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The position of ABC three numbers on the number axis is shown in figure 2.3-2. The number axis c0ab is simplified as | a | / A + | B | / B + | / C | / C!
Because C is less than 0, B is greater than a, and a is greater than 0,
So IAI = a, IBI = B, ICI = -- C,
So IAI / A + IBI / B + ICI / C = 1 + 1 -- 1 = 1
The corresponding points of known numbers a, B and C on the number axis are a, B and C respectively, where B and C are symmetrical about the origin. Try to simplify them: | A-B | - | - a | - | - B + C|
Because B. C is symmetric about the origin, B + C = 0, the original formula = | A-B | - | - a | = | A-B | - | - a | = | B|
The position of ABC on the number axis, B, C0, and the distance between the point of number a and number B and the origin is equal, simplify | a + B | + | a-c | - | B|
a>0,b0,c
Simplification / B-C / + / A-B / - / A + C / A________ ._________ A 0 B C number axis. 0 is the origin a 0 C > O and b-c
Because B - C < 0, a - B < 0, a + C > 0
So | B - C | = C - B, | a - B | = B - A, | a + C | = a + C
So | B - C | + | a - B | - | a + C|
= c - b + b - a - a - c
= -2a
It is known that there are two points a and B on the number axis, which respectively represent two opposite numbers a and B (where a > b), and the distance between a and B is 8
Find a, B
∵ A and B are opposite numbers
∴b=-a
∴a-b=2a=8
∴a=4
∴b=-4
If the numbers represented by the points Mn on the number axis are opposite to each other, and the distance between the two points Mn is 8, calculate the two numbers
M and N are opposite numbers
The distance from the origin to m is equal to the distance from the origin to n
∵|M-N|=8
∴|M|+|N|=8
∴|M|=|N|=4
∵M≠N
Ψ M = 4, n = - 4 or M = - 4, n = 4
It is known that point a on the number axis represents + 8, and the numbers represented by B and C are opposite to each other, and the distance from C to a is 3. What numbers do point B and point C correspond to?
∵ when the point is on the left side of a, + 8-3 = 5, when the point is on the right side of a, + 8 + 3 = 11, ∵ the number represented by C is 5 or 11, ∵ when the number represented by C is 5, the number represented by B is - 5 & nbsp; or & nbsp; when the number represented by C is 11, the number represented by B is - 11
Given that point a and point B on the number axis represent two opposite numbers A.B. and the distance between the two points is 8, find the value of A.B
|a-b|=8
b=-a
So | 2A | = 8
|a|=4
a=±4
So a = 4, B = - 4 or a = - 4, B = 4
The corresponding position of the number a.b.c. on the number axis is shown in the figure C -- 0 -- a -- B -- simplifying | a + C | + | a-c | + | B | + | C|
According to the number axis
a+c0
b>0
c
If the positions of rational numbers a, B and C on the number axis are shown in the figure, then the following conclusion is correct ()
A. a＞b＞0＞cB. b＞0＞a＞cC. b＜a＜0＜cD. a＜b＜c＜0
According to the number on the right side of the number axis is always larger than the number on the left side, we can get B < a < 0 < C
RELATED INFORMATIONS
- 1. The position of rational number ABC on the number axis is shown in the figure, then the size relationship of a, negative a, B, negative B, C, negative C, 0 is?
- 2. All real numbers can be represented by points on the number axis. Conversely, all points on the number axis represent real numbers
- 3. If the latter noun is plural, does the predicate still use the singular
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- 7. When the subject clause guided by what is used as the subject, the number of predicates is determined by the following predicative or object. Shouldn't it be determined by the singular and plural of the preceding subject clause?
- 8. Is the noun after any other plural or not For example, any other student or any other students; or any other country or any other cpuntries? Er The answers are different! Is there anything definite!
- 9. What do you like best
- 10. Why is photo plural phontos According to the grammar book, when the consonant letter is added with O, the plural form is added with ES or s (what's the situation? What's the situation? How to judge when doing the questions) and when the vowel letter is added with O, the plural form is directly added with S. in this way, photo is the consonant letter "t" plus O. according to the grammar, ES or s should be added. When is es added, If the plural of photo is photos and I did a question, the answer is that the plural of photo is photos You just tell me if the answer is an abbreviation with S
- 11. The three elements of the number axis are______ 、______ 、______ ．
- 12. Given that points a and B are on both sides of the origin on the number axis, their corresponding numbers are - 4,3x-5 / 2x + 2, and the distances from points a and B to the origin are equal, find the value of X
- 13. As shown in the figure, it is known that the number represented by point a on the number axis is 6, B is a point on the number axis, and ab = 10. Starting from point a, the moving point P moves uniformly to the left along the number axis at the speed of 6 unit lengths per second, and the movement time is t (T > 0) seconds (1) (1) write the number represented by point B on the number axis______ The number represented by point P______ (expressed by an algebraic expression containing T); ② m is the midpoint of AP and N is the midpoint of Pb. Does the length of segment Mn change during the movement of point P? If it changes, please explain the reason; if it doesn't change, please draw a graph and find out the length of line Mn; (2) moving point Q starts from point a and moves left uniformly along the number axis at the speed of 1 unit length per second; moving point R starts from point B and moves left uniformly along the number axis at the speed of 43 unit length per second; if P, Q and R start at the same time, when point P meets point R, it immediately returns to point Q Then, what is the unit length of the journey from the start to the stop of point P?
- 14. Points a and B are the corresponding points of numbers - 3 and - 12 on the number axis respectively. If line AB moves to the right along the number axis to a ′ B ′ and the number corresponding to the midpoint of line a ′ B ′ is 3, then the number corresponding to point a ′ is______ The distance that point a moves is______ ．
- 15. As we all know, the meaning of | 4 | = | 4-0 |, on the number axis, is the distance between the point of 4 and the origin (that is, the origin of 0). For another example, the meaning of formula | 8-3 |, on the number axis, is the distance between the point of 8 and the point of 3. Similarly, the meaning of formula | a + 5 | on the number axis is________ . If the answer is "the distance between a point and 5 or - 5", please explain the reason in detail!
- 16. If point a represents 7, and now a moves 6 unit lengths along the number axis to point B, then the rational number represented by point B is
- 17. If the distance between the corresponding point of a number on the number axis and its opposite number on the number axis is 5 unit length, then the number is______ Or______ ．
- 18. If f (x) = 2x + 5, then f (2x)= f(X+3)= f(2x+1)= f（-x）= F (x + 1) f（x-4）=
- 19. F (x) = / 2x-1 / - / 2x + 1 /, judge the parity function
- 20. The expression form of high school function