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Judge whether the following propositions are true or false. If they are true, give reasons. If they are false, give counter examples (1) If a is a real number, then the square plus 1 is greater than 0 "; (2) If the square of a is greater than the square of B, then a is greater than B; (3) A quadrilateral with equal sides is a square
1 true
2 false a = - 10 b = 5
3 false diamond
Judge the truth of the following propositions and explain the reasons: 1) (X-2) (x-3) = 0 is a necessary and sufficient condition for (X-2) 2 + (y + 3) = 0
1) A necessary and sufficient condition for (X-2) (x-3) = 0 to be (X-2) 2 + (y + 3) = 0
2) X2 = 4x + 5 is a necessary condition for 4x + 5 = x2 under X radical
3) The equality of internal stagger angles is a sufficient condition for two straight lines to be parallel
4) AB < 0 is a necessary and insufficient condition for absolute value a + B < absolute value a-b
1) If x = 2 or 3, only x = 2 is OK and Y is uncertain
2) Yes
3) Necessary and sufficient
4) Necessary and sufficient
By using counter examples, it is proved that the proposition "if the two sides of one angle are parallel to each other, then the two angles are equal" is a false proposition
The true proposition is that the two sides of the angle are parallel and have the same direction
A group of numbers in regular order √ (2 / 3), √ 6 / 3, √ 4 / 9, 2 / 3, √ (8 / 27), 2 √ 6 / 9
2 / 3 2 / 3 4 / 81 4 / 9 = (2 / 3) & # 178; 8 / 27 8 / 27 = (2 / 3) & # 179;
Should the third one be √ (4 / 9)
If the odd even number term is an equal ratio sequence
The determinant of matrix A of order 3 is / A / = 4, find / - 2A /?
Because a is a matrix of order 3
So / - 2A / = (- 2) times / A/
So / - 2A / = - 32
Mathematics exercise book (1) Chapter 7 review questions
Chapter 7 answers to review questions
1.①③④
2.（1）≠1/2（2）＝3
3.（1）6a^2 (2)a-2
4.(1)(x-3y)/(2x+10y) （2）-（2t-6h)/(5t-3h)
5.(1)-2/m (2)(m-2)/m
6.(1)(15y-2x)/5xy (2)n-3m
7.（1）x＝3 （2）x＝7/3
8.V＝US/(R+S)
9. (1) B ^ 2 / (a-b) (2) original formula = XY ^ 2.2
10. No solution
11. Let the speed of the ship in still water be V km / h, then 21 / (v-4) = [22 / (V + 4)] * 1.5, and V = 18
12. Suppose the original average speed of the bus is x km / h, then 360 / X - [360 / (1 + 50%) x] = 2, and the solution is x = 60
Chapter 6 answers to review questions
1.（1）D （2）B
2.（1）5(x+2)(x-2) (2)m(a+b-c) (3)(8-a)^2 (4)(x-y)(2+a)
3.(1)(0.7x+0.2y)(0.7x-0.2y) (2)-((2ab-a)^2 (3)-3ax(a+2x)(a-2x)
(4)mx(m-n)^2
4. (1) π R ^ 2-4 π R ^ 2 (2) π (R + 2R) (R-2R) ≈ 176 (square centimeter)
5.（1）(m-n)^2(m+n) (2)1/2ab(a+2b)^2
6.(1)2x+5y (2)2（x-1/2)=2x-1
7.(1)x1=0,x2=3/2 (2)y1=-1,y2=-5
8. Simplify the original algebra to get - 2Ab (a + b). - 10
9.3a ^ 2 + 7ab + 2B ^ 2 = (3a + b) (a + 2b)
I hope I can help you
Arrange the positive and even numbers in the following table
Column 1 column 2 column 3 column 4
Line 1 2
Line 2 4 6
Line 3 8 10 12
Line 4 14 16 18 20
.
According to the above rule, the row and column of 2006 are___________
Please use n to express the rule
(please write a good explanation, my understanding ability is too poor, please use more words to explain)
The first column of each row is 2,4,8,14,22... Which conforms to the rule of 2 + n (n-1). Is this the rule you want to find? N is the number of rows. For example, if you look at the fourth row, n = 4, then the number of the first row can be calculated is 2 + (4) (4-1) = 2 + 12 = 14. To get 2 + n (n-1) is the observation rule, and the discovery is the second order arithmetic sequence (each item follows the previous one)
How many times of 3 and 5 are there within 100 (including 100)
The least common multiple of 3 and 5 is 15
15*6100
So there are six numbers within 100 that are multiples of 15
That is, there are 6 multiples of 3 and 5 within 100 (including 100)
Sixth grade volume I practical problems about percentage and score
10 is a little difficult
There are 112 students in the sixth grade, 25% more in the fifth grade than in the sixth grade. How many in the fifth grade? 2
There are seven red, yellow and blue balls of the same size in the box. At least how many balls are taken out must have two balls of the same color?
Band arithmetic
3 + 1 = 4
RELATED INFORMATIONS
- 1. If two sides of an angle are parallel to each other, is it true that the two angles are equal!
- 2. If the quadratic coefficient of equation - 5x + 6x + 3 = 0 is changed to one, why can the equation be changed?
- 3. Given a ＞ 2, B ＞ 2, try to judge whether the equation X2 - (a + b) x + AB = 0 and X2 ABX + (a + b) = 0 have common roots. Please explain the reason
- 4. Given a > 2, b > 2, try to judge whether the equation x * x - (a + b) x + AB = 0 and X * x-abx + (a + b) = 0 have common roots, please explain the reason * denotes a multiply sign The symbols can't be typed with words
- 5. 1. The congruence of two right triangles corresponding to the same angle and one side. 2. The congruence of two triangles corresponding to the same angle and one side. Which is the true proposition Please draw a picture to illustrate
- 6. There are two congruent triangles with two equal angles and one side. Why? Give a counterexample It is suggested to avoid the following multiple-choice questions when preparing the test paper Only the following elements of two triangles are equal, so it can't be determined that two triangles are congruent () (A) Two corners and one side; (b) two sides and included angle; (C) Three corners; (d) three sides We should strictly follow the format of "congruence of two triangles with two corners and the opposite side of one corner corresponding to the same". We should not omit "the opposite side of one corner". We should not use ambiguous language such as "congruence of two triangles with two corners and one side corresponding to the same" to determine congruence of two triangles in class In understanding this concept, do not confuse correspondence with the corresponding edge of congruent triangle. As long as two triangles have two equal angles and one equal side, we can regard these two triangles as having two equal angles and one equal side. It is emphasized in the textbook that there are two equal triangles corresponding to two corners and the opposite side of one corner. How to understand the correspondence here? First of all, I want to make it clear that correspondence and corresponding edge are not a concept. If we stand on the platform of congruence of triangles and understand the correspondence here based on the corresponding edge of congruence triangles, then this problem is very difficult to solve. I think the correspondence here has something in common with the correspondence in the concept of function. The first triangle has one side with a length of 3cm, and only the second triangle has one side with a length of 3cm. We should regard these two triangles as having a pair of equal sides, which means the correspondence here.
- 7. Two angles and the opposite sides of one of them correspond to the congruence of two equal triangles. Do the two angles refer to the two separate angles of two triangles This sentence is incomprehensible What is the equivalence of the opposite sides of a corner
- 8. Proof: there are two equal triangles corresponding to the bisector of two angles and one of them
- 9. Two congruent triangles of similar and equal circumference
- 10. As shown in the figure, in △ ABC, ab = AC, point E is on high ad, find out all congruent triangles in the figure, and explain why they are congruent?
- 11. Judge the true proposition or false proposition and explain the reason
- 12. Judge whether the following propositions are true or false, and give reasons (1) If a + B + C = 180 °, then a, B and C must be the three inner angles of the triangle (2) If a ∩ B ≠ &;, B is really contained in C, then a ∩ C ≠ &;
- 13. a. B ∈ R, then the equivalent proposition of a square + b square = 0 is
- 14. The equivalent proposition to the proposition "if a ∈ m, then B ∉ m" is () A. . if & nbsp; a ∉ m, then & nbsp; B ∉ MB. If B ∉ m, then & nbsp; a ∈ MC. If & nbsp; a ∉ m, then & nbsp; B ∈ MD. if B ∈ m, then & nbsp; a ∉ M
- 15. Let a and B be rational numbers. Judge whether the following statements are correct and explain the reasons ① If a = - B, then | a | = | B| ② If | a | = | B |, then a = - B
- 16. What is the square of rational number 2?
- 17. For any rational number x, x-3 + X-6, is there the smallest absolute value? Why For any rational number x, x-3 + X-6, is there the smallest absolute value and why
- 18. Write down the inverse proposition of the following proposition, and judge the truth of the original proposition and the inverse proposition. (1) natural number must be rational number. (2) if | a | = | B | & _; then a = B (3) If a = B, then a ^ 3 = B ^ 3
- 19. Write a proposition that the sum of two rational numbers is the inverse proposition of rational numbers. If the inverse proposition is not sure of the answer, don't mistake people!
- 20. If the real number a B satisfies a + B < 4, then a = 1 and B = 2 find its inverse proposition, no proposition, inverse no proposition, and its true and false