Olmalar quritilganda o’z og’irligining \(84\% \) ini yo’qotadi. 16 kg olma qoqisi olish uchun qancha olma kerak bo’ladi?

. Agar \(x = 2,6,\;y = - 1,5\) bo’lsa,\(\;\frac{{{x^3} + {y^3}}}{{{x^2} - xy + {y^2}}}\) ifodaning son qiymatini toping.

Hisoblang: 32,7∙21-6∙32,7+67,3∙47-32∙67,3

. Uchburchakning bir burchagi ikkinchisidan \({30^0}\) ga katta, uchinchi burchak esa birinchisidan \({60^0}\) ga kichik. Uchburchakning burchaklarini toping.

∆\(ABC\) uchburchakning A va C uchlaridan tushirilgan balandliklar K nuqtada kesishadi. Agar \(\angle A = {60^0}\) va \(\angle C = {72^0}\) bo’lsa, \(\angle AKC\) ni toping.

Ko’paytuvchilarga ajrating: x(p-a)+y(a-p)-z(p-a)

Tenglamani yeching: 4,8x-0,5=4,2∙(-3,5)

Ko’paytuvchilarga ajrating: \(2{x^2} + 14x + 24\)

Amallarni bajaring: \(\left( {\frac{3}{4}{a^6}{x^3} + \frac{6}{5}{a^3}{x^4} - \frac{9}{{10}}a{x^5}} \right):\frac{3}{5}a{x^3}\)

. Kasrni qisqartiring: \(\frac{{5{m^2} + 10mn + 5{n^2}}}{{15{m^2} - 15{n^2}}}\)

Tenglamani yeching: x(x+2)-(x-3)(x+3)=13

Agar \(a = \frac{1}{2},\;b = 0,9\) bo’lsa, \(\frac{{2a + {b^2} - 0,51}}{{2b - a}}\) ifodaning son qiymatini toping.

Umumiy tomoni BC bo’lgan ∆ABC va ∆DBC uchburchaklar berilgan. Agar \(AC\parallel BD\), \(AB = AC\), \(\angle BAC = \angle BCD = 70\)° bo’lsa, \(\angle \)BDC burchak nimaga teng?

. AB va CD kesmalar AB kesmaning o’rtasi bo’lgan O nuqtada kesishadi, bunda \(\angle OAD = \angle OBC\). Agar CD=26 sm, AD=15 sm bo’lsa, CO ni toping.

. Uchburchakning perimetri 48 sm, tomonlaridan biri esa 18 sm ga teng. Agar qolgan ikkita tomonining ayirmasi 4,6 sm bo’lsa, shu tomonlarni toping.

Soddalashtiring: \(\frac{1}{2}{x^2}{y^2} - \frac{2}{3}ab - \frac{5}{6}{a^2}{b^2} - 1 - {a^2}{b^2} + \frac{1}{3}{x^2}{y^2} - \frac{1}{{12}}ab + \frac{1}{4}\)

. C nuqta \(\angle AMB\) burchak bissektrisasida yotadi. Agar \(\angle AMB = {60^0}\), \(MC = 16\;sm\;\)bo’lsa, C nuqtadan burchak tomonlarigacha bo’lgan masofani toping.

. To’g’ri to’rtburchakning bo’yi enidan ikki marta katta. Agar to’g’ri to’rtburchakning bo’yi 4 m ga, eni esa 5 m ga uzaytirilsa, uning yuzi \(111\;{m^2}\) ga ortadi. To’g’ri to’rtburchakning bo’yi va enini toping.

. Uchburchakning bir tomoni \(a + b\), ikkinchi tomoni birinchisidan \(a - 5\) ga katta, uchinchi tomoni esa \(2b + 5\) ga teng. Uchburchakning perimetrini toping.

Amallarni bajaring: \({\left( {1\frac{1}{4}{a^2}{b^2}{c^3}d} \right)^2}\)∙\(\left( { - \frac{2}{5}{a^3}b{c^2}} \right)\)