Explanation

 A decimal with a finite number of decimal places is called a terminating decimal

These decimals have a specific end to their decimal representation, meaning the digits after the decimal point eventually stop.

For example, 0.25 is a terminating decimal because it has only two digits after the decimal point. 

Explanation

The matrix [a b c] is a row matrix.

A row matrix has only one row and can have multiple columns

Explanation

Given:

sin θ < 0 (sine is negative)

cot θ > 0 (cotangent is positive)

Since cot θ = cos θ / sin θ, and cot θ > 0, we know that cos θ and sin θ must have the same sign (both positive or both negative).

Given sin θ < 0, cos θ must also be negative.

The quadrant where both sine and cosine are negative is the 3rd quadrant.

Explanation

To find the remainder, we can use the Remainder Theorem, which states that the remainder of a polynomial f(x) divided by x - a is f(a). In this case, we need to divide by x + 2, so we'll use x = -2.

f(x) = 2x⁴ - 3x² + 5x - 7

f(-2) = 2(-2)⁴ - 3(-2)² + 5(-2) - 7

= 2(16) - 3(4) - 10 - 7

= 32 - 12 - 10 - 7

= 32 - 29

= 3

Explanation

The points form a scalene triangle:

Calculate the distances AB, BC, and AC. If all sides are unequal, it's a scalene triangle.

AB = √((1 - (-4))² + (4 - (-2))²) = √(5² + 6²) = √61

BC = √((6 - 1)² + (11 - 4)²) = √(5² + 7²) = √74

AC = √((6 - (-4))² + (11 - (-2))²) = √(10² + 13²) = √269

All sides are unequal (√61 ≠ √74 ≠ √269), so the points form a scalene triangle.

Explanation

Given:

a² + b² + c² = 38

ab + bc + ca = -1

Using the identity:

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

= 38 + 2(-1)

= 38 - 2

= 36

a + b + c = √36

= 6

Explanation

Given:

log₈₁ 9 = x

We can rewrite this in exponential form:

81^x = 9

Since 81 = 9², we can rewrite:

(9²)^x = 9

9^(2x) = 9¹

Equating the exponents:

2x = 1

x = 1/2

x = 0.5