A bug landed at a certain point on the number axis, P0. For the first time, it jumped 1 unit to the left from P0 to P1. For the second time, it jumped 2 units to the right from P1 to P2. For the third time, it jumped 3 units to the left from P2

A bug landed at a certain point on the number axis, P0. For the first time, it jumped 1 unit to the left from P0 to P1. For the second time, it jumped 2 units to the right from P1 to P2. For the third time, it jumped 3 units to the left from P2


Let Po be the coordinate origin, then
For the first time, the insect jumps one unit to the left from P0, and the coordinate is - 1;
For the second time, jump 2 units from P1 to P2 = - 1 + 2 = 1;
For the third time, jump 3 to the left from P2 to P3 = 1-3 = - 2
and so on
PN=(-1)^N*[(N+1)/2]
Where [n / 2] means to take the integral part



Write the symmetric points P1, P2 and P3 of P (3,2) about X axis, Y axis and origin respectively


X-axis, y-axis, symmetry points of origin P1: (3, - 2), P2: (- 3,2), P3: (- 3, - 2)



It is known that P1 (x, y ^ 2) at point P2 (x ^ 2, - y) are two different symmetrical points about the origin. Try to find the coordinates of P1 and P2


|x|=x^2,y^2=|-y|
x=+1,-1.y=+1,-1
p1(1,1);p1(-1,1);p2(1,1);p2(1,-1);
P1 (- 1,1) and P2 (1, - 1)



X + (55-4x) / 5 = 12 to solve the equation


x+(55-4x)/5=12
5x+55-4x=60
5x-4x=60-55
x=5



12-3 (X-2) = 10 + 4x to solve the equation


12-3[x-2]=10+4x
12-3x+6=10+4x
-3x-4x=10-12-6
-7x=-8
x=8\7



Solution equation: 4 (x + 12) + 4x = 416


4(x+12)+4x=416
4x+48+4x=416
8x+48=416
8x=416-48
8x=368
x=46



How to solve [4x-2 (10-x)] - [5 (14-x) - 10 + x-14] = 10


The first step is to simplify [4x-20 + 2x] - [70-5x-24 + x] - 10 = 0
Next, 6x-20-46 + 4x-10 = 0
Again, 10x-76 = 0
Finally, x = 7.6



The solution equation is: 1) x △ 14 / 15 = 1 / 7 2) (1-5 / 8) x = 10 3) 1 / 5 + 4x = 4 / 5


1)x÷14/15=1/7
x=(1/7)*(14/15)=14/(7*15)=2/15
2)(1-5/8)x=10
(8/8-5/8)x=10
(3/8)x=10
x=10/(3/8)=10*8/3=80/3
3)1/5+4x=4/5
4x=4/5-1/5
4x=3/5
x=(3/5)/4=3/20



How to solve the equation 4x-2.4 times 3 = 10.8


4x-2.4×3=10.8
4x-7.2=10.8
4x=18
x=4.5



The second power of 3 - 1 = 8 = 8 times 1; the second power of 5 - 3 = 16 = 8 times 2; the second power of 7 - 5 = 24 = 8 times 3 Find the rules,
Use the square difference formula to prove that your conclusion is correct


(2n+1)^2-(2n-1)^2=8n
(2n+1)^2-(2n-1)^2
=[(2n+1)+(2n-1)][(2n+1)-(2n-1)]
=4n*2
=8n