Question

1 Calculati:  a) (7/4+1/6)·12/23
    b) (5/6-1/3):1/4
c) ,media ponderata a numerelor a=2,7 si b=4,8(6) cu ponderile 4 si 6.

2 Rezolvati in Q ecuatiile:
a) 3,5x+3,35=20,85
b) 0,8(x+0,2)=4,96

3 Rezolvati ecuatia:
x+3/5+x+5/6+x+7/7=6

Answer 1

1 a) = 1 . 1 b) = 2

Answer 2

1 a) (7/4+1/6)·12/23=(7x6+4)/24x12/23=
48/24x12/23=2x12/23=24/23
b) (5/6-1/3):1/4=
(5-2)/6x4=
3/6x4=12/6=2
c) ,media ponderata a numerelor a=2,7 si b=4,8(6) cu ponderile 4 si 6.
b=4,8(6)=(486-48)/90=438/90=simplif cu 3=146/30=
a=2,7=27/10
Mp=(27/10x4+146/30x6)/(4+6)=(108/4+876/30)/10=(27+29,2)/10=56,2/10=5,62
Mp=5,62

2 Rezolvati in Q ecuatiile:
a) 3,5x+3,35=20,85
3,5x=20,85-3,35
3,5x=17,5
x=17,5/3,5=175/10:35/10=175/10x10/35=175/35=5
x=5
b) 0,8(x+0,2)=4,96
0,8x+0,16=4,96
0,8x=4,96-0,16
0,8x=4,8
x=4,8/0,8=48/10:8/10=48/10x10/8=48/8=6
x=6

3 Rezolvati ecuatia:
x+3/5+x+5/6+x+7/7=6
3x+(3x42+5x35+7x30)/210=6
3x+(126+175+210)/210=6
3x+511/120=6
3x=6-511/120
3x=(6x210-511)/210
3x=749/210
x=749/3·210
x=749/630
x=1,1(8)