It is proved that the function f (x) = x + 1 / X is a decreasing function on (- 1,0)

For any - 1

It is proved by the definition of monotonicity that f (x) = x 3 is an increasing function over R

Proof: let x1, X2 ∈ R, and x1 ＜ X2, then: F (x1) − f (x2) = x13 − x23 = (x1 − x2) (X12 + X22 + x1x2) = 12 (x1 − x2) [(x1 + x2) 2 + X12 + X22]; ∵ x1 ＜ X2, ∵ x1-x2 ＜ 0, x1, X2 are not all 0, (x1 + x2) 2 + X12 + X22 ＞ 0; ∵ f (x1) ＜ f (x2); ∵ f (x) = X3 is an increasing function on R

It is proved that f (x) = X3 + X is an increasing function on R

Given the function f (x) = X3 + X. (1) judge the parity of function f (x) and prove your conclusion; (2) prove that f (x) is an increasing function on R; (3) if f (M + 1) + F (2m-3) < 0, find the value range of M. (reference formula: a3-b3 = (a-b) (A2 + AB + B2))

(1) F (x) is an odd function on R. it is proved that: ∵ f (- x) = - x3-x = - (X3 + x) = - f (x), and ∵ f (x) is an odd function on R. (2) let any real number X1 and X2 on R satisfy x1 < X2, ∵ x1-x2 < 0, f (x1) - f (x2) = (x1-x2) + [(x1) 3 - (x2) 3] = (x1-x2) [(x1) 2 + (x2

I got a message from Jim

From Jim is an attributive modifier that defines the preceding message

If Mn is a straight line passing through point a, BD ⊥ Mn is at point D, CE ⊥ Mn is at point E,
(1) If Mn is rotated around point a so that Mn and BC intersect at point O, other conditions remain unchanged. Are BD and AE sides equal? Why?
(2) When Mn rotates around point a, what is the relationship between BD, CE and de?
Don't cut corners

First of all, for the first question, according to the meaning of the question, ∠ BDA = ∠ AEC = 90 & ordm;, ab = AC, and ∠ bad + ∠ DAC = 90 & ordm;, ∠ DAC + ∠ ace = 90 & ordm;; (because ∠ AEC is a right angle), we can know ∠ bad = ∠ ace, so with the previous two conditions, we can prove that Δ abd and Δ AEC are congruent, so BD = AE
For the second question, we know that BD = AE and AE + de = ad. because we have proved that Δ abd and Δ AEC are congruent, so ad = EC, so BD + de = AE + de = ad = EC, we can get the relationship between them

Plural of dish and duck

dishes.

As shown in the figure, △ in ABC, ab = AC. (1) draw with a ruler and a compass: make the vertical bisector of AB intersect AB and AC at points m and N respectively, and connect BN; (2) if AB = AC = 20cm, BC = 12cm, calculate the perimeter of △ BNC

This problem is too simple. From t, we can see that Mn is the vertical bisector of AB, then the angle amn = angle BMN = 90 degrees, am = BM Mn is the common edge △ amn ≌ △ BMN, so an = BN ≌ AC = an + NC AC = 20cm ≌ BN + NV = 20cm BC = 12cm [known] ∩ the perimeter of BNC is an + NC + BC = 20 + 12 = 32cm. You can tell by talking about a picture, mmm, I have difficulties in learning

usually children like fish and meat ,( )they don't like vegetables or fruit.A and B but C or

Usually children like fish and meat, and they don't like vegetables and fruit
It's juxtaposed here

Let AB be the two right sides of a right triangle. If the perimeter of the triangle is six, the length of the hypotenuse is two, and the point is five, then what is the value of AB

(a+b)²=a²+2ab+b²
a²+2ab+b²=2ab+2.5*2.5=2ab+6.25
(a+b)²=(6-2.5)²=12.25
2ab+6.25=12.25
2ab=6
ab=3

It is proved that the function f (x) = x + 1 / X is a decreasing function on (- 1,0)