Réponses

2014-09-24T23:48:53+02:00
Salut,

I.

Aire ABCD = AB x BC = (a + b) x k

Aire ABCD = Aire AEFD + Aire EBCF = AE x EF + EB x BC = (a x k) + (b x k)

(a + b) x k = (a x k) + (b x k)

II.

Aire ABCD = AB x BC = (a + b) (c + d)

Aire ABCD = Aire AEIH + Aire EBFI + Aire FCGI + Aire GDHI
                 = (a x c) + (c x b) + (b x d) + (a x d)

(a + c) (c + d) = (a x c) + (c x b) + (b x d) + (a x d).

III.

1. Pour 1:

1; 1²= 1 ; 1 + 3 = 4; 4 x -2 = -8 ; -8 + 1 = -7

Pour 2

2; 2²= 4 ; 4 + 3 = 7; 7 x -2 = -14 ; -14 + 2= - 12

Pour 1/2

1/2; (1/2)²= 0,25 ; 0,25 + 3 = 3,25 ; 3,25 x -2 =  - 6,5; -6,5 + 1/2= - 6.

L'expression pour le calculer est:
y = (x² + 3) x (-2) + x

2. a.

y = x + 2
z = 5 x y
z = 5 (x + 2)

b.

z = 20

5 (x + 2) = 20
x + 2 = 20 / 5
x + 2 = 4
x = 4 - 2
x = 2

Pour z = 20 , x = 2.

c.

Si x = 1.
z = 5 (1 + 2) = 5 x 3 = 15

Si x = 1/3
z = 5 (1/3 + 2) = 5/3 + 10 = 5/3 + 30/3 = 35/3 ≈ 11,6

Si x = -2
z = 5 (-2 +2) = 5 x 0 = 0