Question

Prosze o rozwiazanie dwoch zadan z matematyki:
1.W trojkacie prostokatnym ABC przeciwprostokatna ma 11cm, a bok BC ma 5cm. Oblicz pole tego trojkata.

2. Uklad rownan:
x+y=7
3x+2y=12

Daje naj, z gory dziekuje. :)
Zglaszam zadania rozwiazane do polowy/tylko jedno.

Answer 1

z.1

c = 11 cm

a =  5 cm

----------------

b = ?

P = ?

a² + b² = c²  --> b² = c² - a² = 11²- 5² = 121 - 25 = 96 =16*6

b = √96 = √16 *√6 = 4√6

b = 4√6 cm

---------------

P = (1/2)a*b = (1/2)*5 cm* 4 √6 cm = 10 √6 cm²

====================================================

z.2

x + y = 7  --> y = 7 - x

3x + 2y = 12

---------------------------

3x + 2*(7 - x) = 12

3x + 14 - 2x = 12

x + 14 = 12

x = 12 - 14

x = -2

======

y = 7 - (-2) = 7 +2 = 9

=====================

Odp. x = -2; y = 9

====================================================

Answer 2

 

 

Zad. 1)

 

Dane:

 

b = 5 cm

c = 11 cm

P = ? [cm²]

 

P = 0,5ab

 

b = ? [cm]

 

a² + b² = c²

 

a² =  c² - b²

 

a² =  (11 cm)² - (5 cm)²

 

a² =  121 cm² - 25 cm²

 

a² =  96 cm²

 

a² =  16*6 cm²

 

a = √(16*6 cm²)

 

a = 4√6 cm

 

P = 0,5*(4√6 cm)*(5 cm)

 

P = 10√6 cm²

 

Odp: Pole trójkąta wynosi 10√6 cm².

 

Zad.2)

 

{ x + y = 7 / *( - 2)
{ 3x + 2y = 12

 

{ - 2x - 2y = -14 
{ 3x + 2y = 12

 

{ x = - 2

{ 3x + 2y = 12

 

{ x = - 2

{ 3* ( - 2) + 2y = 12

 

{ x = - 2

{ - 6 + 2y = 12

 

{ x = - 2

{ 2y = 12 + 6

 

{ x = - 2

{ 2y = 18 /:2

 

{ x = - 2

{ y = 9

Answer 3

2. Uklad rownan:
x+y=7
3x+2y=12

 

x+y=7/*-2

3x+2y=12

 

-2x-2y=-14

3x+2y=12_____

+

x=-2

3*-2+2y=12

 

x=-2

-6+2y=12

 

x=-2

2y=18/:2

 

x=-2

y=9