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Summer Clouds moderators
14/09/2017 at 08:40
Answers
1
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Rectangle ABCD, shown here, has point E on side AB such that the ratio of the area of trapezoid EBCD to that of triangle AED is 5:1. What is the value of the ratio AE:EB?
undefined

  • ...
    Phan Thanh Tinh Coordinator 14/09/2017 at 10:55

    \(S_{ABCD}=S_{AED}+S_{EBCD}=S_{AED}+5S_{AED}=6S_{AED}\)

    \(=6.\dfrac{AE.AD}{2}=3.AE.AD\) but \(S_{ABCD}=AB.AD\)

    \(\Rightarrow AB=3AE\Rightarrow EB=AB-AE=3AE-AE=2AE\)

    Hence, the answer is 1 : 2

    Selected by MathYouLike

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Summer Clouds moderators
13/10/2017 at 10:16
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Find x such that \(\left|x+2\right|=\left|3x-1\right|\).

  • ...
    Phan Thanh Tinh Coordinator 13/10/2017 at 11:42

    There are 4 cases :

    + \(x< -2\)

    \(-x-2=1-3x\Leftrightarrow2x=3\Leftrightarrow x=\dfrac{3}{2}\) (asburd)

    + \(-2\le x< \dfrac{1}{3}\)

    \(x+2=1-3x\Leftrightarrow4x=-1\Leftrightarrow x=-\dfrac{1}{4}\) (satisfied)

    + \(x\ge\dfrac{1}{3}\)

    \(x+2=3x-1\Leftrightarrow3=2x\Leftrightarrow x=\dfrac{3}{2}\) (satisfied)

    So, \(S=\left\{-\dfrac{1}{4};\dfrac{3}{2}\right\}\)

    Selected by MathYouLike

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Lê Quốc Trần Anh Coordinator
13/11/2017 at 17:47
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How many squares can be formed on a 16-pin rectangular geoboard?


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Cloud moderators
29/11/2017 at 15:32
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If A represents a digit in the equation 0.0A = \(\sqrt{0,0049}\) , what is the value of A

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    Monster girls 29/11/2017 at 15:41

    \(0,0A=\sqrt{0.0049}=0.07\)

    \(\Rightarrow A=7\)

    Selected by MathYouLike
  • ...
    Trần Quỳnh Anh 27/12/2017 at 19:52

    we have : 0,0A=\(\sqrt{0,0049}\)

    but \(\sqrt{0,0049}=0,07\)

    \(\Rightarrow0,0A=0,07\)

    \(\Rightarrow A=7\)

    So the value of A is 7


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longia
31/12/2017 at 08:01
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5
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We have

A = 545 - 544 

Prove that : A : 3

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    Help you solve math 31/12/2017 at 08:16

    We have : 

    A = 545 - 544 = 544(54 - 1)

        = 544 . 53

    => A : 53

    longia selected this answer.
  • ...
    Lê Quốc Trần Anh Coordinator 31/12/2017 at 08:19
    Do not A4 and self-, Help you solve math.
  • ...
    longia 31/12/2017 at 08:27

    Đề sai xin lỗi


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Lê Quốc Trần Anh Coordinator
07/04/2018 at 09:43
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What is the smallest integer value of $c$ such that the function $f(x)=\frac{2x^2+x+5}{x^2+4x+c}$ has a domain of all real numbers?


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Lê Quốc Trần Anh Coordinator
11/06/2018 at 02:08
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Given a,b,c,d satisfys \(ab=cd\). Prove that: \(a^5+b^5+c^5+d^5\) isn't a prime number.


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Lê Quốc Trần Anh Coordinator
08/07/2018 at 06:15
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On a 12-hour digital clock, at how many times during a 24-hour day will all of the digits showing the time be the same?

Mathcounts


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Face586
03/08/2018 at 14:16
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1
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Everyone has one at the time, down, but it never moves or moves anywhere

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    Cristiano Ronaldo 03/08/2018 at 14:23

    Everyone has one at the time, down, but it never moves or moves anywhere

    Answer: It's a road

     
     
     
     

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Nếu Có Thể
21/03/2017 at 17:12
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The provincial : A = 1.2 + 2.3 + 3.4 + ...... + 100.101

                          B = 1 + 2 + 3 + ...... + 100

                         C = 12 + 22 + 32 + ....... + 1002

  • ...
    Trịnh Đức Phát 22/03/2017 at 12:39

    We have : A = 1.2 + 2.3 + 3.4 + ...... + 100.101

        =>       3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ....... + 99.100.101 

        =>       3A = 99.100.101

        =>         A = 99.100.101/3

        =>         A = 333300

    Nếu Có Thể selected this answer.
  • ...
    →இے๖ۣۜQuỳnh 22/03/2017 at 20:15

    B = 1 + 2 + 3 + ...... + 100

    B is numbered as:

               100 - 1 + 1 = 100 (số)

    Total B is:

               (100 x 101) : 2 = 5050 

  • ...
    →இے๖ۣۜQuỳnh 22/03/2017 at 20:14

    C = 12 + 22 + 32 + ...... + 1002

        = 1.1 + 2.2 + 3.3 + ...... + 100.100

        = 1.(2 - 1) + 2.(3 - 1) + 3.(4 - 1) + ...... + 100.(101 - 1)

        = 1.2 - 1 + 2.3 - 2 + 3.4 - 3 + ....... + 100.101 - 100

        = (1.2 + 2.3 + 3.4 + ...... + 100.101) - (1 + 2 + 3 + ...... + 100)

        From the calculated results of A and B we should compute

     C = 333300 - 5050

     C = 328250 

     

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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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