A problem in 8th grade, a problem in 8th grade math

Hehe, you bring y=mx+3 into the formula x +2y -6=0, and get x +2(mx+3) -6=0, after simplification, it is a one-dimensional quadratic equation about x, with the same solution, then =b -4ac=0, you can solve the value of m.

Substitute y=mx+3 into x +2y -6=0, x 2 + 2(mx+3) 2 - 6 = x 2 + 2m 2 x 2 +12mx +18 - 6 = (1+2m2)x 2 + 12mx +12 = 0

The system of equations has two identical solutions to real numbers, i.e. the discriminant equation of the above equation (12m) 2 - 4(1+2m 2)*12 = 144m 2 - 48(2m 2+1)= 0, i.e. 3m 2 - 2m 2 -1=m 2-1=0, m=+1 or m=-1

The solution of the equation: m=1, 3x 2 +12x +12 = 3(x+2) 2=0, x=-2 , y =x+3=1

or m=-1, 3x 2 12x +12 = 3(x-2) 2=0, x=2, y=-x+3 =1

i.e. when m 1, x 2, y 1

or m1, x 2, y 1

Solution: Bring y=mx+3 into x +2y-6=0 and get.

x²+2（mx+3）²-6=0

x²+2（m²x²+6mx+9）-6=0

2m²+1) x²+12mx+12=0

If the equation has two identical real solutions, then: 144m -4(2m +1)*12=0

That is: 48m -48 = 0

m = 1 solution yields: m = 1

Brother, it's not easy to type these words.

Maybe a little wordy.

Because abc= adc=rt

So the quadrilateral ABCD is rectangular.

So ad=bc, dac= bca

Again, because the point e is the midpoint of the diagonal AC.

So ae=ce

So the triangle ADE is all equal to the triangle CBE

So be=de

1) There is a wheat field of x hectares, which is completed in m days if n people harvest, and the work efficiency of one person is: x mn;

Another harvester harvests m 2 days earlier than n people harvest.

The working efficiency of a harvester is: x (m-m 2) = 2x m;

The working efficiency of a harvester is (2x m) (x mn) = 2n times the working efficiency of a person.

2) If the harvesting efficiency of the person is constant, (2n) the number of days required for 3 people to harvest the wheat field is; (x/mn)*(2n)^3=8xn^2/m;

If a harvester is used and the harvester takes half the time of human harvesting, the number of days taken by the harvester is (8xn 2 m) 2=4xn 2 m;

And because of x hectares of wheat fields, the total amount of wheat fields harvested by the harvester per day is: x (4xn 2 m) = m 4n 2;

So the number of harvesters needed is: (m 4n 2) (2x m) = m 2 8xn 2

Human efficiency: x mn hectares per person*day.

Machine efficiency 2x m hectares per day.

Multiple: 2x*mn mx=2n folds.

The efficiency of people remains the same, and the number of harvesting days is m days.

then harvest wheat fields 2n 3*x hectares.

Machine harvesting time m 2, efficiency 2x m

Number of units: 2n 3*x (m 2*2x m)=2n 3

Set the efficiency of people to x

2n 3*x (m 2*2x m)=2n 3 solution gives x=2n 3

A: It is more suitable to need 2n 3 harvesters.

1"a(6/k,6) b(0,6) o(0,0)s=ab*ob/2=|6/k-0|*6 2=12 gives k=3 2, or k=-3 2.

2 set the coordinates of point a (x,6), s aob = 1 2 * (absolute value of x) * 6 = 12

The solution is x = plus or minus 4, and substituting (plus or minus 4, 6) into y=kx is solved to get y = plus or minus two-thirds x

Because AD is the midline of BC, ADB = 90 degrees.

And because of EF AB, EFB = 90 degrees.

And because of the bisector bg of abc next to the book, fbe= dbebe is the common side, so the triangle fbe=triangle car block dbe, so ef=ed

Solution: In the isosceles triangle ABC, ab=ac, and AD is the midline on the side of BC.

AD BC and EF Ab ABC's bisector BG

mega ed=ef

First of all, what is the bottom edge AO of trapezoidal ABCD!! Are you sure it's not a trapezoidal abco......I'll press ABCO to make ...... for youを should be the origin ......

Let c(x0,y0), b(x1,y0), then k=x0*y0.

Since the hyperbola y=k x and ob have an intersection point over c, x0 has the same sign as x1.

Set x0>0 first

Let d(x2,y2), d satisfy x2*y2=k=x0*y0, x2 y2=x1 y0. So x2 = under the root number (x0*x1), y2 = under the root number (y0 2 x0).

From od:db=1:2, x1=3*x2 is obtained. So x1=9*x0

The area of the triangular OBC is.

So k=

Answer: There are x children and y toys.

then: y=3x+4, and y=4(x-1) sail carries -a, where: a=1 or a=2 or a=3

So: 3x+4=4(x-1)+a, solution: x=8-aWhen a=1, x=7, the game has 3*7+4=25 pieces.

When a=2, x=6, play pants with 3*6+4=22 pieces.

When a=3, x=5, the sedan chair has 3*5+4=19 pieces.

The next day she spent x hours typing.

2*w*60+x*(w+10)*60=120002w+xw+10x=200

x=(200-2w)/(10+w)

So the next day she typed for (200-2w) (10+w) hours.

Hope it helps

Let the inverse proportional function be y=k x

1) Substitution (-3,2).

2=-k/3，k=-6

Hence the inverse proportional function is y=-6 x

2) Function the inverse proportionality to xy=-6

The products of a, b, and c axials are calculated separately.

The product of the horizontal and vertical coordinates of b and c is -6

So on the function graph.

The product of the horizontal and vertical coordinates of point A is 6 and is not on the function image.

Solution: 1. Let the analytic formula of the inverse proportional function be y=k x.

According to the title, it can be obtained: 2k=-3

So k=-6

So the analytic expression of the inverse proportional function is y=-6 x.

2. Substituting the coordinates of the points a b c into the analytic formula respectively obtains:

2*3 is not equal to -6

Negative root number 6 * root number 6 = -6

So point A is not on the inverse image, and point B c is on the inverse image.