1)
a=5-11
a=-6
[tex]b=\frac{6}{2}\times \frac{1}{9} =\frac{1}{3}[/tex]
[tex]\frac{a}{b} =-\frac{6}{\frac{1}{3} }=-18[/tex]
2)
AB=AD=DC
∡BAD=40°
Daca AB=AD⇒ΔABD isoscel
∡ABD=∡ADB=(180-40):2=70° (∡B)
Daca ∡ADB=70°⇒ ∡ADC=180-70=110°
AD=DC⇒ΔADC isoscel
∡DAC=(180-110):2=35°
∡A=40+35=75°
∡EAB este unghi exterior lui ∡A⇒ ∡EAB=180-75=105°
3)
[tex]\frac{0,7}{2} =0,35[/tex]
[tex]0,3 < 0,35[/tex]
[tex]\sqrt{0,25} =0,5\\\\\frac{1}{4} =0,25\\\\0,5 > 0,25[/tex]
[tex]\frac{2}{\sqrt{2} }=\frac{2\sqrt{2} }{2} =\sqrt{2} \\\\ \sqrt{2}=\sqrt{2}[/tex]
[tex]\frac{1}{100}:2=\frac{1}{100}\times \frac{1}{2} =\frac{1}{200} =0,005[/tex]
[tex]0,005 < 0,05[/tex]
4)
Vom rationaliza prima fractie amplificand cu opusul numitorului
[tex]\frac{8(3-\sqrt{5} )}{(3-\sqrt{5})(3+\sqrt{5}) } -4+2\sqrt{5} =\\\\\frac{8(3-\sqrt{5} )}{9-5 } -4+2\sqrt{5} =\\\\\frac{8(3-\sqrt{5} )}{4 }-4+2\sqrt{5} =\\\\6-2\sqrt{5} -4+2\sqrt{5} =2\ numar\ intreg[/tex]
5)
3x²+5x-2=0
Calculam solutiile ecuatiei
Calculam delta
Δ=b-4ac
a=3 b=5 c=-2
Δ=25+24=49
[tex]x_1=\frac{-b+\sqrt{\Delta}}{2a} =\frac{-5+7}{6}=\frac{1}{3}\\\\ x_2=\frac{-b-\sqrt{\Delta}}{2a} =-2[/tex]
[tex]A=\{\frac{1}{3},\ -2\} \\[/tex]
A∩(0,7]=[tex]\frac{1}{3}[/tex]
