Question

determine em cada figura o valor de x. URGENTE PARA HJ!
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Answer 1

Explicação passo-a-passo:

Utilizando potência de ponto nas figuras:

$\overline{PA}.\overline{PB}=\overline{PC}.\overline{PD}$

b)

$2x.x=9.2\\\\2x^{2} =18\\\\x^{2} =\dfrac{18}{2} \\\\x^{2} =9\\\\x=\pm\sqrt{9} \\\\x=\pm3\\\\\boxed{x=3 \, \ \text pois\ x>0}$

c)

$6.12=x.4\\\\4x=72\\\\x=\dfrac{72}{4} \\\\\boxed{x=18}$

e)

$(3+x).1=3.2\\\\3+x=6\\\\x=6-3\\\\\boxed{x=3}$

f)

$(x-1).2x=(3x-4).x\\\\2x^{2} -2x=3x^{2} -4x\\\\3x^{2} -4x-2x^{2} +2x=0\\\\x^{2} -2x=0\\\\x(x-2)=0\\\\x=0\\\text ou\\x-2=0\\\\x=2\\\\\boxed{x=2 \ , \text pois\ x>0}$

h)

$x.8=6.(18-6)\\\\8x=6.12\\\\8x=72\\\\x=\dfrac{72}{8} \\\\\boxed{x=9}$

i)

$2x.x=8.9\\\\2x^{2} =72\\\\x^{2} =\dfrac{72}{2} \\\\x^{2} =36\\\\x=\pm\sqrt{36} \\\\x=\pm 6\\\\\boxed{x=6 \ , \text pois\ x>0}$

k)

$x.x=3.27\\\\x^{2} =81\\\\x=\pm\sqrt{81}\\\\x=\pm 9\\\\\boxed{x=9 \ , \text pois\ x>0}$

l)

$x.(4x-1)=(x+1).3x\\\\4x^{2} -x=3x^{2} +3x\\\\4x^{2} -x-3x^{2} -3x=0\\\\x^{2} -4x=0\\\\x(x-4)=0\\\\x=0\\\\\tetx ou\\\\x-4=0\\\\x=4\\\\\boxed{x=4\ , \text pois\ x>0}$