It is known that the numbers corresponding to two points a and B on the number axis are - 1 and 3 respectively It is known that the numbers corresponding to two points a and B on the number axis are - 1 and 3 respectively, and point P is a moving point on the number axis, and its corresponding number is X (1) If the distances from point P to point a and point B are equal, find the number corresponding to point P; (2) Whether there is a point P on the number axis, so that the sum of the distances from point P to point a and point B is 5? If there is, ask for the value of X; if not, explain the reason; (3) When point P moves to the left from point o at a speed of 1 unit per minute, point a moves to the left at a speed of 5 units per minute, and point B moves to the left at a speed of 20 units per minute. Ask them to start at the same time. In a few minutes, are the distances from point P to point a and point B equal?

It is known that the numbers corresponding to two points a and B on the number axis are - 1 and 3 respectively It is known that the numbers corresponding to two points a and B on the number axis are - 1 and 3 respectively, and point P is a moving point on the number axis, and its corresponding number is X (1) If the distances from point P to point a and point B are equal, find the number corresponding to point P; (2) Whether there is a point P on the number axis, so that the sum of the distances from point P to point a and point B is 5? If there is, ask for the value of X; if not, explain the reason; (3) When point P moves to the left from point o at a speed of 1 unit per minute, point a moves to the left at a speed of 5 units per minute, and point B moves to the left at a speed of 20 units per minute. Ask them to start at the same time. In a few minutes, are the distances from point P to point a and point B equal?

It is known that the numbers corresponding to two points a and B on the number axis are - 1 and 3 respectively, and point P is a moving point on the number axis, and its corresponding number is X
(1) If the distances from point P to point a and point B are equal, find the number corresponding to point P;
|x+1|=|x-3|;
x²+2x+1=x²-6x+9;
8x=8;
x=1;
P is 1;
(2) Whether there is a point P on the number axis, so that the sum of the distances from point P to point a and point B is 5? If there is, ask for the value of X; if not, explain the reason;
|x+1|+|x-3|=5；
When x ≤ - 1; - X-1 + 3-x = 2-2x = 5;
X = - 3 / 2; so there is such a number
-When x ≠ 3 + 5, X ≠ 1;
When x ≥ 3, x + 1 + x-3 = 5;
2x=7;
X = 7 / 2;
Ψ x = - 3 / 2 or x = 7 / 2;
(3) When point P moves to the left from point o at a speed of 1 unit per minute, point a moves to the left at a speed of 5 units per minute, and point B moves to the left at a speed of 20 units per minute. Ask them to start at the same time. In a few minutes, are the distances from point P to point a and point B equal?
20x-5x=3-(-1);
15x=4;
x=4/15;
So in 4 / 15 minutes
I'm very glad to answer your questions. Skyhunter 002 will answer your questions
If you don't understand this question, you can ask,
It is known that there are three ABC points on the number axis, which represent - 24, 10 and 10 respectively
The speed of a is 4 units / s, and that of B is 6 units / s. two electronic ants a and C are facing each other at the same time. Which point of the number axis does a and B meet?
It takes the same time to walk in opposite directions. Set X as the distance between AC, that is 34
If we get the equation 4x + 6x = 34 and calculate x = 3.4, then the distance a takes is 3.4 times 4 = 13.6, and the meeting position is 13.6 units to the right from - 24, then it is - 10.4
Known number axis has a, B, C three-point expression - 24, - 10, 10 have formula expression! Don't use algebra
It is known that there are three points a, B and C on the number axis, which represent - 24, - 10 and 10. Two electronic ant beetles, a and C, have been moving towards each other from two points a and C at the same time. The speed of a is 4 units / second
(1) Ask how many seconds after a to a, B, C distance sum of 40 units
(2) Which two ants meet at the same time on the axis of a and B?
(3) Under the condition of (1) (2), when the distance sum of island a, B and C is 40 units, a turns back and asks whether a and B can still meet on the number axis. If so, ask for the meeting point. If not, please explain the reason
(1) When a is between AB, the sum of distances from a to a, B and C is 40 units. Let the sum of distances from a to a, B and C be 40 units after x seconds. From the meaning of the title, we get 14 + 14-4x + 20 = 40. The solution is x = 2
When a is between BCS, the sum of distances from a to a, B and C is 40 units. Let the sum of distances from a to a, B and C be 40 units after x seconds. From the meaning of the title, 4x + 20 = 40. The solution is x = 5
Answer: the sum of distances from a to a, B and C in 2 or 5 seconds is 40 units
(2) Let a and B meet in x seconds. From the meaning of the question, we get 4x + 6x = 34. The solution is x = 3.4
-24 + 3.4 * 4 = - 10.4 A and B meet at the point - 10.4 on the number axis
(3) After 2 seconds, Party A and Party B can't meet each other. After 5 seconds, Party A and Party B can't meet again. Because in 3.4 seconds, after the first meeting, Party A goes to C and Party B goes to a. the speed of Party B is faster than that of Party A, so Party A and Party B can't meet again
Given the function f (x) = loga ^ (x + B / X-B) and a > 0, b > O, a is not equal to 1, find the range?
Because x + B / X ≥ 2 open root (x * B / x) = 2 * root B
So the maximum value of the formula in brackets is 2 * radical B-B
When 2 * radical B-B ≤ 0 holds, f (x) is undefined
When 2 * radical B-B > 0, the other maximum value is obtained at the position of 0 in brackets
When 0
Given the function f (x) = - √ A / A ^ x + √ a (a > 0 and a ≠ 1), it is proved that if X1 + x2 = 1, then f (x1) + F (x2) = - 1
Evaluation: F (- 2) + F (- 1) + F (0) + F (1) + F (2) + F (3)
There is something wrong with your function input, which makes me work hard for a long time
f(x)=-√a/（a^x+√a）
∵x1+x2=1
∴f(x1)+f(x2)
=-√a/（a^x1+√a）-√a/（a^x2+√a）
=-√a[1/(a^x1+√a）+1/(a^x2+√a）
=-√a(a^x1+√a+a^x2+√a)/[(a^x1+√a）(a^x2+√a)
=-√a(a^x1+a^x2+2√a)/[a^(x1+x2)+√a（a^x1+a^x2)+a]
=-√a(a^x1+a^x2+2√a)/[√a（a^x1+a^x2)+2a]
=-√a(a^x1+a^x2+2√a)/[√a（a^x1+a^x2+2√a)]
=-1
∴f(-2)+f(-1)+f(0)+f(1)+f(2)+f(3)
=f(-2)+f(3)+f(-1)+f(2)+f(0)+f(1)
∵f(-2)+f(3)=f(-1)+f(2) =f(0)+f(1)=-1
∴f(-2)+f(-1)+f(0)+f(1)+f(2)+f(3)= -3
Given that the range of function f (x) = loga (x + ax − 4) (a > 0, and a ≠ 1) is r, then the range of real number a is ()
A. （0，1）∪（1，2]B. （2，+∞）C. （4，+∞）D. （0，1）∪（1，4]
The range of function f (x) = loga (x + ax − 4) (a > 0, and a ≠ 1) is R ⇔ y = x + ax − 4 (a > 0, and a ≠ 1) is (0, + ∞) ⇔ y = x2-4x + a (a > 0, and a ≠ 1), and the range of function f (x) = loga (x + ax − 4) (a > 0, and a ≠ 1) is (0, + ∞) ⇔ △ = (- 4) 2-4a ≥ 0, a > 0, and a ≠ 1
Given the function f (x) = 2x / x + 1. (1) when x > = 1, prove the inequality f (x)
Take F (x) into 0 with 2x / (x + 1) = 1
What is this?! What do you mean
If the range of function f (x) = loga (x + ax-4) (a > 0, and a ≠ 1) is r, find the range of real number a
Let g (x) = x + ax-4, ∵ f (x) = loga (x + ax-4) (a > 0, and a ≠ 1) have the range of R, ∪ g (x) ≥ 2a-4, ∪ 2a-4 ≤ 0. The solution is a ≤ 4, a > 0, and a ≠ 1. In conclusion, the value range of real number a is (0,1) ∪ (1,4]
Given the function f (x) = 2x / (x + 1) (1), when x > = 1, the inequality f (x) is proved
Make equivalent deformation
Inequality f (x) 0, X-1 ≥ 0, x + 1 > 0,
So - x (x-1) / (x + 1) ≤ 0
The base of logarithmic function y = LNX = E > 1, so when x ≥ 1, LNX ≥ 0
So the inequality f (x)
(x²-7x+6)(x²-x-6)+56
(x²-7x+6)(x²-x-6)+56=(x-1)(x-6)(x-3)(x+2)+56=(x-6) (x+2) (x-1) (x-3)+56=( x²-4x-12)( x²-4x+3)+56=( x²-4x) ²-9( x²-4x)-36+56=( x²-4x) ²-9( x²-4x)+20=( ...
Original formula = (X-2) (x ^ 3-6x ^ 2-5x-46)
almost. That's it~~
What about the question
Original formula = (x-1) (X-6) (x + 2) (x-3) + 56
=( x²-4x-12)( x²-4x+3)+56
=( x²-4x) ²-9( x²-4x)-36+56
=( x²-4x) ²-9( x²-4x)+20
=( x²-4x-5)( x²-4x-4)
=(x-5)(x+1) ( x²-4x-4)