Explanation

Let's simplify the expression:

√3 × √5 × √15

= √(3 × 5 × 15)

= √(225)

= 15

Explanation

In the Cartesian coordinate system:

• 1st quadrant: (+, +)
• 2nd quadrant: (-, +)
• 3rd quadrant: (-, -)
• 4th quadrant: (+, -)

Given point P(-4, -7):

Both x (-4) and y (-7) coordinates are negative.

This point lies in the 3rd quadrant.

Explanation

Given:

a = 2

b = 3

c = 1

Let's calculate the expression:

a² + 3c + 4ab²

= (2)² + 3(1) + 4(2)(3)²

= 4 + 3 + 4(2)(9)

= 4 + 3 + 72

= 79

Explanation

Given the expression:

[(2/13)⁶ + (2/13)³]³ × (2/13)^-⁹

Let's simplify:

= [(2/13)³((2/13)³ + 1)]³ × (2/13)^-⁹

= (2/13)⁹[(2/13)³ + 1]³ × (2/13)^-⁹

The (2/13)⁹ and (2/13)^-⁹ cancel out:

= [(2/13)³ + 1]³

Given the result is 1, let's assume:

[(2/13)³ + 1]³ = 1

Explanation

Let's simplify the equation:

(-16k) + (-k) - 15k - (-11k) - (-17k) = 1

Combine like terms:

-16k - k - 15k + 11k + 17k = 1

-4k = 1

Divide by -4:

k = -1/4

Explanation

(1+2⁰+3²+4⁰) / (5+6⁰):

(1 + 1 + 9 + 1) / (5 + 1)

= 12 / 6

= 2

Explanation

1 + tan²θ = Sec²θ

This is a fundamental trigonometric identity.

Explanation

The phrase "delighted with" is correctly used to express pleasure or satisfaction about something.

So, "delighted with the generosity" is grammatically and idiomatically correct.

Explanation

The correct phrase is "associated with", meaning connected or linked to something.

So, "associated with agriculture" correctly shows the relationship between village life and farming.

Explanation

The correct phrase is "Let such in peace depart".

It often used in formal or poetic expressions like prayers or blessings.

It means to allow someone or something to leave peacefully or in a state of peace.