Junior high school math questions, thank you, junior high school math questions, thank you

Proof: ADB corresponds to arc AB with BAC, so ADB = BCA. It should be ab=ac, so abc= bca, i.e. adb= abc.

And because de bc, abc= e, i.e., adb= e.

Connecting OA, OB, and OC, extending AO to cross BC to F, and by ob=OC, the triangle AOB is all equal to the triangle AOC, so AF is the bisector of the isosceles triangle angle. According to the three-line combination theorem, AF is perpendicular to BC, and F is the midpoint of BC.

In the right triangle ABF, AF=4 is obtained according to the Pythagorean theorem, and in the right triangle OFB, the radius of the circle is assumed to be X, according to the Pythagorean theorem (4-X) 2+3 2=X 2

The solution is x=25 8

Therefore the radius of the circle o 25 8.

<>2.Solution: <>

as oh ac in h ; ap bc on p

That is, PC=1 2BC=3, ah=1 2AC=5 2, then APC is a right triangle, AP 2=AC 2-PC 2=25-9=16

So ap=4

Let the radius of the circle be r

In the right-angled triangle BOP:

op^2+bp^2=ob^2

i.e. (ap-r) 2+9=r 2

4-r)^2+9=r^2

Solution: r=25 8

The radius of the circle is 25 8

1) Because BC is parallel to ED, the angle ABC=angle AED, and because AB=AC, the arc AB= arc AC, so the angle ADB= angle ABC

So the angle adb = the angle e

(1) Proof of: AD BE

Arc ab arc de

ab＝dead∥bf，ab∥df

The quadrilateral abfd is a parallelogram.

ab＝dfde＝df

Solution: (1) When x=2000, the number of unrented vehicles is 0, when x=2000+50k(k=1,2,3...).When the number of unrented vehicles is k (2) x = 2000, y = 2000 * 100 = 200000 x = 2000 + 50k (k = 1, 2, 3...)

Earnings y = (2000 + 50k) * (100-k) - 50 * k = 200000 + 2950k - 50k2

3)y=-50k2+2950k+200000=-50[k2-59k]+200000

When k = 29 or 30, the benefit is the largest, satisfied thank you for adopting!

You should be a junior high school student, you should develop the habit of solving problems by yourself, if you help you make it directly, I don't think this will help you, so I will tell you the idea of this problem, you can solve it yourself.

1. You should be able to do this. Let me tell you, we can know the coordinates of the two points of ab from the graph, and we can find the slope of the straight line ab from the coordinates of the two points of ab, and then follow the formula y=ax+b (a is the slope), and substitute the point a (or point b) into the formula to find b, so that the function expression of the straight line ab comes out, and in the same way, the function expression of the straight line en is also found in this way.

2. From (1) we can get the function expression of two straight lines, and then find the intersection of these two expressions, and then find the intersection of the straight line CG and the straight line DM, to see if these two intersection points are the same point, if yes, then these two are bit-like graphs, if not, they are not bit-like graphs (in fact, as long as the intersection of the straight line ab and the straight line en is in the x-axis, you can draw conclusions).

3. In fact, in (2), it is a bit like a diagram, so it is very simple, because the problem just asks you to draw a graph, so you only need to connect AB and extend it in reverse, and the perpendicular line of the X axis will cross the point M to the reverse extension line of AB at the point X, in the same way, make the reverse extension line of En, make the perpendicular line of the Y axis through the X point, and cross the reverse extension line of En to the point Y, so that it is easy to find the fourth point.

The two points of ab are ( and (

So 3k+b=2 gives k=2 3

6k+b=4 b=0

So the functional relation of the straight line ab is y=2 3x

The two dots on en are (,(

So 5k+b=2 gives k=2 5

10k+b=4 b=0

So the functional relation of the straight line en is y=2 5x

2.Because the b=0 of the two functionsis a proportional function, with the origin of the pass, so.

The two squares are bit-like figures.

Solution: (2) The original system of equations is: x2 --4y2 = 0 --

x2 --6xy + 9y2 = 1 --

Yield: x2 = 4y2 = (2y)2

x = 2y or x = --2y

Given by: (x --3y)2 = 1

x --3y = 1 or x - 3y = --1

So we get the following four equations: x = 2y, x = --2

x --3y = 1 solution: y = --1

x = 2y x = 2

x --3y = 1 solution: y = --1

x = --2y x = 2/5

x --3y = 1 solution: y = --1 5

x = --2y x = --2/5

x --3y = 1 solution: y = --1 5

Therefore, the original equation has the above four sets of solutions.

2. Solution: Let the original profit per piece be x yuan.

Then the profit per piece after the price reduction is ( x --yuan.

By the title, the original sales volume was (1000x) pieces.

The sales volume after the price reduction is [ 1000 x ) 200 ] pieces.

From "the total profit is 200 yuan more than the original" can be listed in the equation:

1000 / x ) 200 ] x --= 1000 + 200

Reduced to an integer equation, we get: 2x 2 --3x --5 = 0

The solution gives x = x = --1 (rounded).

After testing, x = is the root of the original fractional equation (don't forget to check the root of the fractional equation!). ）

Then the original sales volume is: 1000 x = 1000 = 400 (pieces).

A: The original profit per piece was RMB, and the original sales volume was 400 pieces.

3. According to the title, the quadratic coefficient of the original equation is 1, which is a quadratic equation.

When m = 0, the equation becomes x2 + 2x = 0, and there are two different real roots x1 = 0 x2 = --2, which satisfies the problem.

When m = 2, the equation becomes x2 --1 = 0, and there are two different real roots x1 = 1 x2 = --1, which satisfies the problem.

When m takes another solid number where m is not equal to 0 and m is not equal to 2, the discriminant expression of the root of the original equation.

b2 --4ac

m --2 )]2 --4 × 1 × m2 / 4 )

m - 2 )2 + m2

m is not equal to 0 m2 0

m is not equal to 2 m - 2 )2 0

Discriminant 0 of the root of the original equation

The original equation, no matter what real value m takes, always has two different real roots. (The square is too big, forgive me.) ）

Let the original profit of each piece be x yuan, then there will be a total of 1000 x pieces, and there will be an equal relationship:

1000/x）+200】*（

It can be solved: x = yuan.

The sales volume of 400 pieces was also easily obtained.

After a product is sold according to the original **, a total profit of 1,000 yuan, if the pricing is reduced, each piece of less profit yuan, can increase the sales volume by 200 pieces, the total profit is 200 yuan more than the original, how many yuan is the original profit per piece? How many pieces are sold?

The function image is exactly the same as y x, when bc 6, x 3, y 9, so sabc 1 2 * 6 * 9 27.

Analysis: Knowing the vertex a of the parabola y=x 2+(m- 3)x+ 5, let the parallel x-axis line y=n, and the line intersects the parabola b and c, and solve this equation x 2+(m- 3)x+( 5-n)=0,|xb-xc丨=6, so (m-3) 2-4( 5-n)=6, the square of the formula is arranged to get (m- 3) 2+(4n-4 5-36)=0, because (m- 3) 2 0, so 4n-4 5-36=0, and m- 3=0 is true, m= 3, n=6+ 5, the parabola is written as y=x 2+ 5, the straight line y=6+ 5, and the solution is s abc=18

Look at the triangle ade and triangle abc

According to the known conditions, de bc = 1 2, and the ratio of the height of the triangle ade to the triangle abc is 1 2

The area ratio of the triangle ADE and the triangle ABC is 1 4 so the area of the quadrilateral DBCE.

Accounts for 3 of the triangle ABC 4

The area of the quadrilateral DBCE is 6

DE is the median line of the triangle ABC.

s△abc=s△ade×2^2

i.e. s ade 2 2 = 8

sade=2

s quadrilateral = s abc-s ade = 8-2 = 6

First, it is proved that rbe is an isosceles triangle, then br=be=2 5, and ac de, c is the midpoint of be, bp=pr=5

Reuse the similarity certificate PQ qr QC RE 1 2, PQ = 5 3