Explicație pas cu pas:
1)
[tex]2(3 + 6\sqrt{2}) + 3(2 - 4 \sqrt{2}) = 6 + 12 \sqrt{2} + 6 - 12 \sqrt{2} = 12 \\ [/tex]
2) f(x) = 2x + a
P(1; 1) ∈ Gf => f(1) = 1
2•1 + a = 1
a = 1 - 2 => a = -1
3)
[tex]{2}^{x} + {2}^{x + 1} = 6 \\ {2}^{x} + 2 \cdot {2}^{x} = 6 < = > 3 \cdot {2}^{x} = 6 \\ {2}^{x} = 2 < = > {2}^{x} = {2}^{1} \\ = > x = 1[/tex]
4) preț inițial obiect: 500 lei
ieftinire 10% => p = 10%
[tex]500 - 500 \times \frac{10}{100} = 500 - 50 = 450 \\ [/tex]
=> preț final obiect: 450 lei
5)
[tex]d_{1} : 2x + y = 0 <=> d_{1} : y = - 2x[/tex]
[tex]d_{2} : x + my + 2017 = 0 <=> my = -x - 2017 \\ d_{2} : y = - \frac{1}{m}x - \frac{2017}{m} [/tex]
drepte paralele => pante egale
[tex]m_{d_{1}} = m_{d_{2}} <=> - 2 = - \frac{1}{m} = > m = \frac{1}{2} \\ [/tex]
6)
[tex]A = \frac{\pi}{2} = > A = 90 \\[/tex]
=> ΔABC este dreptunghic isoscel
AC = 6 => AB = 6
[tex]Aria_{(ABC)} = \frac{AB \times AC}{2} = \frac{6 \times 6}{2} = 18 \\ [/tex]
