Given:
a < b
b < c
Using transitive property, if a < b and b < c, then a < c.
(3a - 2b)² = (3a)² - 2(3a)(2b) + (2b)²
= 9a² - 12ab + 4b²
Using Pythagoras' theorem:
c² = a² + b²
c² = 6² + 8²
c² = 36 + 64
c² = 100
c = √100
c = 10 cm
The length of the hypotenuse is 10 cm.
Let's denote the cost of one pizza as P and the cost of one donut as D.
From Farhan's purchase:
4P + 3D = 1670 ... (1)
From Hamid's purchase:
6P + 2D = 2280 ... (2)
We can multiply equation (1) by 2 and equation (2) by 3 to make the coefficients of D equal:
8P + 6D = 3340 ... (3)
18P + 6D = 6840 ... (4)
Now, subtract equation (3) from equation (4):
10P = 3500
P = 350
Let's expand both expressions:
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
Now, add them:
(a + b)² + (a - b)² = a² + 2ab + b² + a² - 2ab + b²
= 2a² + 2b²
To find the percentage of spaces reserved, divide the number of shaded spaces by the total number of spaces and multiply by 100.
Number of shaded spaces = 8
Total number of spaces = 20
Percentage reserved = (8 / 20) * 100 = 40%
