Explanation

Let's check each pair in the equation:

2x + 3y = 24

{6, 4} → 2(6) + 3(4) = 12 + 12 = 24 ✓

{12, 0} → 2(12) + 3(0) = 24 + 0 = 24 ✓

{0, 8} → 2(0) + 3(8) = 0 + 24 = 24 ✓

{9, -2} → 2(9) + 3(-2) = 18 - 6 = 12 ✗

Explanation

To convert a percentage to decimal, divide by 100: 40 ÷ 100 = 0.4.

Explanation

The value of cosec 30° is the reciprocal of sin 30°.

Since sin 30° = 1/2,

cosec 30° = 1 / (1/2) = 2

Explanation

Given the area A = 172.1 cm², and the formula for the area of a circle is A = πr²:

Step 1: Find the radius

172.1 = πr²

r² = 172.1 / π

r² = 172.1 / (22/7)

r² = 172.1 * (7/22)

r² = 54.77

r ≈ √54.77

r ≈ 7.4

Step 2: Calculate the circumference

Circumference C = 2πr

C = 2 * (22/7) * 7.4

C ≈ 2 * 3.14 * 7.4

C ≈ 46.51

Explanation

Let's denote the number as x.

Step 1: Formulate the equation based on the given information

(4/9)x = 12

Step 2: Solve for x

x = 12 * (9/4)

x = 3 * 9

x = 27

Explanation

To evaluate the expression, follow the order of operations:

Multiply 2 and 3: 2 × 3 = 6

Subtract 5 from 4: 4 - 5 = -1

Divide -1 by -1: -1 ÷ -1 = 1

Add 6 and 1: 6 + 1 = 7

Explanation

Partial fractions refer to expressing a complex rational expression as the sum of simpler fractions.

Each resulting fraction has a single factor in the denominator, making calculations and integration easier.

Explanation

1 is not a prime because a prime number has exactly two distinct positive divisors (1 and itself), and 1 only has one.

1 is not composite because a composite number has more than two factors.

Explanation

Substitute the given values:

a = 1, b = 0, c = -1

Now, evaluate the expression:

(a - c) - (a + b) + ab

= (1 - (-1)) - (1 + 0) + 1(0)

= (1 + 1) - 1 + 0

= 2 - 1

= 1

Explanation

Given cosx(tan x + cot x):

Step 1: Express tan x and cot x in terms of sin x and cos x

tan x = sin x / cos x

cot x = cos x / sin x

Step 2: Substitute and simplify

cosx(tan x + cot x) = cosx(sin x / cos x + cos x / sin x)

= sin x + cos² x / sin x

= (sin² x + cos² x) / sin x

= 1 / sin x (since sin² x + cos² x = 1)

Step 3: Identify the result

1 / sin x = cosec x