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Math questions, correct answers, score recovery 1. If m square + M-1 = 0, find m cube + 2m square + 20142. Prove that the value of polynomial (A-2) (a square + 2A + 4) - [3A (a + 1) square - 2A (A-1) square - (3a + 1) (3a-1)] + a (1 + a) has nothing to do with the value of A
Square of M + M-1 = 0, then
Square of M + M = 1;
M cube + 2m square = m place + m square + m square = m (m square + m) + m square = m + m square = 1
Three math problems, urgent
1. Given that the line y = MX-1 passes through the point (1, - 3), then the area of the line and the two axis fortress triangle is equal to_______
2. It is known that the line y = KX + 4 passes through the point P (1, m) and is parallel to the line y = 2x + 1. It intersects with the X axis at the point a, and the area of △ OPA is calculated
3. The whole journey from Shanghai to Hangzhou is about 200 km. If the average speed of the new bullet train is 0.5 km faster than that of the original express train per minute, it will take 20 minutes less than that of the original express train from Shanghai to Hangzhou. How many minutes will it take for the new bullet train to reach Hangzhou? (just list the equation.)
specific
1.
Substituting (1, - 3) into the linear analytical formula, we get the following results:
-3=m-1
m=-2
The analytical formula of the straight line is y = - 2x-1
When x = 0, y = - 1
When y = 0, x = - 0.5
The triangle area is: 1 / 2 × | - 1 × | - 0.5 | = 0.25
two
The two lines are parallel with the same slope
So k = 2
Substituting the P coordinate into y = 2x + 4, we get the following result:
m=2+4=6
P coordinates are (1,6)
When y = 0, x = - 2
The a coordinate is (- 2,0)
The area of △ OPA is:
1/2*|-2|*6=6
three
It takes X minutes for a new train to arrive in Hangzhou, while the original train takes x + 20 minutes
200/x-200/(x+20)=0.5
200(x+20)-200x=0.5x(x+20)
200x+4000-200x=0.5x²+10x
0.5x²+10x-4000=0
x²+20x-8000=0
(x-80)(x+100)=0
X = 80 or x = - 100 (rounding off)
A: it takes 80 minutes for the new train to arrive in Hangzhou
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