Help, math problems, fast. Math problems, hurry, hurry, thank you

Let one diagonal of the rhombus be x centimeters long, and the other diagonal 10-x centimeters long.

The area of the diamond.

The product of two diagonals is 2

x(10-x)/2

So. x(10-x)/2=12

x(10-x)=24

x^2-10x+24=0

x-4)(x-6)=0

x=4 or x=6

The other diagonal is 10-4=6 or 10-6=4 so. The two diagonals of this rhombus are 4 cm and 6 cm long, respectively.

The circumference of this rhombus.

Root number [(4 2) 2 + (6 2) 2] * 44 times root number 13 cm. Centimeter.

Let the two diagonal lines be x and y

x+y=10

The area of the diamond is half of the product of the diagonal.

Thus xy 2 = 12 and xy = 24

Because the diamond diagonal bisects perpendicular to each other, the diamond is divided into four congruent right triangles.

The hypotenuse of each right triangle is the side of the diamond, and the two right sides are half of the two diagonals of the diamond.

According to the Pythagorean theorem, the length of the side of the diamond is (x 2) +y 2) = (x +y ) 2

Because x +y = (x + y) -2xy = 100-48 = 52, the length of the diamond side is 52 2= 13

The perimeter is the length of each diagonal without having to solve the quadratic equation.

Solution: The two diagonals of the rhombus are a and b, and the side length is c.

Then: a+b=10 (1).

1/2ab=12 (2)

From (1) to a=10-b to (2) to obtain: b = 4 or b = 6 then a = 6 or a = 4

c 2 = (1 2a) 2 + (1 2b) 2 = 2 2 + 3 2 = 13, so c = root number 13

Therefore, the circumference of the diamond shape is 4 times the root number 13cm.

Let the two diagonals be x and y;

x+y=10；

Because the diagonals of the diamond are perpendicular to each other;

2xy=12, i.e. xy=6;

Solving the equation gives two diagonal lines of cm;

So the side length is the root number 13 of the half;

Because the four sides of the diamond are equal;

So the circumference is 2 root number 13 ie.

1: 2178, the three numbers are 2: the 8th number is 21 81, the denominator is 9 squared, and the numerator is the sum of the first two numbers. 3: Let this number be x, and move it to the right by one decimal place.

1. The time for the tortoise to finish the race: 5000 80 = minutes) The time for the rabbit to finish the race: 5000 100 = 50 (minutes) The number of times the tortoise presses when it arrives at the same time: (times).

The tortoise had to press at least 7 times to win.2 Burn every day: (200-b) a The cafeteria bought 200 kilograms of coal, which had been burned for a day, and B kilograms remained, burning ((200-b) a) kilograms per day on average.

3 The sum of a natural number and 4 is a multiple of 6, and the difference with 4 contains a factor of 8, then the minimum natural number that satisfies the condition is 20

4. Sawing a long cylindrical timber into 3 small cylinders, increasing the surface area by 80 square decimeters, the volume of this timber is (cubic meters.

5. Let the speed of car B be v kilometers per hour.

The speed of car A is 4v 3 km/h.

The distance between A and B is 4v 3 7 km.

Find v below, i.e., solve the problem.

7v + 210 = 4v/3 × 7

v + 30 = 4v/3

3v + 90 = 4v

v = 90

The distance between A and B is.

4v 3 7 = 840 km.

Mitsubishi column volume = base area times height.

Mitsubishi cone volume = 1 3 base area times height.

So: the volume of the triangular prism is 4 times the root number 3

Base area = (root number 3) * 2 2 4 = root number 3

Volume = (1 3) Base Area * Height = (1 3) (Root No. 3) * 4 = (4 3) Root No. 3

Set the top to be x the pants to be y

Because: 10x+8y=24

2x=3yso:x=3 2y

The calculation is slightly x=36 23 meters, y = 24 23 meters, 36 23 meters of cloth for each jacket, 24 23 meters for each pair of pants A: 85 * B: 80*

Option B.

1) Because ef=af-ae and ae= af=, so ef=

In the same way: hg=

2) A; Equal.

Because efgh is the midpoint of the four sides, ef=

The same goes for EH, FG.

So efgh is diamond-shaped.

By vector ab-vector ad=vector db, vector cb-vector cd=vector dbVector EF and vector HG can be introduced

1.It takes 5000 80 = minutes for the turtle to run the whole distance, and in order to win, the rabbit must run for at least a minute, and the rabbit only needs 50 minutes to run the whole distance, so let's say that when the rabbit is in the last 1 meter, the turtle will press the remote control on the line, and press it until the turtle enters the finish line, so how many times has it been pressed? Hehe, after the turtle presses the remote control, the rabbit will press n*10% to go backwards for 1 minute, and the turtle can press it again after 1 minute, then the distance of the rabbit backwards is 10 meters for the first time, and 20 meters for the second time. . . .

After 4 times, just 100 meters, then the rabbit needs 1 minute to reach the end point, that is, 5 minutes later, the turtle has to press the 5th time, 50 meters, the 6th time after 60 meters, and let the rabbit run forward for 1 minute, 10 meters from the end point, that is, 8 minutes later, the turtle according to the 7th time back 70 meters, the 8th time back 80 meters, and then let the rabbit run forward for 1 minute, 10 + 50 60 meters from the end point, at this time it has reached 11 minutes, the turtle has not yet reached the end point, and you need to press the 9th time, back 90 meters, Then the rabbit is 150 meters away from the finish line, the rabbit needs minutes to reach the finish line, and the turtle needs minutes to arrive. Therefore, the turtle needs to press the remote control 9 times.

The column formula is like this, after pressing the nth time, the rabbit's backward distance is n 2*(10+10n), and the backward time takes n minutes, then the rabbit runs the backward distance time is (n 2*(10+10n)) 100, and the inequality equation (n 2*(10+10n)) 100+n>=, and the solution is n>=, then you need to press the remote control at least 9 times.

2. (200-b)/a

There are so many questions, and the first question also took me a lot of brains, and I actually gave 5 points, which seriously despised the landlord. :)

The canteen brought 200 kg of coal, burned it for a day, and there was b kg left, burning () kg per day on average?

200-b）/a

m = 15 dm 80 4 = 20 square dm 15x20 = 3 square meters.

logax is a monotonic function.

So. loga2+loga8=4

So the repentant lead is high a=2

1) When x 0, g(x)=log2(x+1), so when x<0, g(x)=-g(-x)=-log2(-x+1)2), and draw a g(x) image.

is a continuous function.

So the excitation is based on the image to get -1< x "Blue Ruler ((Root No. 2)-1)< p>

First of all, say hello to the head of the regiment. After reading the answers of everyone upstairs, only wstx2008 answered the best, but in the third question, he said that s cmdn is equal to s chdg, which is not true, because this only occurs when d is the midpoint.

Regarding this third question, I think there is a problem with the question, and if you look at the answer, it is when EF is parallel to AB, and D is a trisect. I did my own calculations and found that when the EF is not parallel to the AB, there is also a D point that meets the requirements (the D point at this time is difficult to calculate and is far beyond the secondary school level). Perhaps it would be better to change the intersection in the title "Two right-angled edges intersect with two right-angled edges of RT ABC" to vertical.

This will make the question a little more meaningful (both to determine existence and to ask for a specific location, which is enough for middle school students), and besides, this is only the 23rd question, not the last one.

Existence can be considered in this way, from the second question it can be seen that when d is the midpoint, and the right-angled side is vertical, the proportion of the coincident part is 1 2, move the point d to point a (at this time, keep the vertical of the right-angled edge), the limit case is that d and a coincide, then the proportion of the coincident part is 0, in this way, from 1 2 to 0, there will definitely be 4 9 in the middle. The specific calculation can be seen in the answer of wstx2008, of course, there are other practices, such as you may wish to think that ac=1 (because this question has nothing to do with the specific length, some are only the ratio of length, of course, it can also be set to other numbers), let ad=x, you can use x to represent the length and width of the coincident rectangle, and then find x.

(1)1/2

3) Let AB and EF be parallel, the overlapping area formed is a rectangle, the area is DM*MC, and DM+MC=AB can find a value to meet the requirements.

Do the task, I don't know, I'm sorry, help you down.

(1)1/2 (2)1/2

3) The position of d on ab is 1 3 of ab, exists,

Looking at the high score is powerless.

I can only find the answer - -

I don't even know how to do it...

(1) Certify that the S triangle BMD + S triangle DNA is certain, because D is the midpoint of AB.

1.Perimeter =

So radius = circumference 2

So half a circle area = 1 2 * 25 * 25 * square meters.

2.The area of the garden = (square meters.)

The area of the square = the area of the folded desktop, the hypotenuse is the diameter of the circle, and the length of the side of the square is found using the Pythagorean theorem =

So the area of the folded table top = .85*.85 = square meters.

The area of the folded part = square meters.

==r= = area pi*r2=

2.The radius of the garden is, so the length of the square is root number 2, and the area of the square is. The area of the fold is the area of the circle minus the area of the square, which is approximately.