Three math problems for the first year of junior high school to process! Speed!

1.The test is the condition for the binary equation to be true.

In the first case: 2a+2=2, 3a-2b+2=1, you can solve the equation yourself.

In the second case: 2a+2=1, 3a-2b+2=2, you can solve the equation yourself.

2.Substituting x=7, y=1 into 3x-ay=16, 2x+by=15, the values of a and b are solved.

Substituting the values of a and b into 3(x+y)-a(x-y)=16,2(x+y)+b(x-y)=15, you get a binary equation about x,y, and you can solve the equation yourself.

3.Test inequalities.

Set the number of correct questions to x

A score of not less than 60 points will be awarded, that is, the score after deducting the deducted points should be greater than or equal to 60, so 4x-2 (25-x) 60

x≥55/3

x is an integer, so you should pick at least 19 questions correctly to win a prize.

1.According to the question, only 2a 2 of x and 3a 2b 2 of y are 1 to satisfy the meaning of the question, so a 1, b 1 2 2Substituting x 7 and y 1 gives 21 a 16, 14 b 15, solves a 5, b 1, and then substitutes the last equation to get x 4, y 3 3

Answer at least one question correctly. 4x 2 (25 x) > = 60, simplified to 6x> = 110, and x is an integer, so the minimum value of x is 19 hopes!

The first and second questions are purely calculations, too simple, I won't talk about them, the third question process - let the correct x wrong and the unfilled y be derived from the question, 4x-2y=60 x＋y=25..Write the rest yourself

Set the water speed v1 and the ship speed v2

When found, the distance between the two = 5v1 + 5 (v2-v1) = 5v2 catch up time = 5v2 ((v1 + v2)-v1) = 5v2 v2 = 5, so it takes 5 minutes to catch up.

If the speed of the ship is v1 and the water speed is v2, then when the barrel falls into the water, it will be separated by s=5(v1-v2)+5v2=5v1 within five minutes, which is the movement of the barrel and the boat in the opposite direction, and then the boat turns its head to chase the barrel, then the relative velocity is v1, then there is t=s v1=5.

From the example of the given special form, the law can be derived, which can be directly applied:

One-third (1*2*3-0*1*2) + one-third (2*3*4-1*2*3)+....one-third (100*101*102-99*100*101).

One-third (100*101*102).

In the same way: 1*2+2*3+......n(n+1)

One-third (1*2*3-0*1*2) + one-third (2*3*4-1*2*3)+....one-third (n*(n+1)*(n+2)-(n-1)*n*(n+1)).

One-third (n*(n+1)*(n+2)).

Let's look at the special form first:

1*2*3=1/4 (1*2*3*4-0*1*2*3).

2*3*4=one-quarter (2*3*4*5-1*2*3*4).

3*4*5=1/4 (3*4*5*6-2*3*4*5).

Adding these three equations gives us the following equations: 1*2*3+2*3*4+3*4*5=one-quarter (3*4*5*6)=90

So. 1*2*3+2*3*4+……n(n+1)(n+2)

Quarter (1*2*3*4-0*1*2*3) + quarter (2*3*4*5-1*2*3*4) + quarter (3*4*5*6-2*3*4*5) + ....Quarter (n(n(n+1)(n+2)(n+3)-(n-1)n(n+1)(n+2)).

Quarter (n(n+1)(n+2)(n+3)).

Be good at finding patterns and analogies! As can be seen from the example given by the sum of the formula: 1*2+2*3+......n(n+1) as an example.

The first factor, 1*2, is equal to one-third of the difference between (the product of the last term of 1, 3 and these terms) minus (the product of the previous term 0 of 1 and these two terms), where 1 is the first term.

The last factor, n*(n+1), is equal to one-third of the difference between (the product of the last term of n(n+1) and these terms) minus (the product of the previous term of n(n-1) and the product of these terms), where n is the nth term.

The factors on both sides of all equations are added separately, and the previous product on the numerator of each factor cancels out the next product on the next factor.

If you want to calm down and look at this question, although the description is more complicated, it will be much clearer after writing on straw paper!

Hope it helps!!

1.The bottom side of the carton is 16-2x cm long

Base area = (16-2x) squared.

The height of the carton is x cm

So the volume is the square volume of the bottom surface area * height = x * (16-2x) = 3 * (16-2 * 3) * (16-2 * 3) = 3 * 10 * 10 = 300 cubic centimeters.

x= volume= cubic centimeter.

Therefore, when the side length of the cut small square is 3, the carton volume is larger.

2.Just put x=3 or substitute it into the above formula.

v=（16-2*3)^2*3=300

v=（16-2*

v=（16-2x)*(16-2x)*x

v=（16-6）*（16-6）*3=300v=（16-7）*（16-7）*

So when x is 3, the volume is large.

1: (16-2x) squared by x

2: Bring it in.

The epitaph of Diophantus is a poem of harmony: 1 6 of his life was a happy childhood, and he lived another 1 12, and the thin beard climbed up his face, and after 1 7 of his life, he had a companion called Zi Hu, and he teased him for another 5 years, and he had a little angel, but the child's life was only half of his father's, and the old man who was overly sad suffered for 4 years, and he also said goodbye to the world.

In fact, Diophantus stated the length of his life in his epitaph:

The solution is: Set the loss of the figure to live to be x years old.

x=1/6x+1/12x+1/7x+5+1/2x+4x=25/28x+9

3/28x=9

x=84 So he lived to be 84 years old.

Age of marriage: 1 6 * 84 + 1 12 * 84 + 1 7 * 84 = 33

(1) A household uses electricity in May, and pays a total of yuan for electricity, and the value of a is because of yuan.

So the monthly electricity consumption exceeds.

Therefore, if the average electricity bill of the household in June is $, how many kWh of electricity will be shared in June? How much is the electricity bill?

Set the shared electricity consumption x kWh in June.

x 90 kWh.

Electricity charges should be paid.

Yes a kW cost 84-a is the excess electricity cost is * 70% electricity consumption is xa* + x-a) * = x*

x* is the fee.

After a few minutes, when the two water pipes are opened at the same time, and the total water output per minute is found when both water discharge pipes are opened=(17-8) (12-2)=

2. The amount of water received by each student = (18-17) 4=, the remaining 18 students received the water = 18 * minutes, and the total time of 22 people is 5 + 2 = 7 minutes.

3. First of all, judge whether the water is enough to put it for 10 minutes, 2+17 is greater than 10, so the water will not be discharged within 10 minutes.

First remove the 4 people who received the water in the first 2 minutes, and after 2 minutes, each water pipe will come out every minute, and after 8 minutes, a single water pipe will come out of the water, people, 2 water pipes are 28 people, plus 4 people in the first 2 minutes, a total of 32 people.

1. When both drain pipes are open, find that the total water output per minute is 1 liter. Because a water pipe puts two liters of water in two minutes.

2. The first 22 students need to receive water at the end, and from the beginning to 2 minutes, there are exactly 4 students at the end of the water connection, indicating that one water pipe can connect two students to water in one minute, and then two water pipes can make four students receive water in one minute. When two minutes later, there are still 18 students, and it takes minutes, plus the first two minutes, so it's minutes.

3. According to the water discharge method, find out that within 10 minutes between classes, a maximum of 36 students in the class can receive the water in time. There are 4 people in the first two minutes, and 4 people per minute after that, for a total of 4+(10-2)*4 36 people.

1.liters per minute.

2.Which method is used Method 1: 9 minutes Method 2: Each student uses liters of water, 3 32

1, -2 (n-1) power multiplied a to the nth power.

2, -2014 I am deeply skeptical that 2016 can be drawn upstairs.

3. Correct Because 4x -3x-2<6x -3x+6 so m134 so there is no discount for the first time, and the actual shopping is 134 yuan.

500*90%=450 (yuan) Because 466>450, the second actual purchase exceeds 500 yuan.

466-450) (1-20%) = 20 (yuan) 500 + 20 = 520 yuan The second actual purchase is 520 yuan.

A total discount of 20 yuan.

9) 85 5 = 15 15 * 2 = 30 Because 30-1=29 so October 29 is Saturday and the third Saturday is October 15.

4*ab=ab=11)（1）1×2+2×3+3×4+……10×11

2）1×2+2×3+3×4+……n×（n+1）

1/3*(n^3 + 3n^2 +2n)

12) Solution: Set a total of x people.

x/3+2=x/2-9/2

x/6 =13/2

x =39x/3+2 =15

A: There are 39 people in total and 15 albums.

13) 3 old men, 4 pears.

Solution: If there are x pears, then (x-1) old man.

x=2(x-1)-2

x=4x-1=3

15) 1. 5000-40*92=1320 (yuan).

2. Solution: If there are x people in school A, then there are people in school B (92-x).

50x+60(92-x)=5000

10x=520

x =5292-x=92-52=40 A: 52 students from school A and 40 students from school B.

3. Buy the two schools together.

1) -2n to the nth power Because n is a positive integer, it is multiplied by -2 each time, so the result is -2n to the nth power.

That's a lot, think about the rest.

The n-1 square of question 1 (-2) is multiplied by a to the nth power.

2 Question: 2016

Question 3: Correct. m-n can be used to find out.

4 questions, 1 in A. s1`s2=2 s2`s3=2...One is s1 = s3 = s5 = ....s2009=2a so s2010=...

Leave the rest to someone else, you take so much at once, it's a headache to watch.

Question 12: Solution: There are x people.

3x+2=2x-9

x =-11

There are 11 people. 3 11 + 2 = 35 albums.