Question

zad. 13 Rozwiąż układy równań

a)\left \{ {{x+y=5} \atop {x+2y=6}} \right
b)\left \{ {{2x+2y=18} \atop {x+3y=17}} \right
c)\left \{ {{3x+y=6} \atop {5x-2y=10}} \right

zad.15 Oblicz pole

a) trójkąta o boku 6cm i h=4cm ,a=2,5m i h=6m, a =4,5m h=10,5dm

b) kwadratu o boku a=4cm, a=2,5cm, a=a jedna druga m

c) prostokąta o bokaCH a=2m b=7m, a=3,5cm, b=4,5cm,a=7dm, b=2,9dm

d)Równologłoboka o boku a=5dm, h=12dm, a=16m, h=13ch, a=7,5km, h=5,5km

e)Rombu o przekątnych d1=6cm d2=12cm, , d1=0,5m d2=3m, d1=jedna druga km d2=2jedna trzecia km

f))koła o promieniu h r=7m, r=6 dwie trzecie km, r=3,4m

Answer 1

13. 

a) 

{x + y = 5

x + 2y = 6

 

{x = 5 - y

5 - y + 2y = 6

 

{x = 5-y

y = 1

 

{ x = 4

y = 1

 

 

b)

{2x + 2y = 18

x + 3y = 17

 

{x + y = 9

x + 3y = 17

 

{x = 9 - y

9 - y + 3y = 17

 

{ x = 9 - y

2y = 8

 

{x = 9-y

y = 4

 

{x = 5

y = 4

 

 

c)

{3x + y = 6

5x - 2y = 10

 

{y = 6-3x

5x - (6-3x) = 10

 

{y = 6-3x

5x - 6 + 3x = 10

 

{y=6-3x

8x = 16

 

{y = 6 -3x

x = 2

 

{ y = 6-3*2

x = 2

 

{y=0

x = 2

 

 

 

zad. 15

a)

₁)

a = 6 cm

h = 4 cm

P = 1/2*a*h

P = 1/2 * 6 * 4

P = 12 [cm²]

 

₂)

a = 2,5m

h = 6m

P = 1/2 * a * h

P = 1/2 * 2,5 * 6

P = 7,5 [m²]

 

₃)

a = 4,5m = 45 dm

h = 10,5dm

P = 1/2*a*h

P = 1/2* 45*10,5

P = 236,25 [dm²]

 

 

b)

₁)

a = 4cm 

P = a²

P = 4²

P = 16 [cm²]

 

₂)

a = 2,5cm

P = a²

P = 2,5²

P = 6,25 [cm²]

 

₃)

a = 1/2m

P = a²

P = (1/2m)²

P = 1/4 * m²

 

 

c)

₁)

a = 2m

b = 7m

P = a*b 

P = 2*7

P = 14 [m²]

 

₂)

a = 3,5 cm

b = 4,5 cm

P = a*b

P = 3,5*4,5

P = 15,75 [cm²]

 

₃)

a = 7 dm

b = 2,9 dm

P = a*b

P = 7*2,9

P = 20,3 [dm²]

 

 

d)

₁)

a = 5dm

h = 12dm

P = a*h

P = 5*12

P = 60 [dm²]

 

₂)

a = 16m=1600cm

h = 13cm

P = a*h

P = 1600*13

P = 20800 [cm²]

 

₃)

a = 7,5 km

h = 5,5 km

P = a*h

P = 7,5*5,5

P = 41,25 [km²]

 

 

e)

₁)

d₁ = 6cm

d₂ = 12 cm

P = 1/2 * d₁*d₂

P = 1/2 * 6*12

P = 36 [cm²]

 

₂)  

d₁ = 0,5m

d₂ = 3m

P = 1/2 * d₁*d₂

P = 1/2 * 0,5 *3

P = 0,75 [m²]

 

₃)

d₁ = 1/2 km

d₂ = 1/3 km

P = 1/2*d₁*d₂

P = 1/2*1/2*1/3

P = 1/12 {km²]

 

 

f)

₁)

r = 7m

P = πr²

P = 49π [m²]

 

₂)

r = 6 2/3 km = 20/3 km

P = πr²

P = (20/3)²π

P = 400/9 π

P = 44 i 4/9 π [km²]

 

₃)

r = 3,4m

P = πr²

P = π *3,4²

P = 11,56π [m²]

 

 

Pozdrawiam ;)