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Formulae of Algebra
31.10.2012, 1:19:05 AM

Algebra

 Word Excel
 a+b=b+a a+b=b+a
 a+(b+c)=(a+b)+c=a+b+c a+(b+c)=(a+b)+c=a+b+c
 a±0=0±a=a a(+-)0=0(+-)a=a
 a−(b+c)=a−b−c a-(b+c)=a-b-c
 (a+b)−c=a+(b−c), c≤b (a+b)-c=a+(b-c), c(<=)b
 (a+b)−c=(a−c)+b, c≤a (a+b)-c=(a-c)+b, c(<=)a
 a−a=0 a-a=0
 ab=ba ab=ba
 a(bc)=abc a(bc)=abc
 1n=n, 0n=0 1n=n, 0n=0
 (a±b)c=ac±bc (a(+-)b)c=ac(+-)bc
 n!=1×2×3×…×(n−2)(n−1)n, n ∈ ℤ n!=1*2*3*...*(n-2)(n-1)n, n=element(integer())
 aaa…aaa=aˣ, x ∈ ℕ aaa...aaa=a^x, x=element(natural())
 x/y=zx/zy, y≠0, z≠0 x/y=zx/zy, y(!=)0, z(!=)0
 x(y/z)=xy/z, z≠0 x(y/z)=xy/z, z(!=)0
 (x/y)×(z/t)=xz/yt, y≠0, t≠0 (x/y)*(z/t)=xz/yt, y(!=)0, t(!=)0
 (x/y)×(y/x)=xy/xy=1, x≠0, y≠0 (x/y)*(y/x)=xy/xy=1, x(!=)0, y(!=)0
 (x/y)/(z/t)=xt/yz, y≠0, z≠0, t≠0 (x/y)/(z/t)=xt/yz, y(!=)0, z(!=)0, t(!=)0
 x/y/z=x/yz, z≠0, y≠0 x/y/z=x/yz, z(!=)0, y(!=)0

 x/y=z/t, xt=yz, y≠0, t≠0

 x/y=z/t, xt=yz, y(!=)0, t(!=)0

 CIRCLE:

C=2πr

S=πr²

π=3.1415926535897932384626433832795028841971693993751

 CIRCLE:

C=2*pi()*r

S=pi()*r^2

 pi()=3.1415926535897932384626433832795028841971693993751

 0−x=−x, 0−(−x)=x, x+(−x)=0  0-x=-x, 0-(-x)=x, x+(-x)=0
 x±(−y)=x∓y  x(+-)(-y)=x(-+)y
 |x|=|−x|  |x|=|-x|

 ISOSCELES TRIANGLE ABC WITH THE BASE AC:

AB=BC, ∠A=C, BH⊥AC, AH=CH, ∠ABH=∠CBH

 ISOSCELES TRIANGLE ABC WITH THE BASE AC:

AB=BC, angle(A)=angle(C), BH=perpend(AC), AH=CH, angle(ABH)=angle(CBH)

 T-ANGLES #1 AND #2:

1+∠2=180°

 T-ANGLES #1 AND #2:

angle(1)+angle(2)=180*degree()

 X-ANGLES #1 AND #2:

∠1=2

 X-ANGLES #1 AND #2:

angle(1)=angle(2)

 PARALLEL LINES a, b AND SECANT c:

∠4=∠5, ∠3=∠6, ∠1=∠5, ∠2=∠6

∠3+∠5=180°, ∠4+∠6=180°

 PARALLEL LINES a, b AND SECANT c:

angle(4)=angle(5), angle(3)=angle(6), angle(1)=angle(5), angle(2)=angle(6)

angle(3)+angle(5)=180*degree(), angle(4)+angle(6)=180*degree()

 CONGRUENT TRIANGLES ABC AND A₁B₁C₁:

AB=A₁B₁, BC=B₁C₁, ∠B=∠B

AC=A₁C₁, ∠A=∠A₁, ∠C=∠C

AB=A₁B₁, BC=B₁C₁, AC=A₁C

 CONGRUENT TRIANGLES ABC AND A(1)B(1)C(1):

AB=A(1)B(1), BC=B(1)C(1), angle(B)=angle(B(1))

AC=A(1)C(1), angle(A)=angle(A(1)), angle(C)=angle(C(1))

AB=A(1)B(1), BC=B(1)C(1), AC=A(1)C(1)

 CONGRUENT TRIANGLES ABC AND A₁B₁C₁, B=90°:

AB=A₁B, BC=B₁=C

AC=A₁C₁, ∠C=∠C

AC=A₁C₁, AB=A₁B

 CONGRUENT TRIANGLES ABC AND A(1)B(1)C(1), angle(B)=90*degree():

AB=A₁B, BC=B₁=C

AC=A₁C₁, ∠C=∠C

AC=A₁C₁, AB=A₁B

 △ABC, ∠B=90°, C=30°:

AC=2AB

 triangle(ABC), angle(B)=90*degree(), angle(C)=30*degree():

AC=2AB

 aᵐaⁿ=aᵐ⁺ⁿ, aᵐ/aⁿ=aᵐ⁻  a^m*a^n=a^(m+n), a^m/a^n=a^(m-n)
 (−a)ˣ=aˣ, x ∈ ℕ, x/2 ∈ ℕ  (-a)^x=a^x, x=element(natural()), x/2=element(natural())
 (−a)ˣ=aˣ, x ∈ ℕ, x/2 ∉ ℕ  (-a)^x=-a^x, x=element(natural()), x/2(!=)element(natural())
 a⁰=1, a≠0  a^0=1, a(!=)0
 xᶻyᶻ=(xy)ᶻ x^zy^z=(xy)^z
 (aᵐ)ⁿ=a  (a^m)^n=a^(mn)
 (a±b)²=a²±2ab+b² (a(+-)b)^2=a^2(+-)2ab+b^2
 (a±b)³=a³±3a²b+3ab²±b³ (a(+-)b)^3=a^3(+-)3a^2b+3ab^2(+-)b^3
 (a+b)(a−b)=a²−b²  (a+b)(a-b)=a^2-b^2
 a³±b³=(a±b)(a²∓ab+b²)  a^3(+-)b^3=(a(+-)b)(a^2(-+)ab+b^2)
 ∑=(n−2)×180°, n ∈ ℕ, n≥3  sum()=(n-2)*180*degree(), n=element(natural()), n(>=)3

 PARALLELOGRAM ABCD WITH CENTER O:

AB=CD, BC=AD, ∠A=∠C, ∠B=∠D, AO=CO, BO=DO

AD+MC=a, DM⊥AB=h, S=ah

 PARALLELOGRAM ABCD WITH CENTER O:

AB=CD, BC=AD, angle(A)=angle(C), angle(B)=angle(D), AO=CO, BO=DO

AD+MC=a, DM=h, S=ah

 RECTANGLE ABCD:

AC=BD

 RECTANGLE ABCD:

AC=BD

 RHOMBUS ABCD:

AC⊥BD, ∠BAO=∠DAO, ∠ABO=∠CBO

 RHOMBUS ABCD:

AC=perpend(BD), angle(BAO)=angle(DAO), angle(ABO)=angle(CBO)

 x̄=(x₁+x₂+…+xₙ)/n average(x)=(x(1)+x(2)+...+x(n))/n
 S²=((xx̄)²+(xx̄)²+…+(xx̄)²)/n  S^2=((x(1)-average(x))^2+(x(2)-average(x))^2+...+(x(n)-average(x))^2)/n
 H=n/(1/a₁+1/a₂+…+1/aₙ)  H=n/(1/a(1)+1/a(2)+...+1/a(n))
 P(A)=N(A)/N P(A)=N(A)/N


Category: My files | Added by: Elektronika_XQ-19 | Tags: math, algebra
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