Question

As dori sa-mi raspundeti la toate. Va multumesc ! Imi este de folos sa raspundeti si la o problema.

Answer 1

7. Nr. 4a6 in baza zece e divizibil cu 9 <=> 10 + a  e divizibil cu 9 <=> a = 8; atunci x = ( 2 * 486 ) / 5 => x = 194,4.

8. x = 3k; y = 5k; le inlocuiesti in relatia 3x - y = 12 => 9k - 5k = 12 => 4k = 12 => k = 3 => x = 9 si y =15;

9. O idee similara ca la 8; ai a = ck si b = dk, unde k e nenul; le inlocuiesti in prima fractie, dai factor comun pe k, il simplifici si gata.

Bafta!

Answer 2

$7) \\ a=8 \\ deoarece \\ 4+8+6=18 \\ \frac{x}{2}=\frac{486}{5} \\ 5x=2*486 \\ x= \frac{2*486}{5}= \frac{972}{5}=194,4$

$8) \\ \left \{ {{3x-y=12} \atop { \frac{x}{y}= \frac{3}{5}}} \right. \\ \left \{ {{3x-y=12} \atop {5x-3y=0}} \right. \\ y=3x-12 \\ 5x-3(3x-12)=0 \\ 5x-9x+36 = 0 \\ 4x=36 \\ x= \frac{36}{4}=\boxed{9} \\ y=3x-12 \\ y=3*9-12=27-12=\boxed{15}$

9)
Prima fractie o simplificam fortat cu b, iar a doua fractie o simplificam fortat cu d

$\frac{a}{b}=\frac{c}{d} \\ \frac{5a+2b}{13a+7b}=\frac{5c+2d}{13c+7d} \\ simplificam..fortat: \\ \frac{5 \frac{a}{b} +2 \frac{b}{b} }{13 \frac{a}{b} +7 \frac{b}{b}}= \frac{5 \frac{c}{d} +2 \frac{d}{d} }{13 \frac{c}{d} +7 \frac{d}{d}} \\ \frac{5 \frac{a}{b} +2 }{13 \frac{a}{b} +7}= \frac{5 \frac{c}{d} +2 }{13 \frac{c}{d} +7} \\ Dar:\frac{a}{b}=\frac{c}{d} \\ => \frac{5 \frac{a}{b} +2 }{13 \frac{a}{b} +7}= \frac{5 \frac{a}{b} +2 }{13 \frac{a}{b} +7} \\ cctd$