Question

1) Determinati a,b daca:ab+ba =33
2)Determinati a,b,c daca: abc+bc+c=148
3)Numarul 1010 scris in baza 2 ,se scrie in baza 10:
A)100000
B)10001
C)1110
D)1011
E)1101
4)Numarul 1010 scris in baza 2,se scrie in baza 10:
A)8
B)4
C)10
D)12
E)9
Va rog !

Answer 1

1 )
ab+ba=33
(10×a+b)+(10×b+a)=33
11×a+11×b=33 | :11
a+b=3
Variante :
a=1,2
b=1,2

3 )
$32_(10)= \\ \\ 32:2=16~rest~0 \\ \\ 16:2=8~rest~0 \\ \\ 8:2=4~rest~0 \\ \\ 4:2=2~rest~0 \\ \\ 2:2=1~rest~0 \\ \\=> \boxed {100000_(2)}$

4 )
$1010_(2)= \\ \\ 1 \times {2}^{3}+1 \times {2}^{1}=1 \times 8+1 \times 2=10$

2 )
abc+bc+c=149
(100×a+10×b+c)+(10×b+c)+c=149
100×a+20×b+3×c=149
100×1+20×2+3×3=149
123+23+3=149

Answer 2

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