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As shown in the figure, the straight line y = - 2x-2 intersects the hyperbola y = KX (K ≠ 0) at point a, intersects the X axis and Y axis at point B, C, ad ⊥ X axis at point D, if & nbsp; s △ ADB = s △ cob, then K=______ ．
Y = - 2x-2 and hyperbola y = KX (K ≠ 0) intersect at point a, the solution is: the coordinates of point a are: (- 1 − 1 − 2k2, 1 − 2k-1), and the straight line y = - 2x-2 intersects with X axis and Y axis at points B, C, B (- 1, 0), C (0, - 2), ∫ s △ ADB = s △ cob, that is, 12 × | - 1 − 1 − 2k2 + 1 × (1 − 2K 1) = 12 × 1 × 2, the solution is: k = - 4, so the answer is: - 4
The image with positive scale function y = KX (k > 0) and inverse scale function y = 1 / X intersects at two points a and C. cross a as the vertical line of x-axis, cross X-axis at point B, cross C as the vertical line of x-axis, and cross X-axis at point D. verification: when k takes different positive numbers, the area of quadrilateral ABCD is a constant
Y = KX, y = 1 / xkx = 1 / x, x ^ 2 = 1 / KX = ± 1 / √ Ka (- 1 / √ K, √ K), C ((1 / √ K, √ K) B (- 1 / √ K, 0), D (1 / √ K, 0) quadrilateral area of ABCD = area of triangle BDC + area of triangle BDA area of triangle BDC = (1 / 2) * | BD | * | = (1 / 2) (2 √ K) * (1 / √ K) =
Mathematics second semester function
1. The area of △ ABC is ()
2. It is known that the straight line y = (5-3m) x + 2 / 3 M-4 is parallel to the straight line y = 1 / 2 x + 6
3 given the first-order function y = (6 + 3M) x + (n-4), find:
(1) When m is sum value, y decreases with the increase of x value?
(2) When n is the sum value, the intersection of function image and Y axis is above X axis?
(3) When m, n are sum values, the image of the function passes through the origin?
Can you type the first-order function "+ 4" is a molecule or a single function
1. We know the first-order function y = ax + B
(1) When the point P (a, b) is in the second quadrant, which quadrant does the line y = ax + B pass through
(2) If ab
1 (1) ∵ P (a, b) is in quadrant 2 ∵ A0. So y = ax + B passes through quadrant 1, 2 and 4;
(2) ∵ y increases with the increase of X ∵ a > 0. And ∵ Ab1. And ∵ y decreases with the increase of X ∵ 2k-3
Lower quadrilateral and function in the second grade of junior high school
1. As shown in the figure, given the rectangle ABCD, fold △ BCD along the diagonal BD, and note that the corresponding point of point C is C '. If ∠ ADC' = x °, then the degree of ∠ BDC is y °, then the functional relationship between Y and X is----------
2y-90°=x
Some problems of the second grade function in junior high school
1. Given that the image of a linear function y = KX + B passes through a point (- 2,4) and is perpendicular to a straight line y = 3x, the analytic expression of the linear function is obtained
2. The intersection of the image of the first-order function y = (3a + 1) x + 2A + 1 and the Y axis is below x, and Y decreases with the increase of X. the value range of a is obtained
3 translate the line L1: y = 2X-4 to the left by 5 unit lengths to get the line L2
(1) Finding the function analytic expression of line L2
(2) If L2 and the line L3: y = kx-2 and the Y axis form a triangle, and the area is 12 square units, the function analytic formula of the line L3 is obtained
1. Substituting (2,4) point, then: 4 = - 2K + B, and the line is perpendicular to y = 3x, so k = - 1 / 3, then the solution is: function analytic formula: y = - 1 / 3x + 10 / 3; 2. At the intersection of line and Y axis, x = 0, then y = 2A + 1, and the intersection of Y axis is below x, so y < 0, that is, 2A + 1 < 0, so a < - 1 / 2; 3. (1) y = 2x + 6 (2) L2, the linear equation is y = 2x
1. It is known that the square of M = - N + 2, the square of n = - M + 2, (M is not equal to n), then the value of M + n is ()
The answer to this question is 1, but I don't know why,
2. The line y = 2X-4 can be regarded as y = 2X-4 ()
A translation left 2 unit length after the line
B the straight line after translating 2 units of length to the right
C translation left 1 unit length after the line
D shift the line to the right by 1 unit length
The correct answer to this question is D, but I think we should choose C, because when y = 2X-4 moves down 2 units, according to the upper plus lower minus, the analytical formula should be y = 2x-6, at this time, x = 2 / 1y + 3, and in y = 2X-4, x = 2 / 1y + 2, so, if x adds 1, according to the left plus right minus, we should move left one unit, so why choose D
If it's OK, I'll add points,
One
Subtract the square of N from the square of M and bring it in on both sides
There is m2-n2 = 2-n-2 + M
That is, (M + n) * (m-n) = m-n
Because m is not equal to N, M-N can be reduced
So m + n = 1
2
The first half of your solution is right. After translation, y = 2x-6. Then according to left plus right minus, the original equation is y = 2X-4, so you can only translate one unit to the right, y = 2 (x-1) - 4, that is, y = 2x-6,
If you translate to the left, it will become y = 2 (x + 1) - 4, that is, y = 2x-2, which is not in line with the law
Note that only the X in brackets changes when you translate left and right
In 2010, Southwest China suffered a once-in-a-hundred-year drought, but in this drought, a city was less affected by the construction of "forest city" in recent years. According to statistics, in 2009, the city planted 500 million trees and conserved 300 million cubic meters of water. If the city planted 500 million trees every year in the future, the construction of "forest city" will be completed in 2015, at that time, the trees can be protected for a long time 1.1 billion cubic meters. (1) from 2009 to 2015, how many billion trees have been planted in the city? (2) If 2009 is regarded as the first year, and Y (100 million cubic meters) of water conservation capacity of trees is a function of the x year, the analytical formula of the function is obtained, and how much water can be conserved in the third year (that is, 2011)?
(1) (2) let the primary function be y = KX + B (K ≠ 0), when x = 1, y = 3, we get K + B = 3; when x = 7, y = 11, we get 11 = 7K + B, we get 3 = K + B11 = 7K + B, we get k = 43b = 53
Some function problems of grade two
1. Write out the functional relations in the following problems, and point out the constants and variables
(1) The functional relationship between circumference C and radius r of a circle;
(2) The train runs at the speed of 60 km / h, and the functional relationship between the distance s (km) and the time t (H) is obtained
(3) The functional relationship between the sum of inner angles s and the number of edges n of n-sided graphs
2. Point out the constants and variables of the following relations respectively
(1) One side of a triangle is 5cm long. The relation between its area s (CM & sup2;) and its height h (CM) is s = 5 / 2 h
(2) If the degree of an acute angle of zhennanguan is α, then the relation between the degree of another acute angle β and α is β = 90 - α
(3) If the unit price of a newspaper is a yuan and X is the number of copies of the newspaper, then the relationship between the total price of the newspaper and X is y = ax
1、 1 C = 2 π r constant 2 π variable C R
2 s = 60 t constant 60 variable s t
3 s = 180 (n-2) constant 180 2 variable s n
2、 1 s = 5 / 2 h constant 5 / 2 variable s h
2 β = 90 - α constant 90 variable β α
3 y = ax constant a variable y x
1. In order to enhance the residents' water-saving knowledge, a city formulates the following water use charge standards: each household uses no more than 7 tons of water per month, and the water charge per ton is 1.20 yuan (including sewage treatment fee, the same below); for the part more than 7 tons, the charge per ton is 1.90 yuan, and each household uses X tons of water per month, and the water charge should be y yuan
(1) Write out the function analytic formula between water charge y yuan and water consumption x ton;
(2) There are 50 users in a unit, and the monthly water fee is 541.6 yuan, and the water consumption of each household is less than 10 tons. How many users are there that the monthly water consumption is less than 7 tons?
2. If the line Y1 = K1X + B1 intersects with the line y2 = K2 + B2 at (- 3,2) and passes through (- 3 / 2,3) and (1, - 2) respectively, the area of the triangle formed by the two lines and the y-axis is calculated
3. In rectangular coordinate system, there are two jump lines: y = 3 / 5x + 9 / 5 and y = - 3 / 2x + 6. Their intersection point is m. The first line intersects with X axis at point a, and the second line intersects with X axis at point B
(1) Find the coordinates of two points a and B;
(2) Using image method to solve equations [3x-5] = - 9
3x+2y]=12
(3) Find the area of △ mAb
I wish you a happy new year in advance
1. (1) if X7, then y = 1.2 × 7 + (X-7) × 1.9 (2) ok. - 2. Substitute (- 3,2) and (- 3 / 2,3) into Y1, get K1 and B1, and get Y1 = (- 2 / 9) x + 4 / 3. Similarly, get y2 = - X-1. Substitute x = 0 into Y1 and Y2, and get the intersection of two lines and y-axis. Let's set a and B two points (- 3,2) as point cab
RELATED INFORMATIONS
- 1. Please write a function analytic expression that meets the following two conditions___ ① In the second quadrant, y increases with the increase of X
- 2. Formula of symmetry axis of function
- 3. The functional relationship between price f (T) and time t of a commodity in recent 30 days is f (T) = t + 10 (0
- 4. Set proof: Let the set {a = a | a = 3N + 2, n ∈ Z} and the set B = {B | B = 3K-1, K ∈ Z}, prove that a = B
- 5. tan22.5°1-tan222.5°= ___ ．
- 6. The vertex of isosceles triangle is a (4,2), and the bottom end is B (3,5). Find the trajectory equation of the other vertex C, and explain what its trajectory is?
- 7. It is known that the three vertices of △ ABC are a (0,3), B (1,5), C (3, - 5). (I) find the linear equation of edge AB; (II) find the linear equation of middle line ad
- 8. Several mathematical geometry proof questions! In a known parallelogram, extend Da to F, make AF = AC, connect CF with ab at point E, angle ABC = 120 degrees, angle CEB = 45 degrees, BC = 2, and find the length of BD (which cannot be proved by similar triangle) It is known that in the quadrilateral ABCD, ad = BC, F and m are the midpoint of DC and ab respectively, the extension lines of AD and MF intersect at g, and the extension lines of MF and BC intersect at E It is known that in the triangle ABC, e is the midpoint of BC, ad is perpendicular to BC, the perpendicular foot is D, de = 1 / 2Ab Magic snow baby 22:50:10
- 9. Two elementary geometry problems 1. In rectangle ABCD, point O is the midpoint of AC, AC = 2Ab, extend AB to g, make BG = AB, connect go to intersection BC to e, extend go to intersection ad to point F, prove: quadrilateral aecf is diamond 2. Make three equilateral triangles △ abd, △ BCE, △ ACF on the same side of BC with △ ABC three times (1) Quadrilateral what is ADEF and why? (2) When △ ABC satisfies what condition, the quadrilateral ADEF is a rectangle (3) When △ ABC satisfies what conditions, the quadrilateral ADEF is a diamond, why? (4) When △ ABC satisfies what conditions, quadrilateral with a, D, e, F as vertex does not exist? Thank you~
- 10. A geometry problem in the third grade of junior high school In the circle O, the diameter AB intersects with the diameter CD, passing through three points a, O and B respectively to make the vertical line of CD, and the vertical feet are e, h and f respectively
- 11. There are three function expressions
- 12. A problem of finding function expression in the first year of senior high school Given that the minimum value of the function y = 1-2a-2ax + 2x ^ 2 (- 1 ≤ x ≤ 1) is f (a), the expression of F (a) is obtained (what I don't know is that if you bring a into a function, it means that f (a) = 1-2a, and how to find an expression.)
- 13. In the arithmetic sequence {an}, if A3 + A9 + A15 + A17 = 8, then a11=______ ．
- 14. If the equation x ^ 2 + (m-1) x + 1 = 0 has a solution in the interval [0,2], find the value range of M
- 15. A high school on the concept of function to understand the problem Why should we pay attention to the change of the value range of the independent variable when we use the substitution method in the method of finding the analytic expression of a function, otherwise we may not get the incorrect result?
- 16. Finding the number of zeros of a function ①-x^2-3x-2 x≤0 g(x)=f(x)+x={ ②x-2 x>0 Step by step I'm not very good at it { ①-x^2-3x-2 x≤0 g(x)=f(x)+x={ { ②x-2 x>0
- 17. A school needs to hold a student congress, which stipulates that each class selects one representative for every 10 students. When the remainder of the number of students divided by 10 is greater than 6, another representative will be selected. Then, the functional relationship between the number of Representatives y elected by each class and the number x of students in the class can be expressed as () A. y=[x10]B. y=[x+310]C. y=[x+410]D. y=[x+510]
- 18. Given f (x) + 2F (1 / x) = x (x is not equal to 0), how to find f (x)?
- 19. A high school function problem do somebody a favour, Y ^ 2 = - x ^ 2 + 4ax-3 x ∈ [1,2] to find the range,
- 20. Add 150 points! Is the formula of Dao algebra! Challenge the limit~ Find the difference between the quadratic power of 2x - 3xy + 7Y and the quadratic power of 6x - 5xy - 2Y! Note that it is difference! Is it the quadratic power of - 4x + 2XY + 9y! : if the input value of X is 1, the output value is 1: if the input value of X is - 1, the output value is - 3. When the input value of X is half, the output value is - 4 / 3? As shown in the figure: the cube of input x * k + B, output K should be 2, B should be - 1, right? Two full answers ~ add 200 points!