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Igoryamba
2 years ago
9

What is the gcf of 60 and 72

Mathematics
1 answer:
MariettaO [177]2 years ago
4 0
       60              72
        /\                /\
     10x6            9x8
     /\     /\          /\    /\
  2x5  2x3      3x3    2x4                  60 GCF= 2
                                    /\                  72 GCF = 2
                                    2x2
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Please prove this........​
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Answer:  see proof below

<u>Step-by-step explanation:</u>

Given: A + B + C = π    →     C = π - (A + B)

                                    → sin C = sin(π - (A + B))       cos C = sin(π - (A + B))

                                    → sin C = sin (A + B)              cos C = - cos(A + B)

Use the following Sum to Product Identity:

sin A + sin B = 2 cos[(A + B)/2] · sin [(A - B)/2]

cos A + cos B = 2 cos[(A + B)/2] · cos [(A - B)/2]

Use the following Double Angle Identity:

sin 2A = 2 sin A · cos A

<u>Proof LHS → RHS</u>

LHS:                        (sin 2A + sin 2B) + sin 2C

\text{Sum to Product:}\qquad 2\sin\bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A - 2B}{2}\bigg)-\sin 2C

\text{Double Angle:}\qquad 2\sin\bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A - 2B}{2}\bigg)-2\sin C\cdot \cos C

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\text{Sum to Product:}\qquad 2\sin C\cdot 2\cos A\cdot \cos B

\text{Simplify:}\qquad \qquad 4\cos A\cdot \cos B \cdot \sin C

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7 0
3 years ago
F(x) = (3x + 6) (x - 3)²
Sever21 [200]

f(x)= 3x³ - 18x +9

Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Algebraic identities are employed in this manner for the computation of algebraic expressions and the solution of various polynomials.

Identity I: (a + b)² = a² + 2ab + b²

Identity II: (a – b)² = a² – 2ab + b²

Identity III: a² – b²= (a + b)(a – b)

Identity IV: (x + a)(x + b) = x² + (a + b) x + ab

Identity V: (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

Identity VI: (a + b)³ = a³ + b³ + 3ab (a + b)

Identity VII: (a – b)³ = a³ – b³ – 3ab (a – b)

Identity VIII: a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca)

f(x) = (3x + 6) (x - 3)²

      = ( 3x + 6) ( x - 3 )²

      = ( 3x + 6)( x² - 6x + 9)

      = 3x( x² - 6x + 9) + 6( x² - 6x + 9)

      = 3x³ - 6x² + 18x + 6x² - 36x +9

      = 3x³ - 18x +9

To learn more about algebraic expansions, refer to brainly.com/question/4344214

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When solving the equation x2 – 8x - 7 = 0 by completing the square, which equation
IgorLugansk [536]
<h3><u>A</u><u>n</u><u>s</u><u>w</u><u>e</u><u>r</u><u>:</u><u>-</u></h3>

Lets Solve

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4 0
3 years ago
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