The equation a(b + c) = ab + ac shows how multiplication distributes over addition.
This is called the distributive property in algebra.
Given:
(x, 6) = (2, y - 6)
Equating the corresponding components:
x = 2
6 = y - 6
Solving for y:
y = 6 + 6
y = 12
Now, finding x + y:
x + y = 2 + 12
= 14
The trigonometric identity is:
Sec²θ - Tan²θ = 1
15 divided by -3:
15 ÷ (-3) = -5
In inverse proportion, when one quantity increases, the other decreases in the same ratio.
Their product remains constant: x × y = constant.
Cost per bag = $10.32 ÷ 8 = $1.29
For 20 bags: $1.29 × 20 = $25.80
10 pipes fill the tank in 1 hour 40 minutes = 100 minutes
Let's find the rate of 1 pipe:
Rate of 10 pipes = 1 tank / 100 minutes
Rate of 1 pipe = 1 tank / (10 × 100) minutes
= 1 tank / 1000 minutes
Rate of 8 pipes = 8 tanks / 1000 minutes
= 1 tank / (1000 / 8) minutes
= 1 tank / 125 minutes
Let's use the Pythagorean theorem:
Height of pole (perpendicular) = 12m
Length of string (hypotenuse) = 20m
Distance between foot of pole and end point of string (base) = √(hypotenuse² - perpendicular²)
= √(20² - 12²)
= √(400 - 144)
= √256
= 16m
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40 → HCF = 8
A chord is a line segment with both endpoints on the circle.
If the chord passes through the center, it's called the diameter.