Question

Dau coroana daca ma ajutati---ajutor temai pentru maine
1. Numerele x si y sunt direct proportionale cu 5 si 4. Aflati numerele stiind ca x+y=4100.
2. Daca x si y sunt proportionale cu numerele 2 si 3 calculati:
a)2x+3y supra 7x-4y
b)7x-4y supra x+2y
c)3x+5y supra 2x+7y
d)2x la puterea a 2 +4xy-3y la puterea a 2 supra x la puterea a 2+xy_y la puterea a 2.

Answer 1

1.
x=5k
y=4k
5k+4k=4100
9k=4100
k=4100/9=455,(5)
x=5*4100/9=20500/9=2277,(7)
y=4*4100/9=16400/9=1822,(2)

2.x=2k
y=3k
a)(2x+3y)/(7x-4y)=(2*2k+3*3k)/(7*2k-4*3k)=14k/2k=7

b)(7x-4y) (x+2y)=(7*2k-4*3k)/(2k+2*3k)=2k/8k=2/9

c)(3x+5y)/(2x+7y)=(3*2k+5*3k)/(2*2k+7*3k)=21k/25k=21/25

d)(2x² +4xy-3y²) /(x²+xy-y²)=
x²=4k²
y²=9k²
xy=6k²
=(2*4k²+4*6k²-3*9k²)/(4k²+6k²-9k²)=
=(8k²+24k²-27k²)/k²=
=5k²/k²=5