Explanation

The transitive property states that if a = b and b = c, then a = c.

Explanation

In a class interval (e.g., 10–20), the greatest value is called the upper class limit.

The lower class limit is the smallest value (e.g., 10), and the upper class limit is the largest value (e.g., 20).

Explanation

In the ratio a : b, a is called the antecedent (the first term), and b is called the consequent (the second term).

The antecedent represents the part of the ratio that comes before the colon.

Explanation

Explanation

The sum of the roots of a quadratic equation ax² + bx + c = 0 is given by -b/a.

Given equation:

x² - 3x - 4 = 0

a = 1

b = -3

Sum of roots = -(-3)/1

= 3

Explanation

Let's simplify the expression:

tanθ + cotθ

= sinθ/cosθ + cosθ/sinθ

= (sin²θ + cos²θ) / (sinθcosθ)

Since sin²θ + cos²θ = 1:

= 1 / (sinθcosθ)

= 1/sinθ * 1/cosθ

= cosecθ * secθ

= secθcosecθ

Explanation

Let's solve for x:

9 - 3x = 12

Subtract 9 from both sides:

-3x = 3

Divide both sides by -3:

x = -1

Explanation

The number of subsets of a set with n elements is 2^n.

Here, A = {a, b, c} has 3 elements, so:

Number of subsets = 2^3

= 8

The subsets are:

{}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}

Explanation

The square root of any real number is never negative, so √x = -10 has no real solution.

Hence, the solution set is empty, written as { }.

Explanation

Let's factor:

x^2 - y^2 = (x + y)(x - y)

x^2 - xy = x(x - y)

The common factor is (x - y).