Parallelogrammning perimetri 40 sm, uning balandliklari 2:3 kabi nisbatda bo’lsa, parallelogrammning katta tomonini toping.

\(\left| {\frac{1}{{1,5 - \frac{x}{2}}}} \right| > \frac{4}{{15}}\)tengsizlikning barcha butun sonlardagi yechimlari yig’indisini toping.

\(\arccos \frac{{36}}{{85}} - \arccos \frac{{15}}{{17}} = ?\)

\(y = \frac{{{x^2} + ax + b}}{{{x^2}}}\) egri chiziq A(-3;0) nuqtada x o’qiga urinsa, a+b=?

\(\frac{{t - 6}}{{m - 10}} = \frac{m}{t}\) tenglama m ning nechta natural qiymatida ildizga ega emas?

y=9 – 0,5x funksiyaning qiymatlar sohasini toping. A) \(\left( {9;\infty } \right)\)

) \(\sqrt {a + \sqrt {a + \sqrt {a + ...} } } = 4\) tenglikdan a ni toping.

m ning qanday qiymatlarida \(\left\{ {\begin{array}{*{20}{c}}{2x - y = 3m - 4}\\{x - y = m - 1}\end{array}} \right.\)tenglamalar sistemasining yechimi koordinata tekisligining IV choragiga tegishli bo’ladi.

ABC tomoni 16 sm bo’lgan teng tomonli uchburchak. \(\left[ {BH} \right] \bot \left[ {AC} \right],\left[ {HK} \right] \bot \left[ {BC} \right],\) \(\left[ {KT} \right] \bot \left[ {BH} \right]\) bo’lsa, \({S_{\Delta THK}}\)necha sm2?

\(a,b \in N\) va \(b = \frac{{a + 3}}{4} + \frac{{a + 3}}{5}\) bo’lsa, a eng kamida nechaga teng?

) Uchburchakning 6 ga teng balandligi uning asosi uzunligini 7:18 kabi nisbatda bo’ladi. Shu balandlikka parallel va uchburchakning yuzini teng ikkiga bo’ladigan to’g’ri chiziq kesmasining uzunligini toping.

Arifmetik progressiya uchinchi va to’qqizinchi hadlarining yig’indisi 10 ga teng. Shu progressiyaning dastlabki 11 ta hadlari yig’indisini toping.

\(\begin{array}{l}\sin {10^0}\sin {20^0}\sin {30^0}\sin {40^0}\sin {50^0} \cdot \\ \cdot \sin {60^0}\sin {70^0}\sin {80^0} = ?.\end{array}\)

Quyida keltirilgan tengliklardan qaysilari ayniyat emas? 1) \((x + a) \cdot (x - b) = {x^2} - (a - b)x - ab;\) 2) \((x - c) \cdot (x - d) = {x^2} + (c - d)x + cd;\) 3) \((x - c) \cdot (x + d) = {x^2} - (c - d)x - cd;\) 4) \(\begin{array}{l}6ab + (2{a^3} + {b^3} - (3a{b^2} - ({a^3} + 2a{b^2} - \\ - {b^3}))) = 3{a^3} - a{b^2} + 6ab;\end{array}\) 5) \(\begin{array}{l}5{a^2} - 3{b^2} - (({a^2} - 2ab - {b^2}) - (5{a^2} - 2ab - \\ - {b^2})) = 9{a^2} + 4ab - 3{b^2}.\end{array}\)

\({\log _{\sqrt 5 }}\sqrt {5 \cdot \sqrt {5 \cdot \sqrt {5 \cdot ...} } } = ?\)

Bir bola bilyard sharchalarini 9 tadan to’plarga ajratganda 5 ta, 12 tadan ajratganda 8 ta, 14 tadan ajratganda 10 ta sharcha yetmayapti. Bunga ko’ra bolada kamida nechta sharcha mavjud?

\(\frac{{({{8,7}^2} - {{11,3}^2})({{13,3}^2} - {{12,3}^2})}}{{({{4,2}^2} - {{5,8}^2})({{2,3}^2} - {{0,3}^2})}}\) ni hisoblang.

\(\frac{{{3^9} \cdot {2^{19}} + 15 \cdot {4^9} \cdot {9^4}}}{{{6^9} \cdot {2^{10}} + {{12}^{10}}}} \cdot {\left( {1\frac{1}{2}} \right)^{ - 1}}\) ni hisoblang.

) To’g’ri burchakli uchburchakning balandligi gipotenuzani 3 va 12 ga teng kesmalarga ajratsa, shu balandlikni toping.

) \(\sin {18^0}\sin {54^0} = ?\)

\({\left( {3\frac{3}{8}} \right)^{ - \frac{2}{3}}} + {27^{\frac{2}{3}}} \cdot {9^{0,5}} \cdot {3^{ - 2}} + {\left( {{{\left( {\frac{7}{9}} \right)}^3}} \right)^0} - {\left( { - \frac{1}{2}} \right)^{ - 2}}\) ni hisoblang.

P(x) ning (x-3)2 ga bo’linmasidan qolgan qoldiq (2x-3) bo’lsa, (x-3) ga bo’linmasidan qolgan qoldiqni toping.

Agar \(3 \le x \le y \le z \le t \le 27\) bo’lsa, \(\frac{x}{y} + \frac{z}{t}\) ifodaning eng kichik qiymatini toping.

To’gri burchakli ABC uchburchakda C burchak to’g’ri burchak bo’lib, AN bissektrisa va AB gipotenuzada D nuqta olingan bo’lib, AD=2 va \({S_{\Delta ANC}}:{S_{\Delta AND}} = 3\) bo’lsa, AC=?

\({\log _2}25\)ning butun qismini toping.

) Bir ishxonada ishchi soni yarimga tushirilsa, kunlik ish vaqti 3 barobarga va ish hajmi 6 barobarga oshirilsa, ishni bitirish vaqti necha barobarga oshadi?

\(\frac{{3\sin \alpha + 2}}{{5 + \cos \beta }} + \frac{3}{{t{g^2}\gamma + ct{g^2}\gamma }}\) ifodaning eng katta qiymatini toping.

\(\left\{ {\begin{array}{*{20}{c}}{3 - 4x > 5}\\{2 + 3(x - 1) \le 4x + 3}\end{array}} \right.\)tengsizliklar sistemasi nechta butun yechimga ega?

) Teng yonli to’g’ri burchakli uchburchakka ichki chizilgan aylana radiusining uchburchak gipotenuzasiga o’tkazilgan balandlikka bo’lgan nisbatini toping.

\(\frac{{\cos 2x}}{{\frac{{\sqrt 2 }}{2} + \sin x}} = 0\) tenglamaning \(\left[ {0;6\pi } \right]\) kesmada nechta ildizi bor?