A math problem for the second year of junior high school, a math problem for the second year of juni

When you say, "Try to determine whether P is also on the bisector of AC" should be "Try to determine if P is also on the bisector of BC".

Answer: P is also on the perpendicular bisector of BC.

Proof: Because p is on the perpendicular bisector of ab, it is based on "the distance from the point to the end of the line segment on the perpendicular bisector is equal".

So pa pb

Because p is on the perpendicular bisector of AB, according to "the distance from the point on the perpendicular bisector of the line segment to both ends of the line segment is equal".

So pa pb

So PB PC

According to "Points with equal distances to both ends of the segment are on the bisector of the segment".

So p is on the perpendicular bisector of bc.

FYI! Good luck with your learning and progress.

The original ID "Jiangsu Wu Yunchao" is known to be unusable, and the account has been permanently banned (nearly 30,000 points, in fact, it can't be regarded as cheating), it is recommended that you do not cheat and brush points, and the operation should be standardized. Otherwise, it will be useless to appeal after the seal.

on the vertical bisector of AC.

bp=ap=cp

So bp=cp

Let E be the focus of BC to prove that PE can be bisected vertically by BC.

So whether p is also on the bisector of bc.

Of course, I will pay a little. Theorem.

Three hearts of a triangle.

Center (where the midlines of the three sides intersect at one point).

Perpendicular center (the perpendicular lines of the three sides meet at one point).

Inner (triangular bisector intersects at one point, again: the center of the inscribed circle) Another: Outer center (the three perpendicular bisectors intersect at one point, the center of the circumscribed circle) This is what you are asking.

1.Let the equation be a*t+b=y

5 tons of water exchange: 5a+b=

8 tons of water crossing: 8a+b=

Solve the system of equations, a=

b = functional relation.

2.A = yuan.

B = yuan. t = (9+ tons).

Excluding the 3-pointer, it is 16 points in 12, so the two-point shot has 16-12=4, so the one-point shot is 8

If it's convenient, take a picture of the question and send it or write it in a notebook and take a picture and send it.

Solution: The abscissa of point e is a+b

So the ordinate is 1 (a+b)=b

So b 2 + ab = 1

And 1 a = a

a=1, so b=(root number, 3-1) 2

That is, e(a+b,1 (a+b)) can be substituted!

**If you don't understand, remember to consult me! Thank you!

The intersection points of squares a and b and the function image are a and b respectively, and the side lengths of the two squares are m, n because y=1 x, a(m, m).

So m=1b(1+n,n) is substituted into the function.

So n=(5-1 under the quadratic root number) 2

So b((5+1) 2,(5-1) 2).

If 3 pairs of a+b are divisible by 3, then 4 (a+b)+6b is divisible by 3.

So 3 and 4 are opposites.

Hence Simultaneous a=2b+5

A+1 is divisible by b.

2b+5+1 is divisible by b, i.e., 2b+6 is divisible by b (2b+6) b gives 2+6 b, i.e. 6 b is an integer.

b may be 1 2 3 6

If 3 pairs are obtained from 2 to a+b=b+5, then (b+5) is an integer and b may be 2 6

Then b can be the corresponding value of a

Then, if 4 pairs are proved in a similar way, there are two sets of solutions: a= or a=, in summary. Because it must be right.

So when two sets of solutions a=8 b=1 or a=11 b=3 when paired, there are two groups of unburying a= or a=

Whew: It's finally over

You may not know how to calculate the gap between four balls, but you don't need to calculate this, and you don't need to use the volume formula of the ball, you can imagine this: in a cube of two cubic centimeters, how many small cubes can be divided into 6 10 -3cm side length? Apparently 2 (6 10 -3) 3 = pcs, and a cube with a side length of 6 10 -3 cm can fit a sphere with a radius of 3 10 -3.

In other words, the number of bacteria is also one.

Well, you can give points.

(1) The consumption amount is 800 yuan.

Because, 500<640<700

So, get a discount of 800 yuan.

Preferential rate 260 800

So, the preferential rate that customers get is:

2) Because the price of the suit is higher than 700 yuan and lower than 850 yuan, the maximum consumption amount is 850 yuan, and the minimum is 700 yuan, because the consumption amount is less than 700 yuan and higher than 500 yuan, so the amount of the lottery ticket is 100 yuan, and the price of the suit is x yuan, and the equation can be listed according to the meaning of the question (i.e., the solution is obtained, x=750 (after testing, x=750 is the root of the original equation), therefore, the price of the suit is 750 yuan

It turns out that the discount rate is 1 3.

1) Purchase consumption: 800 80% = 640 yuan, at this time the discount is 800-640 = 160 yuan.

500 p 700, the lottery ticket is 100 yuan.

The discount rate is: (160+100) 800=

2) The highest purchase spend: 850 80% = 680 yuan 500 p 700, so the lottery ticket is 100 yuan.

Set the list price to $x.

1-80%）x+100=x/3

x=750

The consumption amount is RMB), and the preferential amount is RMB) The preferential rate of purchasing goods =

260/800x100%=

Proof: AD BC

E is the midpoint of AC.

Therefore, DE is the midline of the hypotenuse of the RT ADC.

de=(1/2)ac

and f and g are the midpoints of ab and bc, respectively.

fg=(1/2)ac

ef∥bcde=fg

Therefore, the quadrilateral defg is an isosceles trapezoid.

Solution: (1) Because the price of each box is reduced by 1 yuan, 2 more boxes will be sold, then the price of each box will be reduced by 20 yuan, and 2 * 20 = 40 boxes will be sold.

The total number of drinks sold per day is 100 + 40 = 140 cases.

So the profit is a = 140 * (120-20) = 14,000 yuan.

2) Set: The price should be reduced by X yuan.

When the profit is 80 yuan per case, the drinks sold are the most. When the profit is 120 yuan, the drink is sold the least.

Then (120-x)*(100+2x)=14400 solves: -30 or -40 (rounded).

The answer is a $30 price reduction.

1) For every one yuan drop, there will be two more boxes, and if you drop twenty yuan, you can sell forty more boxes, then a total of 140 boxes can be sold, and the profit is one hundred yuan, 100 * 140 = 14000

In the equilateral triangle ABC, c= bae=60°, ac=ab, and an ae=cd is given to prove congruence. It can be obtained that CAD is equal to EBA because CAD+ BAD=60° and CAD is equal to ABF, so ABE+ BAF is equal to 60° according to the outer angle of the triangle BFD=60°