Упр.54 ГДЗ Муравин 7 класс (Алгебра)

Задача

1) 2х — 5у при х = 1,45; у = -0,32;
2) 3а + 4b при а = -2 1/3, b = 1 3/4;
3) n^2 — 3nk + 2k^2 при n = -4, k = -7;
4) с^2 — 2сy + 3у^2 при с = 8, у = -3;
5) (2а + 5b)/(4а — 2b) при a = 3/7, b = 2/7;
6) (5p — 3q)/(3p + 2q) при p = 0,12; q = -0,2;
7) (0,7x — 1,3)/(0,095 + 0,19y) при x = 2,17; y = 3,71;
8) (a^2 + 1,37)/(3,b — 0,763) при a = 5,3; b = 0,73.

Подробный ответ

При $$x=1{,}45,\ y=-0{,}32$$:
$$2x-5y=2\cdot 1{,}45-5\cdot(-0{,}32)=2{,}9+1{,}6=4{,}5.$$
При $$a=-2\frac{1}{3},\ b=1\frac{3}{4}$$:
$$3a+4b=3\cdot\left(-2\frac{1}{3}\right)+4\cdot 1\frac{3}{4}=-7+7=0.$$
При $$n=-4,\ k=-7$$:
$$ n^2-3nk+2k^2=(-4)^2-3\cdot(-4)\cdot(-7)+2\cdot(-7)^2 $$
$$ =16-84+98=30. $$
При $$c=8,\ y=-3$$:
$$ c^2-2cy+3y^2=8^2-2\cdot 8\cdot(-3)+3\cdot(-3)^2 $$
$$ =64+48+27=139. $$
При $$a=\frac{3}{7},\ b=\frac{2}{7}$$:
$$ \frac{2a+5b}{4a-2b} = \frac{2\cdot \frac{3}{7}+5\cdot \frac{2}{7}}{4\cdot \frac{3}{7}-2\cdot \frac{2}{7}} = \frac{\frac{6}{7}+\frac{10}{7}}{\frac{12}{7}-\frac{4}{7}} = \frac{\frac{16}{7}}{\frac{8}{7}} =2. $$
При $$p=0{,}12,\ q=-0{,}2$$:
$$ \frac{5p-3q}{3p+2q} = \frac{5\cdot 0{,}12-3\cdot(-0{,}2)}{3\cdot 0{,}12+2\cdot(-0{,}2)} = \frac{0{,}6+0{,}6}{0{,}36-0{,}4} = \frac{1{,}2}{-0{,}04} =-30. $$
При $$x=2{,}17,\ y=3{,}71$$:
$$ \frac{0{,}7x-1{,}3}{0{,}095+0{,}19y} = \frac{0{,}7\cdot 2{,}17-1{,}3}{0{,}095+0{,}19\cdot 3{,}71} = \frac{1{,}519-1{,}3}{0{,}095+0{,}7049} = \frac{0{,}219}{0{,}7999} \approx 0{,}2738. $$
При $$a=5{,}3,\ b=0{,}73$$:
$$ \frac{a^2+1{,}37}{3{,}1b-0{,}763} = \frac{5{,}3^2+1{,}37}{3{,}1\cdot 0{,}73-0{,}763} = \frac{28{,}09+1{,}37}{2{,}263-0{,}763} = \frac{29{,}46}{1{,}5} =19{,}64. $$