Question

ATIVIDADE (TEOREMA DE TALES) 1) Nas figuras, a//b//c, calcule o valor de x. A) D) 3x+1 4 5 -b 5x-1 6 c 12 B) E) 4x+1 +12 3x **3 711 X 3x C) 2x-1 6 24 4x - 1​

Answer 1

Resposta:

Explicação passo a passo:

A)

(3x+1)/(5x-1) = 4/6 (:2)/(:2)

(3x+1)/(5x-1)= 2/3

3.(3x+1)=2.(5x-1)

9x+3= 10x - 2

3+2= 10x - 9x

5 = X

X = 5

========

B)

3/2= (4x+1)/3x

3.3x = 2.(4x+1)

9x = 8x + 2

X = 2

=========

C)

(2x-1)/(4x-1)= 6/24 (:6)/(:6)

(2x-1)/(4x-1)= 1/4

4.(2x-1)= 4x - 1

8x - 4 = 4x - 1

8x - 4x = - 1 + 4

4x = 3

X = 3/4

==========

D)

5/x = 3/(12-x)

5.(12-x)= 3x

60 - 5x = 3x

60 = 3x+5x

60 = 8x (:4)

15 = 2x

2x = 15

X = 15/2

X = 7,5

E)

3x/(x+6) = (x+3)/x

3x^2 = (x+6)(x+3)

3x^2 = x^2 + 3x + 6x + 18

3x^2 - x^2 = 9x + 18

2x^2 - 9x - 18 = 0

a = 1; b = - 9, c = - 18

/\= b^2 - 4ac

/\= (-9)^2 - 4.1.(-18)

/\= 81 + 72

/\= 153

153:3

51:3

17: 17

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1

\/153 = \/9.\/17 = 3\/17

X = ( - b +/- \/ /\)/2a

X = [-(-9) +/- \/153)/2.1

X' = (9 + 3\/17)/2

X " = (9 - 3\/17)/2 (negativo descartar)