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Carter
21/04/2017 at 08:05
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Show that if a convex quadrilateral with side-lengths a, b, c, d and area \(\sqrt{abcd}\)  has an inscribed circle, then it is a cyclic quadrilateral.

 


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No Name
29/05/2017 at 07:19
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4
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in a garage has 2 bikes,  3 cars and 4 three wheelers. ask , how many wheels in the garage??

whjbe

  • ...
    Vũ Hà Vy Anh 29/05/2017 at 07:21

    2 x2+3x4+4x3 =28

    there are 28 wheels in the garage

    No Name selected this answer.
  • ...
    Tina 29/05/2017 at 22:19

    Have: \(2\cdot2+3\cdot4+4\cdot3=28\left(wheels\right)\)in the garage

  • ...
    Phan Minh Anh 29/05/2017 at 15:36

    2x2+3x4+4x3=28

    There are 28 wheels in the garage.


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Summer Clouds moderators
04/07/2017 at 14:16
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1
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A triangle has sides of lengths 6, 10 and 11. An equilateral tri angle has the same perimeter. What is the side length of the equilateral triangle?
A. 18
B. 11
C. 10
D. 9
E. 6

  • ...
    Phan Thanh Tinh Coordinator 04/07/2017 at 18:04

    The perimeter of each triangle is : 6 + 10 + 11 = 27

    The length of each side of the equilateral triangle is : 27 : 3 = 9

    Hence,the answer is D


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Tôi tên ĐÔng
26/07/2017 at 11:15
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2
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How many 4 - digit numbers contain the digit 2, or the digit 3 or both?

Help me

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    Searching4You 26/07/2017 at 11:18

    Hiệp Dương : You answer very fast, sir :))

    More than 8 lines but you just answer in one minute.

    Probably copier :))

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    Hiệp Dương 26/07/2017 at 11:16

    The number of 4 - digit numbers is:

                        (9999 - 1000): 1 + 1 = 9000 (number)
    If you do not use numbers 2 and 3, then you have eight digits left to form units, tens and hundreds. Since zeros can not be used to make thousands of digits, there are only seven digits left to make thousands.

    According to the kernel rule, we have:

                   8 x 8 x 8 x 7 = 3584 (number)
    Inference: A 4-digit number containing two digits, or three or both, is                 9000 - 3584 = 5416 (number).

                       Answer : 5416 (number).

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Kaya Rengest
04/09/2017 at 14:55
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2
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450 +20 + 50 + 80 + 100=?Dễ

 

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    Math You Like 04/09/2017 at 14:56

    450 + 20 + 50 + 80 + 100

    =(450 + 50) + (20 + 80) + 100

    =500 + 100 + 100

    =700

    Kaya Rengest selected this answer.
  • ...
    Kaya Rengest 04/09/2017 at 15:14

    Thank you. You are very good


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Summer Clouds moderators
21/09/2017 at 09:16
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Lines AC and BD meet at point O. Given that OA cm OB cm OC cm = = = 40 , 50 , 60 and OD cm = 75 , find the ratio of the area of triangle AOD to the area of triangle BOC.  
undefined

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    Phan Thanh Tinh Coordinator 21/09/2017 at 09:51

    \(\Delta AOD,\Delta COD\) have the same altitude drawn from D to AC and bases \(\dfrac{OA}{OC}=\dfrac{40}{60}=\dfrac{2}{3}\) , so \(\dfrac{S_{AOD}}{S_{COD}}=\dfrac{2}{3}\)

    \(\Delta BOC,\Delta COD\) have the same altitude drawn from C to BD and bases \(\dfrac{OB}{OD}=\dfrac{50}{75}=\dfrac{2}{3}\), so \(\dfrac{S_{BOC}}{S_{COD}}=\dfrac{2}{3}\)

    \(\Rightarrow S_{AOD}=S_{BOC}\) or the answer is 1

    Selected by MathYouLike

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Summer Clouds moderators
19/10/2017 at 14:11
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A circular pizza was cut into 12 congruent slices, as shown. If 2 slices were eaten, what is the sum of the central angles of the slices that were not eaten? 
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    ForOver Coordinator 19/10/2017 at 16:22

    The whole angles of the square is \(360^0\)

    The pizza is cut into 12 congruent slices => Each slice has the angle of \(\dfrac{360}{12}=30^0\)

    So the sum of the central angles of the slices that were not eaten after ate 2 slices is :

    \(360-30\cdot2=360-60=300^0\)

    Answer : \(300^0\)

    Selected by MathYouLike

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Cloud moderators
06/12/2017 at 13:58
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In right triangle ABC, m\(\angle\)B = 30 degrees and BC = 9 cm. If D is on side BC so that segment AD bisects acute \(\angle\)A, what is DC?
undefined

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    Dao Trong Luan Coordinator 06/12/2017 at 16:13

    \(\widehat{CAB}=180^o-90^o-30^o=60^o\)

    \(tan\widehat{CAB}=\dfrac{BC}{CA}\)

    \(\Leftrightarrow tan60^o=\dfrac{9}{CA}\Leftrightarrow CA=\dfrac{9}{\sqrt{3}}=3\sqrt{3}\) cm

    \(\angle CAD=\dfrac{60^o}{2}=30^o\Leftrightarrow\angle ADC=180^o-90^o-30^o=60^o\)

    \(tan\angle ADC=\dfrac{CA}{CD}\)

    \(\Leftrightarrow tan60^o=\dfrac{3\sqrt{3}}{CD}\)

    \(\Leftrightarrow\sqrt{3}=\dfrac{3\sqrt{3}}{CD}\Leftrightarrow CD=3cm\)

    Selected by MathYouLike

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Lê Quốc Trần Anh Coordinator
03/01/2018 at 17:03
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 When a dart hits within the center circular region of this circular target, the score is 50, and when a dart hits within the outer ring, the score is 7. If three darts randomly hit the target, what is the probability that the total score is 64? Express your answer as a common fraction. 


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Lê Quốc Trần Anh Coordinator
01/05/2018 at 02:49
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In a $3\times 4$ grid, Rob starts at $(0,0)$ and needs to reach $(3,4)$ while only moving right or up. Given that he cannot pass through $(2,2)$, how many distinct paths are possible?


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Trigonometric
sin cos tan cot sinh cosh tanh
Lim-log

Combined operations

 

α β γ δ θ σ ∂ ε ω φ ϕ π μ λ Ψ ξ η χ ζ ι κ ν ψ Ω ρ τ υ Γ Δ Λ Φ Π Σ Υ Ξ ϑ Θ ς ϰ
∞ ⊻ ⩞ ⋎ ⋏ ≀ ∪ ⊎ ⋓ ∩ ⋒ ⊔ ⊓ ⨿ ⊗ ⊙ ⊚ ⊛ ⊘ ⊝ ⊕ ⊖ ⊠ ◯ ⊥
⇔ ⇒ ⇐ → ← ↔ ↑ ↓
Operations
+ - ÷ × ≠ = ⊂ ⊃ ⊆ ⊇ ≈ ∈ ∉ ∃ ∄ ≤ ≥ ± ∓ ≠ ∅ ≃ ≅ ≡ ⋮ ⋮̸ ∀
(□) [□] {□} |□|

The type of system

m×n 1×2 1×3 1×4 1×5 1×6
2×1 2×2 2×3 2×4 2×5 2×6
3×1 3×2 3×3 3×4 3×5 3×6
4×1 4×2 4×3 4×4 4×5 4×6
5×1 5×2 5×3 5×4 5×5 5×6
6×1 6×2 6×3 6×4 6×5 6×6

Recipe:

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