle (the angle is obtuse angle)
Try to explain everything

Answer: in two triangles, there are two equal triangles corresponding to the opposite angles of two sides and one side (this angle is obtuse angle)

Given the function f (x) = x ^ 3-ax ^ 2-A ^ 2x + 1 g (x) = 1-4x-ax ^ 2, where the real number a ≠ 0, if f (x) and G (x) are increasing functions in the interval (- A, - A + 2),
Find the value range of a

F (x) and G (x) are increasing functions in the interval (- A, - A + 2)
It shows that the derivative function is greater than 0
So we list the inequalities and find out the range of A

Factorization in grade eight
Do it and add ten
x²（a-1）+y²（1-a）
-x³+x²-1/4x
（m²+n²）²-4m²n²
（a+3b）-（3a+b）²
x^4-2x²y²+y^4
x²（a-2）+4y²（2-a）
（5m²+3n²）²-（3m²+5n²）²
3a²-1/3b²
I hope you can help me, thank you!
The fourth question is wrong (a + 3b) & sup2; - (3a + b) & sup2;
Thank you for your help

x²（a-1）+y²（1-a）=x²（a-1）-y²（a-1）=(x²-y²)（1-a）=(x+y)(x-y)(1-a)-x³+x²-1/4x=x(-x²+x-1/4)=-1/4(4x²-4x+1)=-1/4(2x-1)^2（m²+n²）²-4m...

Graph of quadratic function y = 1 / 2x square y = - 1 / 3x square y = 3x square

In the picture
The green parabola is y = 3x ^ 2
The purple parabola is y = 1 / 2x ^ 2
The black parabola is y = - 1 / 3x ^ 2

How to calculate 2 / 7 (3x + 7) = 2-1.5x

2（3x+7）/7=2-1.5x
2（3x+7）=14-10.5x
6x+14=14-10.5x
6x+10.5x=0
16.5x=0
So x = 0

The analytic formula of parabola y = X2 - (2m-1) x + m2-m proves that there are two intersections between parabola and x-axis, and the intersection of parabola and straight line y = x-3m + 4 is on y-axis, and the value of M is calculated

Let x = 0 be taken into two formulas, and then y = M & # 178; - m y = - 3M + 4. By subtracting the two formulas, we can get: 0 = M & # 178; + 2m-4, M1 =, M2 = (I forgot the formula for finding the root ····) there are two intersections between the parabola and the x-axis, then

An applied problem about meeting problem
A. B is 693 kilometers away. Car a drives from a to B at 8 a.m., driving 42 kilometers per hour. Car B drives from B to a at 9:30 a.m., driving 48 kilometers per hour. When and when do the two cars meet on the way in the afternoon?

(693-42x1.5) / (42 + 48) = 7 hours
9:30 am plus 7 hours
So we met at 16:30 p.m

If the distance between point m and point F (4,0) is less than 1, then the trajectory equation of point m is______ ．

According to the meaning of the question, the distance between point m and point F (4,0) is 1 less than the distance from point m to line L: x + 5 = 0, which means that the distance between point m and point F (4,0) is equal to the distance from point m to line L: x + 4 = 0, which satisfies the definition of parabola, so p = 8, the trajectory equation of point m is y2 = 16x, so the answer is: y2 = 16x

The equation (3x + 2) & sup2; + (X-5) (X-5) = 49 is reduced to a general form
No, the wrong number is (3x + 2) & sup2; + (X-5) - (3x + 2) (X-5) = 49

（3X+2）²+（X-5）-（3x+2)（X-5）=49
9x²+12x+4+ (x-5)(1-3x-2)=49
9x²+12x+4+ (x-5)(-1-3x)=49
9x²+12x+4-x-3x²+5+15x=49
6x²+26x+9=49
6x²+26x-40=0
Divide each item by two
3x²+13x-20=0