Let's directly calculate:
x - y = 5
x² - y² = 65
(x + y)(x - y) = 65
(x + y)(5) = 65
x + y = 13
Solving these equations:
Adding both: 2x = 18
x = 9
y = 4
Let's check:
9 - 4 = 5
9² - 4² = 81 - 16 = 65
In a triangle, if two angles are congruent, their opposite sides are also congruent (equal in length).
This is a property of isosceles triangles, where equal angles face equal sides.
To find the profit percentage:
Cost Price (CP) = Rs. 50
Selling Price (SP) = Rs. 75
Profit = SP - CP = 75 - 50 = Rs. 25
Profit Percentage = (Profit / CP) × 100
= (25 / 50) × 100
= 50%
Let's calculate:
5! = 5 × 4 × 3 × 2 × 1 = 120
√120 + 1
√121 = √11×11
= 11
Adjacent angles share a common vertex and a common arm.
They do not overlap, meaning no point lies in both interiors.
Let's find the fourth proportional.
If 8 : 4 :: 2 : x, then
8/4 = 2/x
2 = 2/x
x = 1
1 + tan²θ = Sec²θ
This is a fundamental trigonometric identity.
BODMAS stands for: Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction.
Operations must be performed in this order to solve expressions correctly.