If LG (X-Y) + LG (x + 2Y) = LG2 + lgx + lgY, find the value of XY

If LG (X-Y) + LG (x + 2Y) = LG2 + lgx + lgY, find the value of XY

∵ LG (X-Y) + LG (x + 2Y) = LG2 + lgx + lgY, ∵ LG (X-Y) (x + 2Y) = lg2xy. ∵ LG (X-Y) (x + 2Y) = 2XY, that is, (x-2y) (x + y) = 0. Then from X and Y are positive numbers, we can get x + y ≠ 0, ∵ x-2y = 0, ∵ xy = 2

The circumference of the bottom surface of a cone is 12.56 decimeters, the height is 6 decimeters, and its volume is 1______ Cubic decimeter

The bottom radius is: 12.56 △ 3.14 △ 2, = 2 (decimeter); the bottom area is: 3.14 × 22, = 3.14 × 4, = 12.56 (square decimeter); the volume is: 13 × 12.56 × 6, = 12.56 × 2, = 25.12 (cubic decimeter); a: its volume is 25.12 cubic decimeter

Given a = (4a + b) (a-5b), B = 2A (2a-10b), find a-b

Given a = (4a + b) (a-5b), B = 2A (2a-10b), then:
A-B
=﹙4a＋b﹚﹙a－5b﹚- 2a﹙2a－10b﹚
=(4a+b)(a-5b)- 4a(a-5b)
=(4a+b-4a)(a-5b)
=b(a-5b)
=ab-5b²

The length of a triangle, three sides AB, AC and BC are 20 cm, 21 cm and 29 cm respectively. Find the area of the shadow in the figure

Where is the shadow

A number that is both prime and even is______ ．

From the meaning of prime number and even number, the number that is both prime number and even number is 2

It is known that the side lengths of the two right sides of a right triangle are (5 + √ 3) cm and (5 - √ 3) cm?

The square of the hypotenuse of a right triangle is equal to the sum of the squares of the two right angles
Then: square of hypotenuse = (√ 3 + 5) & # 178; + (5 - √ 3) & # 178; = (√ 3) & # 178; + 5 & # 178; + 10 √ 3 + 5 & # 178; - 10 √ 3 + (√ 3) & # 178; = 3 + 25 + 10 √ 3 + 25-10 √ 3 + 3 = 6 + 50 + 0 = 56 (CM)
(1) The perimeter of the triangle: (√ 3 + 5) + (5 - √ 3) + 56 =: √ 3 + 5 + 5 - √ 3 = 10 + 0 = 10 (CM)
The area of a right triangle is equal to the product of two right angles and multiplied by 1 / 2
Then: area of triangle = (√ 3 + 5) * (5 - √ 3) * 1 / 2 = (5 + √ 3) * (5 - √ 3) * 1 / 2 = 5 & # 178; * (√ 3) &# 178; * 1 / 2 = 25 * 3 * 1 / 2 = 37.5 (CM & # 178;)
(2) The area of the triangle: 37.5cm & # 178;

AB is the diameter of the circle O, ad is the tangent point of the circle O, C on the circle O, BC is parallel to OD, AB is 2, OD is 3, then BC is long

cosAOD=AO/OD=1/3
In the right triangle ABC, BC = AB * cosabc
Because od is parallel to BC
So angle AOD = angle ABC
BC=2×1/3=2/3
What else do you need to do

Given that the line segment AB = 8cm, there is a point C on the line AB, and AC = 3cm, m and N are the midpoint of AC and BC respectively, find the length of Mn
Draw a graph and write the process in geometric language

Draw a picture and the answer will come out
（1）AC + BD = AB - CD = 8 - 3 = 5
（2）MN = MC + CD + DN = AC/2 + CD + BD/2 = 3 + 5/2 = 5.5
（3）MN = MC + CD + DN = AC/2 + CD + BD/2 = (AC + BD)/2 + CD = (AB - CD)/2 + CD = (a - b)/2 + b = a/2 - b/2 + b = a/2 + b/2

As shown in the figure, in ⊙ o, AB is the chord of ⊙ o, C and D are two points on the straight line AB, and AC = BD. it is proved that △ OCD is an isosceles triangle

It is proved that: (1) the vertical foot is m when passing through O, and ∵ om ⊥ AB, ∵ am = BM, ∵ AC = BD, ∥ cm = DM, and ∵ om ⊥ AB, ∥ OC = OD, ∥ OCD is isosceles triangle. (2) connecting OA, OB; ∵ OA = ob, ∥ OAB = ∥ oba, ≌ CBO ≌ Dao, ∥ OC = OD, ∥ OCD

If the solution of the equation X-2 / 2x + a = - 1 is a positive number, find the value range of A

X－2/2X＋a=-1
X = (2-A) / 3 and X is not equal to 2
And x > 0
Then (2-A) / 3 > 0 and not equal to 2
a