Xiao Ming and xiao gang went to the boutique stationery store to buy the same kind of pens and exercise books. The following is their dialogue with the salesman: Xiao Gang: auntie, how much do I need to buy three pens and two exercise books? Xiao Ming: auntie, I have 21 yuan with me. I want to buy a pen. I want to buy exercise books for the rest. How many do you think I can buy? Salesperson: let me calculate. A pen is twice as much as an exercise book, and it costs more than 1 yuan. After buying a pen, you can also buy several exercise books. Students, can you fill in the blanks? Give reasons

Suppose the price of an exercise book is x yuan, then the price of a pen is (2x + 1) yuan. According to the meaning of the question, we get 3 (2x + 1) + 2x = 19. If we get x = 2, then 2x + 1 = 5, that is, 2 yuan for each exercise book and 5 yuan for each pen. Suppose Xiao Ming can buy y exercise books, then we get 5 + 2Y = 21, and y = 8

Xiaoming and Xiaogang cycle around the circular track. Xiaoming takes 30 seconds to cycle, while Xiaogang takes 45 seconds to cycle
How long does it take for two people to start from the starting point at the same time to meet again at the same time?

90s

A simple method to calculate (2 + 4 + 6 +. + 2006) - (1 + 3 + 5 +. + 2005) =?

（2+4+6+.+2006）-（1+3+5+.+2005）
﹙2-1﹚+﹙4-3﹚+﹙6-5﹚+.-.+2006-2005
=1003×1
＝1003

In △ ABC, the equation of the line where the height of B (1,2), BC is x-2y + 1 = 0, and the equation of the line where the bisector of ∠ A is y = 0
Finding the area of △ ABC

Let the intersection of BC and X axis be d
By substituting y = 0 into y = - 2x + 4
Get the coordinates of point d (2,0)
Ad long 3
SABC=(3*2)/2+(3*6)/2=12

Using calculator and dichotomy to find approximate value of equation x ^ 3 = 2x + 1 (accuracy 0.1)

Let f (x) = x ^ 3-2x-1
Take x = 0 and x = 2
f(0)=-1①
f(2)=3②
①*②

The selection of free unknowns in linear algebra
Matrix transformation into
-4 1 1
0 0 0
0 0 0
Then, why are the basic solutions (0 1 - 1) 'and (1 04)' obtained? Shouldn't we treat x2 and X3 as free unknowns?

This is the basic system of solutions obtained by taking X1 and X2 as free unknowns
It's OK to treat x2 and X3 as free unknowns,
1 -1/4 -1/4
0 0 0
0 0 0
The basic solution system (1,4,0), (1,0,4) can be obtained

The ratio of the length to the width of a rectangle is 14:5. If the length is reduced by 13 cm and the width is increased by 13 cm, the area will be increased by 182 square cm. What is the area of the original rectangle?

Let the original rectangle be 14x in length and 5x in width. The equation (14x-13) × 13-5x × 13 = 182, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 182x-169-65x = 182, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp

If f (x) is known to be an increasing function on R and f (M & # 178;) > F (- M + 2), then the value range of real number m is ()

f(m²)>f(-m+2)
Increasing function
So M & # 178; > - M + 2
m²+m-2>0
(m+2)(m-1)>0
m1

If we know the fifth power of the algebraic formula MX + the third power of NX + px-4, when x = 2, the value of the algebraic formula is 5, then when x = - 2, what is the value of the subalgebral formula

When x = 2, the value of this algebraic expression is 5,
That is: 2 ^ 5m + 2 ^ 3N + 2p-4 = 5
32m+8n+2p+4=13
When x = - 2, the value of this algebraic expression is:
-2^5m-2^3n-2p-4
=-（32m+8n+2p+4)
=-13

Given function f (x) = (M + 1) x ^ 2 - (m-1) x + M-1 (1) if inequality f (x)

(1) The solution set of F (x) & lt; 1 is r, which indicates that the maximum value of F (x) is less than 1, i.e. the opening is downward, M + 1 & lt; 0. Then the vertex formula is used to solve M & lt; (1-2 times root 7) / 3 (2) (M + 1) x ^ 2-2mx + M-1 ≥ 0

Xiaoming and Xiaogang cycle around the circular track. Xiaoming takes 30 seconds to cycle, while Xiaogang takes 45 seconds to cycle How long does it take for two people to start from the starting point at the same time to meet again at the same time?