Explanation

Given:

f(x) = 5x + x² − 1

g(x) = 2x + 5

Step 1: Find g(4)

g(4) = 2(4) + 5 = 8 + 5 = 13

Step 2: Find f(g(4)) = f(13)

f(13) = 5(13) + 13² − 1

= 65 + 169 − 1

= 233

Last verified on 17-06-2026

Explanation

Standard period of tan x = π

For tan(x/a), period becomes aπ

Here a = 3 ⇒ Period = 3π

Last verified on 17-06-2026

Explanation

Using the double angle identity:

tan 2θ = 2 tan θ / (1 − tan² θ)

If tan θ = A, then tan 2θ = 2A/(1−A²).

Last verified on 17-06-2026

Explanation

The order of a differential equation is the highest derivative present.

Here only dy/dx is present (first derivative).

So the order is 1.

Last verified on 17-06-2026

Explanation

20x² - 9x - 20

Multiply 20 × -20 = -400  

Find 2 numbers for -400 that add to -9 → 16 and -25  

Write 20x² + 16x - 25x - 20

Take common 4x(5x + 4) - 5(5x + 4)

Both have (5x + 4), so (4x - 5)(5x + 4)

Last verified on 17-06-2026

Explanation

3x + 3 = 4

Subtract 3 from both sides:

3x = 1

Divide by 3:

x = 1/3

Last verified on 16-06-2026

Explanation

tanθ = opposite / adjacent = 3/4  

Make a right triangle:  

Opposite = 3, Adjacent = 4  

Find hypotenuse using Pythagoras:  

hypotenuse² = 3² + 4² = 9 + 16 = 25  

hypotenuse = 5

sinθ = opposite / hypotenuse = 3/5

Last verified on 10-06-2026

Explanation

Midpoint formula = (x1 + x2)/2 , (y1 + y2)/2

Given points: (2, 4) and (6, 8)  

So x1 = 2, y1 = 4, x2 = 6, y2 = 8

Add x values: (2 + 6)/2 = 8/2 = 4  

Add y values: (4 + 8)/2 = 12/2 = 6

Midpoint = (4, 6)

Last verified on 10-06-2026

Explanation

x^2 - 5x + 6 = 0

Find 2 numbers: add = 5, multiply = 6

Those numbers = 2 and 3

So (x-2)(x-3) = 0

x = 2, 3

Last verified on 10-06-2026

Explanation

Distance formula: d = √[(x₂−x₁)² + (y₂−y₁)²]  

d = √[(3−0)² + (4−0)²] = √(9 + 16) = √25 = 5

Classic 3-4-5 right triangle

Last verified on 09-06-2026