Question

Ajutoooooooooooooooooooooooor rapid!!!!! Dau coroana

Answer 1

Răspuns:

Explicație pas cu pas:

$0,(3) = \frac{3}{9}=\frac{1}{3}\\\\\frac{AB}{AC} = \frac{1}{3}\\\\AC =3*AB\\AC = AB + BC$

$AB + BC = 3*AB\\BC = 2*AB\\1,5 = 2*AB\\AB = \frac{1,5}{2} = 0,75m$

$AC = AB + BC = 0,75 + 1,5 = 2,25m$

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m(∡BAC) = m(∡CAD) + m(∡BAD)

m(∡CAD) = m(∡BAD) + 20°

m(∡BAC) = 110°

Asadar:

110° = m(∡BAD) + 20° + m(∡BAD) = 2*m(∡BAD) + 20°

2*m(∡BAD) = 110° - 20° = 90°

m(∡BAD) = 90°/2 = 45°

m(∡CAD) = m(∡BAD) + 20° = 45° + 20° = 65°

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Notam cu x suma initiala

A cheltuit 45 de lei, deci a ramas cu (x-45) lei.

Daca a cheltuit apoi 2/3 din rest, inseamna ca la sfarsit a rams cu 1/3 din rest, deci:

$\frac{1}{3} *(x-45)=25 lei$

$x-45 = 3*25\\x-45=75\\x=45+75\\x=120lei$