Explanation

Using the formula for the sum of interior angles of a polygon:

(n - 2) × 180°

For a quadrilateral, n = 4:

(4 - 2) × 180°

= 2 × 180°

= 360°

The sum of the interior angles of a quadrilateral is 360°.

Explanation

The difference between +16 and +28 is:

+16 - (+28) = +16 - 28 = -12

Explanation

The set includes positive integers greater than 2 and less than or equal to 6:

The integers that fit this condition are 3, 4, 5, and 6.

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.