As shown in the figure, in the parallelogram ABCD, P is any point on AC

As shown in the figure, in the parallelogram ABCD, P is any point on AC

Make de ⊥ AC at point E and BF ⊥ AC at point F
ABCD is a parallelogram
∴AD=BC,∠DAE=∠BCF
∴Rt△ADE≌Rt△BCF
∴DE=CF
∵S△ADP=1/2*AP*DE,S△ABP=1/2AP*BF
∴S△ADP=S△ABP

Given the quadratic function y = 2x2 + 9x + 34, when the independent variable x takes two different values X1 and X2, the function values are equal, then when the independent variable x takes X1 + X2, the function values and ()
A. The function values are equal when x = 1, B. the function values are equal when x = 0, C. the function values are equal when x = 14, D. the function values are equal when x = - 94

When the independent variable x takes two different values X1 and X2, the function values are equal, then the two points with X1 and X2 as abscissa are symmetrical about the straight line x = − 94, so there is X1 + X22 = − 94, so X1 + x2 = − 92. Substituting into the analytic expression of quadratic function, we get: y = 2 × (− 92) 2 + 9 × (- 92) + 34 = 34, A. when x = 1, y = 2 + 9 + 34 ≠ 34, so this option is wrong; B. when x = 0, y = 0 + 34 = 34, so this option is correct C. when x = 14, y = 2 × 116 + 9 × 14 + 34 ≠ 34, so this option is wrong; D. when x = - 94, y = 2 × 8116 + 9 × (- 94) + 34 ≠ 34, so this option is wrong, so B

Let z = Sin & sup2; (x + y), find all the second partial derivatives

dz/dx=2sin(x+y)*cos(x+y) dz/dy=2sin(x+y)*cos(x+y)
d(dz/dx)/dx=2cos(x+y)*cos(x+y)-2sin(x+y)*sin(x+y)
d(dz/dy)/dy=2cos(x+y)*cos(x+y)-2sin(x+y)*sin(x+y)
d(dz/dx)/dy=2cos(x+y)*cos(x+y)-2sin(x+y)*sin(x+y)
Yes, three of them are the same

One hundred pieces are placed on the four sides of the square on average. One piece is placed on each corner, and there are several pieces on each side

On each side, except for four corners
（100-4）/4=24
Add back two corners 24 + 2 = 26

If we know that there is no solution for the system of inequalities x greater than or equal to A-3 and X less than or equal to 15-5a, then two images of this function y = (A-2) x squared - x + 4 / 1 and X axis
Are there any intersections

That is, A-3 ≤ x ≤ 15-5a
unsolvable
So A-3 > 15-5a
6a>18
a>3
Quadratic function discriminant = 1 - (A-2) = 3-A

Finding the maximum value of function y = cos square x-3sin

y=1-sin²x-3sinx
=-(sinx+3/2)²+13/4
Axis of symmetry SiNx = - 3 / 2, opening downward
And - 1

Given that the positive integer AB satisfies A2-B2 = 15, find the value of ab

A2-B2 = 15 (a + b) (a-b) = 5 * 3, because a and B are positive integers, a + B = 5a-b = 3, a = 4, B = 1, so AB = 4 * 1 = 4

It is known that: as shown in the figure, in the parallelogram ABCD, ab = 4, ad = 7, the bisector of ∠ ABC intersects ad at point E, and the extension of intersection CD intersects at point F, then the length of DF is ()
A. 6B. 5C. 4D. 3

The bisector of the parallelogram ABCD AB CD Abe = CFE ABC intersects ad at the point e Abe = CBF CBF = CFB CF = CB = 7 DF = cf-cd = 7-4 = 3, so D is selected

One is a trapezoid with an upper bottom of 20 cm and a lower bottom of 32 cm. The lower bottom is extended by 1 / 4 and the area is 76 square cm larger than the original trapezoid

The height of the trapezoid is constant
Height of trapezoid:
76×2÷（32×1/4）
=152÷8
=19 (CM)
Area of original trapezoid:
（20+32）×19÷2
=52×19÷2
=494 (square centimeter)

Given △ ABC and line m, take line m as symmetry axis, draw the figure of △ ABC after axisymmetric transformation

As shown in the picture