As shown in the figure, the rectangle ABCD is folded along AE so that point d falls at point F on the edge of BC. If ∠ BAF = 60 °, then ∠ DAE=______ Degree

The results show that ∵ BAF = 60 ° and ∵ DAF = 30 ° and ∵ AF is obtained by ad folding, ∵ ade ≌ △ AFE and ∵ DAE = ∠ EAF = 12 ∠ DAF = 15 °. So the answer is 15

Given that the image of a function of degree passes through point a (- 2, - 1) and is parallel to the line y = 2x-3, find the expression of the function

Let the analytic expression of a function be y = KX + B,
Given that the image of a linear function is parallel to the line y = 2x-3, then k = 2,
∴y=2x+b
∵ the image of a function of degree passes through point a (- 2, - 1),
∴-4+b=-1
b=3
The expression of this function is y = 2x + 3

As shown in the figure, fold the rectangle ABCD along AE so that the point d falls on the point F on the BC side. If ∠ BAF = 60 °, calculate the degree of ∠ DAE

The rectangle ABCD is folded along AE so that point d falls at point F on the edge of BC
So:
AE vertical bisection DF
AD=AF
∠DAE=1/2∠DAF
And because:
∠BAF=60°,∠BAD=90°
So:
∠DAF=∠BAD-∠BAF=30°
∠DAE=1/2∠DAF=15°

Find the expression of the linear function of the image passing through the point (2, - 1) and parallel to the line y = 2x + 1

The slope of the straight line y = KX + B is k, and the slope of the linear function parallel to it is also K. in this problem, the linear function parallel to y = 2x + 1 must be y = 2x + B. substituting the point (2, - 1), we get b = - 5, and the answer is y = 2x-5

The rectangle ABCD is folded along AE so that point d falls at point F on the edge of BC. If ∠ BAF = 50 °, calculate the degree of ∠ DAE

∵∠BAD＝90, ∠BAF＝50
∴∠DAF＝∠BAD-∠BAF＝40
The ∵ ade is folded into ∵ AFE along AE
∴∠DAE＝∠FAE
∴∠DAE＝∠DAF/2＝20°

The linear function is parallel to the image of y = - 2x + 3, and its expression can be obtained through (1, - 5)

If a linear function is parallel to the image of y = - 2x + 3, then let the function be y = - 2x + B
Substituting (1, - 5) into y = - 2x + B
We get - 5 = - 2 + B
b=-3
The function is y = - 2x-3

As shown in the figure, a rectangular piece of paper ABCD is folded along AE so that point d falls at point F on the edge of BC. If ∠ BAF = 55 °, what degree is ∠ DAE equal to?

=(90-55)/2=17.5

Given the image of the first-order function passing through points (2,1) and (- 1, - 2) (1), the expression of the first-order function can be obtained
(2) Find the coordinates of the intersection point of this function and X, Y axis
(3) Find the area of the triangle formed by the image of the first-order function and the two coordinate axes

Let the expression of a linear function be y = KX + B. substituting points (2,1) and (- 1, - 2) into it, we can get 2K + B = 1. ① - K + B = - 2. ② ① 2, we can get 3K = 3 solution, k = 1. Substituting points (2,1) and (- 1, - 2) into it, we can get 2 + B = 1 solution, we can get b = - 1

E is a point on the edge BC of water chestnut ABCD, and ab = AE, AE intersects BD in O, and ∠ DAE = 2 ∠ BAE, the proof is EB = OA

It is proved that if ∠ BAE = α °, then ∠ DAE = ∠ AEB = 2 α°. AB = AE → ∠ Abe = ∠ AEB = 2 α °→ ∠ abd = ∠ CBD = α °
Therefore, AEB = BOE = 2 α °→ EB = ob; BAE = abd = α °→ ob = OA
So EB = OA

Given that the graph of a function y = KX + B passes through two points a (1,1), B (2, - 1), the analytic expression of this function is obtained

∵ the image of the first-order function y = KX + B passes through two points a (1,1), B (2, - 1), ∵ 1 = K + B − 1 = 2K + B, the solution is k = − 2B = 3, ∵ the analytic expression of the first-order function is y = - 2X + 3

As shown in the figure, the rectangle ABCD is folded along AE so that point d falls at point F on the edge of BC. If ∠ BAF = 60 °, then ∠ DAE=______ Degree