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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=∠B₁
AC=A₁C₁, ∠A=∠A₁, ∠C=∠C₁
AB=A₁B₁, BC=B₁C₁, AC=A₁C₁
| 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=A₁B₁, BC=B₁=C₁
AC=A₁C₁, ∠C=∠C₁
AC=A₁C₁, AB=A₁B₁
| CONGRUENT TRIANGLES ABC AND A(1)B(1)C(1), angle(B)=90*degree():
AB=A₁B₁, BC=B₁=C₁
AC=A₁C₁, ∠C=∠C₁
AC=A₁C₁, AB=A₁B₁ | △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⁻ⁿ
| 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=aᵐⁿ
| (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=((x₁−x̄)²+(x₂−x̄)²+…+(xₙ−x̄)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 |
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Category: My files | Added by: Elektronika_XQ-19
| Tags: math, algebra
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