It costs 165 yuan to buy 3 undergraduate technology and 6 story books; it costs 150 yuan to buy 6 undergraduate technology and 3 story books. What are the unit prices of science and technology books and story books?

It costs 165 yuan to buy 3 undergraduate technology and 6 story books; it costs 150 yuan to buy 6 undergraduate technology and 3 story books. What are the unit prices of science and technology books and story books?

The price of a science and technology book and a story book: (165 + 150) / (3 + 6), = 315 / 9, = 35 (yuan), the price of a story book: (165-35 × 3) / (6-3), = (165-105) / (3, = 60 / 3, = 20 (yuan), the price of a science and technology book: 35-20 = 15 (yuan); a: the unit price of science and technology book and story book is 15 yuan and 20 yuan respectively

It costs 24.6 yuan to buy 3 science and technology books and 5 story books, and 5.8 yuan to buy 1 science and technology book and 1 story book

5.8 * 3 = 17.4 yuan, 24.6-17.4 = 7.2 yuan (for two story books), 7.2 / 2 = 3.6 yuan
5.8-3.6 = 2.2 yuan
Answer: Science and technology book 2.2 yuan, story book 3.6 yuan

Move the decimal point of a number two places to the right, and the number is 183.15 more than the original number. The number is solved by the equation

Move 2 bits to the right, expand 100 times
Increase 100-1 = 99 Times
The original number is 183.15 / (100-1) = 1.85
Let this number be a
100a-a=183.15
99a=183.15
a=1.85

It takes 10 hours for car a from a to B and 15 hours for car B from B to a. the two cars leave AB at the same time. When they meet, car a goes 80 ㎞ AB twice more than car B
How far is the ground from each other?

Meeting time:
1÷（1/10+1/15）
=1÷1/6
=6 hours
The distance between the two places is:
80÷（1/10×6-1/15×6）
=80÷1/5
=400 km

In the triangle ABC, the angle c = 90 degrees and the acute angle a make the equation x square-3sina * x + sin square a + 3sina-1 = 0 and have two equal real roots
If C is the hypotenuse of the right triangle, and the equation CX square - 2x + C = 0 has two equal real roots, find the length of ABC three sides of the triangle

X square-3sina * x + sin square a + 3sina-1 = 0 has two equal real roots
The discriminant is 0
That is (- 3sina) ^ 2-4 * 1 * (3sina-1) = 0
==>9（sinA）^2-12sinA+4=0
==>（9sinA-4）（sinA-1）=0
==>Sina = 4 / 9 or Sina = 1
Since a is an acute angle, Sina = 1 does not hold
So Sina = 4 / 9
CX square - 2x + C = 0 has two equal real roots
The discriminant is 0
That is (- 2) ^ 2-4 * c * C = 0
==>4c^2=4
==>C = 1
According to the sine theorem
a/sinA=c/sinC
A / (4 / 9) = 1 / 1
a=4/9
According to Pythagorean theorem
B = under the root sign (C ^ 2-A ^ 2) = √ (1 ^ 2 - (4 / 9) ^ 2) = √ (20 / 36) = 2 √ 5 / 9

Using proportion method to solve the problem: 900 kilometers from land a to land B, a car has driven 360 kilometers in 6 hours. According to this calculation, how many hours will it take for the car to reach land B

6:360=x:（900-360）
360x=6x（900-360）
x=6x（900-360）/360
x=6x540/360
x=3240/360
x=9
A: it will take 9 hours for the two cars to reach the destination

If both X and y of the fraction X2 (x + y) are expanded by K times, then the value of the fraction should be ()
A. Expand K times B. unchanged C. expand K2 times D. reduce K times

Using KX and KY to replace X and Y in the original fraction respectively, we get (KX) 2kx + KY = k2x2kx + KY = k2x2k (x + y) = kx2 (x + y). It can be seen that the new fraction is k times of the original fraction. So we choose a

Party A and Party B respectively set out from two places AB at the same time and walk opposite each other. As a result, they meet 60 meters away from the midpoint of the two places. It is known that Party A travels 20% more than Party B to find the distance between the two places

Draw a picture to solve the problem. Set the midpoint as C, the meeting point as D, and the distance of B as X, then the distance of a is x + 60 + 60. According to the known condition, the equation is: x + 60 + 60 = x × (1 + 20%), and the solution is: x = 600, the distance between the two places is 2 × (x + 60) = 1320M

It is known that the domain of definition of function y = f (x) is r, and for any a, B ∈ R, f (a + b) = f (a) + F (b), and f (x) < 0 holds when x > 0. It is proved that: (1) function y = f (x) is a decreasing function on R; (2) function y = f (x) is an odd function

It is proved that: (1) let x1 ＞ X2, then x1-x2 ＞ 0, f (x1-x2) ＜ 0, and f (a + b) = f (a) + F (b), f (x1) = f (x1-x2 + x2) = f (x1-x2) + F (x2) ＜ f (x2), y = f (x) is a decreasing function on R; (2) from F (a + b) = f (a) + F (b), f (x-x) = f (x)

On the map with a scale of 1:5000000, the distance between the two places is 6cm,
The speed ratio of car a to car B is 2:3. What is the distance of car a per hour

Actual = 6 × 5000000 = 300000000cm = 300km
Speed sum = 300 △ 2 = 150 km / h
Speed of vehicle a = 150 △ 2 + 3 × 2 = 60 km / h