Respostas
Explicação passo a passo
a
40/100 = 32/x
em cruz
40 * x = 100 * 32
40x = 3 200
x = 3 200/40
x = 80 >>>>>
b
4,5 / 3 = 5,4/x
em cruz
4,5 * x = 3 * 5,4
4,5x = 16,2
x = 16,2 / 4,5
x =3,6 >>>>>>
c
21/27 = 49/x
em cruz
21 * x = 27 * 49
21x =1323
x = 1323/21
x = 63 >>>>>
Resposta:
1) a) x = 80
b) x = 3,6
c) x = 63
d) x = 2,5 e y = 4,4
e) x' = 0,5 e x'' = 8
Explicação passo a passo:
1) a)
40/100 = 32/x
(40:20)/(100:20) = 32/x
2/5 = 32/x
2/5 . 5x = 32/x . 5x
2x = 32 . 5
2x = 160
2x/2 = 160/2
x = 80
b)
4,5/5,4 = 3/x
(4,5 . 10)/(5,4 . 10) = 3/x
45/54 = 3/x
(45:9)/(54:9) = 3/x
5/6 = 3/x
5/6 . 6x = 3/x . 6x
5x = 3 . 6
5x = 18
5x/5 = 18/5
x = 3,6
c)
21/49 = 27/x
(21:7)/(49:7) = 27/x
3/7 = 27/x
3/7 . 7x = 27/x . 7x
3x = 27 . 7
3x/3 = (27 . 7)/3
x = 9 . 7
x = 63
d)
5/8 = x/4 = 2,75/y
5/8 = (x . 2)/(4 . 2) = (2,75 . 8)/(y . 8)
5/8 = 2x/8 = 22/8y
5 = 2x = 22/y
5 = 2x
2x = 5
2x/2 = 5/2
x = 2,5
5 = 22/y
5 . y/5 = 22/y . y/5
y = 22/5
y = 4,4
e)
x/(x + 2) = (2x + 4)/25
x/(x + 2) . (x + 2) . 25 = (2x + 4)/25 . (x + 2) . 25
x . 25 = (2x + 4) . (x + 2)
25x = 2x² + 4x + 4x + 8
25x = 2x² + 8x + 8
2x² + 8x + 8 = 25x
2x² + 8x + 8 - 25x = 25x - 25x
2x² - 17x + 8 = 0
x = [-(-17) ± √((-17)² - 4 . 2 . 8)] / (2 . 2)
x = [17 ± √(289 - 64)] / 4
x = [17 ± √225] / 4
x = [17 ± √15²] / 4
x = [17 ± 15] / 4
x' = [17 - 15] / 4
x' = 2/4
x' = 0,5
x'' = [17 + 15] / 4
x'' = 32/4