Middle School Mathematics. The process is detailed. 7 8 questions

7. Because, a+b+c+d=60

and a=1 2(b+c+d).

b=1/3(a+c+d)

c=1/4(a+b+d)

So, 3a = 60

4b=605c=60

solution, a=20

b=15c=12

So, d = 60-20-15-12 = 13

Choose b8, from the meaning of the title, the dog has been running from the beginning to the meeting of A and B.

Therefore, the meeting time of A and B is 6 (2+4)=1 hour, and the speed of the dog is 12 kilometers, so the distance traveled by the dog is, 12*1=12 kilometers. Pick B

7 Option B solution: Let A pay x, B pay y, C pay z, then Ding pay (60-x-y-z), according to the meaning of the question:

x=1 2(y+z+60-x-y-z) gives x=20, and the same goes for it.

y=1 3(20+z+60-20+y-z) y=15z=1 4(20+15+60-20-15-z) z=12, then the payment is 60-20-15-12=13

8. Choose B because the distance between A and B is 6 kilometers, and the speed of the two is kilometers per hour. Then the time it takes for A and B to meet.

6 (2+4) = 1 hour.

And the speed of the puppy is 12 kilometers per hour.

As can be seen from the title, the angle AOC = 180 degrees.

Angle BOE = 1 2 Angle BOB, Angle BOF = 1 2 Angle BOC and because Angle AOB + Angle BOC = Angle AOC = 180, so Angle EOF = Angle BOE + Angle BOF = 1 2 (Angle BOB + Angle BOC) = 1 2 * 180 = 90 degrees.

From the title oe of so 1 2 respectively

It should be: (4a+3b-17) 2+|8 a-b+1|=0So: 4a+3b-17=0, 8a-b+1=0

Solve the system of equations: a=1 2b=5

are equal to 0, and the solution is about the binary one-time equation. You will.

Both are absolute values, only if the number in the absolute value is equal to zero.

7.To transform a practical problem into a mathematical (functional) problem, let the side length against the wall be x, then 0< x<18, the other two sides are (30-x) 2, so the area equation is f(x)=x(30-x) 2,0

Bring the point (-1,0) and the point (0,1) into y kx+b, so k -1, b 1, so y=2kx+b is y=-2x+1, and the intersection point with the x-axis is (-1 2,0), so choose c

Question 7 12 is a perpendicular line to AB over point D.

Question 8 1 : Connect EF Because ae=af so the triangle aef is an isosceles triangle so the angle aef=afe and because pe is perpendicular ac pf perpendicular ab so the angle afe=aef=90° so the angle pfe=pef so pf=pe

2: Connect pa because pf=pe af=ae angle pea=pfa=90° from the triangle congruence condition it can be seen that the triangle pea is congruent with pfa, so the angle paf=pae, so pa is the angle bisector of angle a.