Explanation

$1 + tan^2 x = sec^2 x$
sec x = √(1 + (3/5)²) = √(34/25) = √34/5
cos x = 1/sec x = 5/√34

Explanation

Explanation

Number of boys = 8% of 40

= (8/100) × 40 = 3.2 ≈ 3 (nearest whole number)

Explanation

The size of information in the computer is measured in: 

• 1024 kilobytes (KB) is equal to 1 megabyte (MB).
• One Megabyte (MB) = 1024 Kilobytes (KB
• One Gigabyte (GB) =  1024 Megabytes MB
• One Terabyte (TB)= 1024 gigabytes (GB).

Explanation

Let the four consecutive odd numbers be:
$n-3, n-1, n+1, n+3$

Their average =$n$.
Given average = 24 →$n=24$

Largest number = $n+3=27$.

Explanation

Expand using distributive property (FOIL):

$$(x+3)(x-2)$$

x⋅x=x^2

x⋅(−2)=−2x

3⋅x=3x

3⋅(−2)=−6

Now combine like terms:

x^2−2x+3x−6=x^2+x−6

Explanation

 y = √(64 / (3x + 1))

Square both sides: 16= 64 / 3x + 1

Now solve:

$$16(3x+1)=64$$

$$48x+16=64$$

$$48x=48$$

$$x=1$$

Explanation

Sequence: 2, 1, 3, 4, 7, 11, ?

Observe the pattern:
Each term is the sum of the previous two terms

• 2 + 1 = 3
• 1 + 3 = 4
• 3 + 4 = 7
• 4 + 7 = 11
• 7 + 11 = 18

Explanation

Explanation

Let numbers be $n,n+1,n+2,n+3$
Product= $n(n+1)(n+2)(n+3)$
Add 1 → expression becomes a perfect square.