Given that the set P = {x | - 2 ≤ x ≤ 5}, q = {x | - K + 1 ≤ x ≤ 2k-1} satisfies P ∩ q = q, the value range of real number k is obtained

Given that the set P = {x | - 2 ≤ x ≤ 5}, q = {x | - K + 1 ≤ x ≤ 2k-1} satisfies P ∩ q = q, the value range of real number k is obtained

∫ P ∩ q = q ∢ Q ⊆ P (1) when K + 1 > 2k-1, i.e. K < 2, q = ⊆ P, satisfying the condition; (2) when K + 1 ≤ 2k-1, i.e. K ≥ 2, K + 1 ≥ - 22k-1 ≤ 5, the solution is - 3 ≤ K ≤ 3, at this time 2 ≤ K ≤ 3; in conclusion, the value range of real number k is k ≤ 3

If f (x) is an even function and a decreasing function on (0, infinity), and f (3) = 1, then the solution set of inequality f (x) is less than 1

If f (x) is an even function and a decreasing function on (0, infinity), the closer the point is to the y-axis (i.e. x = 0), the larger the function value is
From F (3) = 1
F (x) 3 interval
The solution set is x > 3 or X

A and B leave from a and B at the same time. When they first meet, they are 90 kilometers away from a station. Then they go on at the same speed and return to each other's station immediately. By the second meeting, B wakes up 60 kilometers more than A. how many kilometers is the distance between a and B?

When they met for the second time, the total distance between the two places was three times,
So the first time we met, B was more than a 60 / 3 = 20 kilometers
A. B the distance between the two stations is 90 + (90 + 20) = 200 km

123-4-5-6 = 8-9 + 100 move three matches so that the number is still 100 ~ ask the gods to cover

123-4-5-6-8+0=100
1 the first original = sign moves to the - sign in front of 9+
2. The second one in the middle of the original 9 moves to make 9 zero
3. The third one is the original 100, and the number + in front of it moves to become=
People oriented!

15 application questions of linear equation of one variable (with answers) should be short!

The distance between a and B is 162 kilometers. A slow train leaves from station a and goes 48 kilometers per hour. An express train leaves from station B and goes 60 kilometers per hour
If two trains are going towards each other, how many hours will it take for the slow train to run for one hour before they can meet? (solution of linear equation with one variable)
Let the two cars meet in X hours
48(x+1)+60x=162
48x+48+60x=162
108x=114
x=57/53
The data is awkward
Two trains go together at the same time (fast train is behind), how many hours can we catch up with the slow train? (solution of linear equation with one variable)
Let's catch up in X hours
60x-48x=162
12x=162
X = 13.5 hours
A: 13.5 hours later
It took 2.5 hours for a passenger ship to travel downstream from a to B, and 3.5 hours for a passenger ship to travel upstream from B to a. the average speed of the passenger ship in still water can be obtained when the velocity of the current is known to be 4 km / h? (solution of linear equation with one variable)
The static water velocity of passenger ship is set at x km / h
2.5(x+4)=3.5(x-4)
2.5x+10=3.5x-14
3.5x-2.5x=10+14
x=24
A: the still water speed of the passenger ship is 24 kilometers per hour
A group of students practice marching and walk at the speed of 5 kilometers per hour. After 3 hours of departure, the school correspondent catches up with the students at the speed of 60 kilometers per hour. How many hours does it take for the school correspondent to catch up with the student team? (solution of one yuan one time equation)
Let's catch up in X hours
60x=5（x+3)
60x=5x+15
55x=15
x=3/11
Answer
A slow train departs from a certain station and travels 48km per hour. After a period of time, an express train departs from the same station and runs 72km per hour. After another 1.5 hours, it catches up with the slow train. How many hours has the slow train gone before the express train departs
? (solution of linear equation with one variable)
The local train has been running for X hours
48x+48×1.5=72×1.5
48x+72=72*1.5
48x=36
x=0.75
A: the local train has been running for 0.75 hours
If a person walks from village a to village B, if he walks 4 kilometers per hour, then he is 1.5 kilometers away from village B at the scheduled time; if he walks 5 kilometers per hour, then he can reach village B in half an hour less than a certain time. How many hours is the scheduled time and how many kilometers is the distance from village a to village B? (solution of one yuan linear equation)
Set the scheduled time to x hours
4x+1.5=5(x-0.5)
4x+1.5=5x-2.5
5x-4x=1.5+2.5
x=4
Distance: 4 × 4 + 1.5 = 17.5km
A and B walk around a 400 meter runway. If they walk from the same place, they will meet in 2 minutes. If they walk from the same place, they will meet in 20 minutes. If a's speed is faster than B's, how fast can they walk
Let a speed be x meters per minute and B speed be 400 / 2-x meters per minute
20x-20（400/2-x）=400
x-(200-x)=20
x-200+x=20
2x=220
x=110
400/2-x=200-110=90
A: the speed of a is 110 meters per minute, and that of B is 90 meters per minute
A company set out from the station to carry out a mission. The marching speed was 6 km / h. 18 minutes later, the station received an emergency order and sent a correspondent Xiao Wang to deliver the order to the company within a quarter of an hour. Xiao Wang rode a bicycle to catch up with the company along the same road at the speed of 14 km / h and asked if he could complete the task within the specified time?
It takes x hours for Xiao Wang to catch up with the company
14x=6*18/60+6x
14x=1.8+6x
8x=1.8
x=0.225
225 hours = 13.5 minutes ＜ 15 minutes
Xiao Wang can finish the task
A passenger car and a freight car are running in the same direction on parallel tracks. The length of the passenger car is 200 meters, and the length of the freight car is 280 meters. The speed ratio of the passenger car to the freight car is 5:3. The crossing time for the passenger car to catch up with the freight car is 1 minute. Find the speed of each car. If the two cars are running in opposite directions, what is the crossing time? (linear equation with one variable)
It is assumed that the speed of passenger cars is 5x meters per minute and that of freight cars is 3x meters per minute
5x-3x=200+280
2x=480
x=240
5x=240×5=1200
3x=240×3=720
A: the speed of passenger cars is 1200 meters per minute, and that of freight cars is 720 meters per minute
Let the crossover time be y minutes
1200y+720y=200+280
1920y=480
y=0.25
A: the crossing time is 0.25 minutes
1. Two warehouses hold grain. The first one is three times as much as the second one. If 20 tons are taken from the first warehouse and put into the second one, the grain in the second warehouse is 5 / 7 of that in the first one. How much grain does each warehouse have?
2. The three townships of a, B and C jointly build water conservancy projects, and share the cost of 1440 yuan according to the area ratio of 3:2:4. How many yuan are allocated to each of the three townships?
3. For a two digit number, the sum of the ten digit number and the number on the one digit is 11. If you transpose the number on the ten digit number and the number on the one digit number, you can get a number 63 larger than the original number. What are the original two numbers?
4. A project a alone to 10 days, B to 12 days, C to 15 days, a C first do three days, a left B to work! How many days
5. There is 8% salt water 40kg to make the salt water 20%. How much salt should be added? How much kg of water should be evaporated?
6. There are 70% alcohol and 98% alcohol. How much can be mixed into 84% alcohol 100kg?
7. The distance between Party A and Party B is 120 km, and the speed of Party B is 1 km faster than that of Party A per hour. Party A starts from Party A at 2:00, and then Party B starts from Party B and goes opposite party A. after 10:00, Party B meets Party A to find the speed of Party A and Party B
one
The first warehouse has an original capacity of 3x tons, and the second warehouse has an original capacity of X tons
(3x-20)*5/7=x+20
5(3x-20)=7(x+20)
15x-100=7x+140
8x=240
x=30
3x=3×30=90
A: the first warehouse used to be 90 tons, and the second warehouse used to be 30 tons
two
Let a, B and C share 3x, 2x and 4x yuan respectively
3x+2x+4x=1440
9x=1440
x=160
3x=3×160=480
2x=2×160=320
4x=4×160=640
A: 480 yuan for Party A, 320 yuan for Party B and 640 yuan for Party C
three
Let the original tens of digits be x and the individual digits be 11-x
10(11-x)+x-(10x+11-x)=63
110-10+x-9x-11=63
18x=36
x=2
11-x=11-2=9
A: the original two digit number is 29
four
It will take X more days
(1/10+1/15)*3+(1/12+1/15)x=1
1/2+3/20*x=1
3/20*x=1/2
x=1/2*20/3
x=10/3
A: it will take another 10 / 3 days
five
1) Let's add salt x kg
40×8%+x=(40+x)*20%
3.2+x=8+0.2x
0.8x=4.8
x=6
A: add 6kg salt
2) Set evaporation water x kg
(40-x)*20%=40*8%
8-0.2x=3.2
0.2x=4.8
x=24
A: it needs 24 kg of evaporated water
six
It needs 70% alcohol x kg, 98% alcohol 100-x kg
7%x+98%(100-x)=100*84%
0.07x+98-0.98x=84
0.91x=14
x=200/13
100-x=100-200/13=1100/13
A: 70% alcohol 200 / 13kg, 98% alcohol 1100 / 13kg
seven
Let the speed of a be x km / h, and that of B be x + 1 km / h
（2+10）x+10（x+1)=120
12x+10x+10=120
22x=110
x=5
x+1=5+1=6
A: the speed of a is 5km per hour, and that of B is 6km per hour

1+2+3+4+5+6+7+8+9+10=? 1+2+3...+100=? 1+2+3+4...+1000=? 1+2+3+4...+10000=?

1+10+2+9+.+5+6=11*5=55
1+100+2+99+.+50+51=101*50=5050
1+10000+2+9999+.+5000+5001=10001*5000=50005000

18 plus 50% of a number is exactly 22. Find the number

(22 - 18)÷50%
= 4 ÷ 50%
= 8

English translation

Whose book is it on the table?

If the actual distance is 1000000 times the distance on the map, what is the scale of the map______ 1 cm on the figure represents the actual______ Kilometers

If the actual distance is 1000000 times of the distance on the map, then the scale of this map is 1:10000000 cm = 10km; then 1cm on the map means 10km

If integers x, y and Z satisfy the following conditions: x times of (25 / 8), y times of (14 / 25) and Z times of (16 / 35) are equal to 2, find the value of (Z-Y) times of X

(2x of 5 times y of 7 times y of 2 times 4Z of 2) / (3x of 2 times 2Y of 5 times Z of 5 times Z of 7)
Merge with base
(2x-2y-z) times of 5 times (Y-Z) times of 7 times (y + 4z-3x) times of 2 = 2
Let 2x-2y-z = 0, Y-Z = 0, y + 4z-3x = 1
The solution is x = 3, y = 2, z = 2
So (Z-Y) times of x = 1