A few math contest questions!! Urgent!!!

Use the group of inequalities to solve the second problem!

Only the second way is known at the moment.

You can solve it with a system of binary equations, if you can't ......Alas, try your best.

A truck with a load of 6 tons was transported x times, and a small trailer was transported x + 6 times.

4x=12x=3

So this batch of goods is: 6x=6*3=18 tons.

The problem is: if you divide a box of apples among several children, if each child divides 5 apples, there are 12 apples left; If each child has 8 apples, then one child has less than 8 apples, find the number of apples in the box and the number of children.

The answer is: if there are m apples, and there are x children, which one does not get 8 apples, then m=5x+12 m=8(x-1)+y is 8(x-1)+y=5x+12, then 3x=20-y, x can be 6 5

y corresponds to 2 5 then there are two possibilities, namely.

There are 5 apples for children and 37 apples.

There are 6 children and 42 apples.

*1+ tons.

2. Divide 5 apples, and there are 12 apples left.

If there are 8 apples, there is a child who has less than 8 apples, and there are 3 or 6 less.

Because it is human, it must be divisible.

12+3) (8-5) = 5 children.

5*5+12=37 apples.

or (12+6) (8-5) = 6 children.

5*6+12=42 apples.

AN1: 18 tons of cargo, 3 times for large carts, 9 times for small cars.

The shaded part should be fbh

Analysis: Connect the midpoints of each side of the abc, then the abc is divided into four small triangles of equal size.

In the dbg, the midpoints of the sides are joined to divide the dbg into four small triangles. After observation, it is easy to conclude that the area of ABC is (1 2) 4 4 = 32 (square centimeters).

Hope it helps.

The area of this equilateral triangle is 32 square centimeters.

The area of the equilateral triangle is 32 times the area of the shaded part, i.e. 32 square centimeters.

It should be 22 square centimeters. The most earthy way is to do an equal division of BFH in an equilateral triangle, which can make 22 of them.

Without further ado, let's go straight to the picture.

You haven't even figured out how to answer the shadow part?

y=ax^2-2amx+am^2+2m+1=a(x-m)^2+2m+1

a(m,2m+1)

p(1,3)

So b (2-m, 5-2m).

A=1Y=(x-m) 2+2m+1

x,y) the point of symmetry with respect to (1,3) is the analytic equation of (2-x,6-y)l2 6-y=(2-x-m) 2+2m+1b(2-m,5-2m) on x=0.

The analytic formula of m=2l2 y=1 x 2

l1: y=a(x-2)^2+5

l2: y=-a(x)^2+1

c(1/√a,0)

b(0,1)

a(2,5)

ab^2=4+16=20

bc^2=1+1/a=20

a=1/19

The answer is c

Because of the parallelogram ABCD

So it's easy to get a triangle AEG

Similar to triangular CBG.

The triangle def is similar to the triangle bcf.

Because ae:ad=1:3

So ag:cg=1:3

ef:cf=2:3

"Good = 1", "Wonderful = 2", "True = 9", "Question = 0".

Wonderful question"The number of all the factors represented by the four-digit number is: 3

2) This question is wrong, counterexample: e) but r(1, should be amended as: if e( a, b, c), then e(a, b, c). It is enough to use the property that the sum of the two sides is greater than the third side, and then both sides are squared at the same time.

3) This question is wrong, counterexample: 8 4 + 9 4 = 4096 + 6561>10000 = 10 4, so r(8 4, 9 4, 10 4).

Numeric value Divisibility.

Writing even numbers must contain 2 divisors, this second person can't write even numbers, only odd numbers, and 1 is the divisor of any positive number, so only , and how to write is 6, only can be written, B writes one of them, and A is writing the other. then B will be defeated.

This is the easiest way to reason with logic.

Because a complete product requires both processes to be completed, which means that when the first and second processes are produced in the same quantity, the maximum number of production is the case.

Then there is the equation: Let x people do the first way, 14-x people do the second way, the number of products in the first course = 90 * x the number of products in the first way = 120 * (14-x) so 90 * x = 120 * (14-x).

At this time, x=8 means 8 people in the first lane and 4 people in the second lane.

Solution: X people should be arranged to participate in the first process, and Y people should participate in the second process.

x*90=y*120

x+y=14

The solution yields x=8 and y=6

Answer: 8 people should be arranged to participate in the first process and 6 people should participate in the second process.

Add the area of the blank space on the right side of the ab to get the required triangle area smaller than the semicircle area by square centimeters.

So the result is 1 2x25 if you take the approximation is 36 square centimeters.

Isn't that simple? First of all, the area of the right semicircle = 1 2 * 5 squared, that is, = then the area of this semicircle is equal to the area of A plus the area of the blank space of the right semicircle, that is, A + blank area, and the area of the triangle = 1 2 * 10 * BC

So the following formula is derived.

B) + B = area of the triangle.

B + B = triangle area =

Results=36 Hope it helps.

Calculate the area of the semicircle first, then subtract A plus B, A and B can be expressed as unknowns.

Don't overcomplicate this question, the area of A - the area of B =

Then, the area of A + the common area in the semicircle - the area of B + the common area in the semicircle ) =

It is easy to see that the area of A + the common area in the semicircle = the area of the semicircle B + the common area in the semicircle = the area of the triangle to be sought.

A primary school planted 650 trees this year, 30% more than last year, how many trees were planted last year?

Triangle area sabc = semicircle area = 36

The area of the triangle ABC = the area of the semicircle - the area of A + the area of B = the area of the semicircle - (the area of A - the area of B) = half of the square centimeter of R.

Substitution in equal amounts.

square 2 = square centimeter) to calculate the area of the semicircle.

square centimeters) Okay.

Solution: square centimeters.

square centimeters .........The area of the triangle abc.

Solution: As can be seen from the figure, the area of the triangle = the empty area on the right side of the line AB + the area of shadow B = the empty area on the right side of the line AB + (the area of the shadow A and the square centimeter of the area of the semicircle.

The difference between the area of the semicircle and the area of the shadow is the area of the triangle. （πr2÷2－

Area of Figure A = Area of Half Circle - Area of Intermediate Figure.

Area of Figure B = Area of the triangle - Area of the middle figure.

Area of Figure A - Area of Figure B = Area of Half Circle - Area of Intermediate Graph - Area of Triangle + Area of Intermediate Graph =

Semicircle area- - triangle area=

Triangle area =

The ** of buying a kind of book should be 2*, so the price is yuan).

To do this question, you can assume that book A buys a total of A copies, then B buys a total of 60% of A to buy B books, and the amount of money paid to buy A books is 2 times that of B books, so the unit price of buying A books is in yuan, and A books get a 10% discount, so the original price is 2 yuan.

Solution: If there are x copies of book A, and the original price is y yuan, then you need to buy a kind of book, and because the number of books of type B is 60% of the number of books of type A, the number of books paid by the buyer is 2 times that of book B, and it is known that the price of each book of type B is yuan, so there is a kind of book B, then, the solution is: y=2.

Before the discount, the price of each book was $2.

Before the discount, the price of book A is x, and the number of books is y

Get x = 2 yuan.

That is, the ** before the discount is 2 yuan.

Suppose the purchase of book A x and book B y, and the unit price of book A is a, so that the equation x=6y3y=2*

The two equations give a=5 9

Suppose I bought X copies of book A, book B, and the ** after the discount of book A is z, and zx= is obtained from the title

Z=So the original price of book A is yuan.