A few math problems, I hope you can help! Thank you!

1. The original formula = 25 * (12 + 89-1) = 25 * 100 = 2500 is not a problem with the data, and it is not simple).

5.The product of four integers a, b, c, and d whose absolute values are not equal to each other is 24, can you determine the value of the sum of these four integers a+b+c+d? (Hint: there may be even negative numbers in a, b, c, and d).

There are multiple situations to discuss.

6、.Shaped like |a b c d|The formula is called the second-order determinant, and its algorithm is represented by the formula |a b c d |=ad-bc, calculated by the law of order: |-2 3 -1 -5|=（-2）×（5）-3×（-1）=10+3=13

both a and b represent rational numbers, and a+b<0, ab<0, |a|<|b|.

1) Try to represent a, b, -a, -b on the number line;

2) Use "<" to connect a, b, -a, -b with 0.

The first one you can draw yourself.

2) b<-a I wish you happiness.

1. Merge similar items: 25 * 78 = 100 * 78 42, merge similar items: 0

3, through the division, and then split 2007 = 2008-1 In this way, the specific self-counting.

4. Calculate 3*8 first, in the calculation.

5, because it is an integer, decompose the prime factor, 24 = 2 * 2 * 2 * 3 * 1, the absolute values should be 1, 2, 3, 4 respectively

6, this won't, I've forgotten about this thing.

7, b<-a did the rest by himself.

1.The length of the cut is 18 * 2 9 = 4 , so the remaining length is 18-4 = 14 (m).

2.According to the title, because girls account for 5 11, boys account for 6 11, and you know that there are 150 boys, so divide 150 by 6 11 to get the total number! Answer: 275 people.

3.More than the original plan of 1 5, that is, the actual purchase of 1 + 1 5 = 6 5, so the original plan to buy 2520 divided by 6 5, answer: 2100 copies.

4.Pay attention to the three words "planned", according to the title: 2500 * 55% + 2500 * 57% = 2500 * (box) in the first half of the month, so 2800-2500 = 300 (box) more than the original plan was produced

The human box just has nothing to do, so just do it.

But do people who can't do this kind of questions use computers?

I'm skeptical.

(1) 18 (2 9) = 4 (m).

2) Since girls make up 5 11 of the whole school, then boys make up 6 11 of the whole school, so the number of students in the whole school = 150 (6 11) = 275

3) Suppose you originally planned to buy x books.

Then: x(1+

x=2100 So the original plan was to buy 2100 books.

4) Number of boxes completed in the first half of the month = 2500

Number of boxes completed in the second half of the month = 2500

Chalk produced more = number of boxes completed in the first half of the month + number of boxes completed in the second half of the month - number of boxes planned to be produced = 1375 + 1425-2500 = 300 (boxes).

(18 2 9) 18 4 14 (m) Answer: There are 14 meters left.

(1 5 11) 275 (person) Answer: There are 275 students in the whole school.

(1 5 1) 2100 (book) Answer: The original plan was to purchase 2100 books.

(55 57 ) 2500 50 (box) A: This month will produce 50 more boxes of chalk than originally planned.

1.Set x hours later for car A to catch up with car B.

Because car A departs from A and returns to chase B 2 hours later, it takes A 4 hours to return to point A, so: 40x(x-4)=30x

10x=160

x=16 hours.

2.The original road is set up to be x kilometers long.

x÷8=（x+3）÷9 - 1/8

x=8/9x + 8/3 -1

1/9x=5/3

x=15 km.

3.Let the ab distance be x

The time from point B to point C is 3 - X (8+2)].

x - 2 = （8 - 2）x 【3 - x÷（8+2）】x=20 - 3/5x

x= kilometers.

4.Let the total time be x

It should be a round trip up and down the mountain, so the length of the road up the mountain is kilometers, and the length of the road down the mountain is also kilometers x= +

x=2/5÷（m + n）

x=2(m+n) 5mn hours.

5.Motorcycles depart from A to B, trucks depart from B to A, how long does it take for the cars to meet?

Set the time to x45x + 35x = 40

x = hours.

6.Set the time to x

All team members travel 35x distance in x time, as Team 1 travels 10 kilometers and then turns back to meet up with other teammates.

So: 35x + 45 x (x -10 45) = 1080x = 20

x = hours.

1 set: After x hours, car A catches up with car B.

40 (x-2)-30 (x-2) = 2 * (40 + 30) 2 set: the original road length is x kilometers.

x+3)/9-x/8=1/8

To be continued).

Question 1: 40x-30x=40*2 x=8

Question 2: (x+3) 9-x 8=1 8

The questions are not too difficult, so I'll help you solve them first, hehe.

Solution: From point C, CE is perpendicular to AB, (and the tangent should be perpendicular to AB and intersects on the circle, assuming that the tangent is CO, it is only necessary to prove that O and E coincide, CE is already perpendicular, that is, the length of CE = the length of CO, and the two points coincide, that is, the length of CE is the radius of the circle).

A=30 In a triangular CAE, the right-angled side opposite by the 30 degree angle is half the hypotenuse, so CE= AC

So ce is equal to the length of the radius.

Add a guide line from the center of the circle to the tangent point.

Then prove that it is perpendicular to AB and it would be fine

If the ratio of the corresponding height of two similar triangles is 4:5, then the similarity ratio of the two similar triangles is 4:5; The ratio corresponding to the midline is 4:5; The ratio of the corresponding angle bisector is: 4:5.

are equal to the similarity ratio.

1.The ratio of all corresponding line segments of a similar triangle (corresponding to the height, corresponding to the middle line, corresponding to the angle bisector, circumscribed circle radius, inscribed circle radius, etc.) is equal to the similarity ratio. 2.

The ratio of the circumference of similar triangles is equal to the similarity ratio. 3.The ratio of the area of a similar triangle is equal to the square of the similarity ratio.

4.Congruent triangles are a special case of similar triangles, with a similarity ratio of 1, which means that two similar triangles should have the letters representing the corresponding vertices written in the corresponding positions. If it is "abc is similar to def" in the literal language, then it means that the corresponding vertices of the two triangles are not written in the corresponding positions, and if it is "abc def" in the symbolic language, then it means that the corresponding vertices of the two triangles are written in the corresponding positions.

5.Similar triangles correspond to equal angles and proportional edges.

The ratio of the height corresponds to according to the triangle. The ratio of the bisector of the corresponding angle and the ratio of the corresponding midline are both equal to the similarity ratio.

This problem can be converted into a number between 50 and 70, which is divisible by 3, 4, and 5 at the same time, so this number should be 61

If you add 1 person.

This way it is full every time.

So at this point it is a common multiple of 3,4,5.

The least common multiple of 3,4,5 is 3 4 5 = 60

So there are 60-1=59 people.

There are x people, and x+1 is a number that can be 3, 4, and 5; Equivalent to divisible by 60, then x is 59 people.

Explain that the number of people is not a multiple of 3, 4, 5.

3*4*5=60 Then the number of people is 60-1=59.

Set x people.

x+1）/3=0

x+1）/4=0

x+1）/5=0

So, x+1 is divisible by 3 4 5, which is a multiple of their least common multiple 60.

And because we know in the question: x+1=60

x=59

Cubic centimetre.

From the formula of the circumference of the bottom surface of the cone, the radius of the bottom surface is 1 cm, so the length and width of the cuboid are 2 cm and 2 cm respectively, and the height is 5 cm, so the volume is length times width and height, which is equal to 20.

2. The bottom radius is 9 meters from the circumference of the bottom surface of the cone, then the volume of this pile of sand is equal to 1 3 9 2 3 = cubic meters) The second question is to turn cubic meters into tons, and multiply by the density of sand. One side of sand is about a ton, so 128 vehicles are needed.

Fold; 3 times.

1 Square side length = bottom diameter = volume = 2 2 5 = 20 (cubic centimeters) 2 bottom radius = volume = 1 3 · 9 ·3 = number = sand density 5

3 are tripled.

1. The circumference of the bottom surface of the cone is cm, so the radius is 1 cm, so the triangular length of the cuboid with a square cross-section is 2,2,5 volume 2*2*5 = 20 cubic centimeters.

2. The circumference of the bottom surface is meters, so the radius is 9 meters, and the volume of sand r 2h 3 = cubic meters can be transported at least 51 vehicles at one time.

3. The height of the cone is 3 times the height of the cylinder.

If a cylinder and a cone are equal in volume and equal in height, then the base area of the cone is (1 3) of the base area of the cylinder

The first challenge: to cut a square with a cross-section into the largest cone. The base circumference of the cone is known to be centimeters and 5 centimeters high. What is the volume of this rectangle?

Analysis: According to the volume formula of the cuboid, the base area is high, so the most important thing in this problem is to require the volume of the cross-sectional square of the cuboid, and the area of the square only needs to be the side length of the square, and the cuboid is cut into the largest cone, and the side length of the square of the cross-section of the cuboid can be obtained is the diameter of the circle at the bottom of the cone, and the circumference of the bottom surface of the cone is already known, and the value of the radius r can be found according to the circumference formula c 2 r of the circle, and the side length of the square of the cross-section of the cuboid is 2r

2*, r=1 cm, 2r=2 cm.

Box volume = square area * height = 2 * 2 * 5 = 20 cubic centimeters.

The volume of the cuboid is 20 cubic centimeters.

The second puzzle: what is the volume of a pile of sand in the shape of a cone, with a circumference of meters at the bottom and a height of 3 meters? Analysis:

According to the circumference of the bottom surface, find the radius of the bottom surface, then find the bottom area, and finally according to the conic volume formula: the bottom area * height * 1 3 can find the volume.

Column formula: 2*m r=9m.

s = base area * height * 1 3 = cubic meters.

How many vehicles do you need to transport all this sand in a 5-ton truck at once?

Analysis: (Is this a question to know the density of sand, or is the question incomplete?) 1 ton of sand is about equal to a cubic meter, and a 5-ton car can hold a cubic meter of sand, and a cubic meter of sand requires several 5-ton cars, that is, it takes 106 cars.

The third problem: if a cylinder and a cone have the same volume and the same ground area, then the height of the cone is 3 times the height of the cylinder.

Analysis: Cylindrical volume = base area * height.

Cone volume = base area * height * 1 3

The volume is equal, the base area is also equal, and the height of the cone that can be pushed out is 3 times that of the cylinder.

If a cylinder and a cone are equal in volume and equal in height, then the base area of the cone is (3 times) the base area of the cylinder

Analysis: Derived from the volume formula for cylinders and cones.