Explanation

The multiplicative inverse of a number is its reciprocal.

For -1/9, the reciprocal is -9/1 or simply -9.

Explanation

Total length of lace = 19 m 61 cm = 19.61 m

Length used = 8 m 89 cm = 8.89 m

Remaining length = Total length - Length used

Remaining length = 19.61 m - 8.89 m

Remaining length = 10.72 m

Explanation

The average is calculated by dividing the sum of quantities by the number of quantities. Therefore, the number of quantities can be found by dividing the sum by the average.

Number of quantities = Sum / Average

Number of quantities = 5200 / 650

Number of quantities = 8

Explanation

A number divisible by both 2 and 5 is automatically divisible by their LCM = 10.

For example, 20 ÷ 2 = 10, 20 ÷ 5 = 4, and 20 ÷ 10 = 2.

Explanation

The transitive property states that if a = b and b = c, then a = c.

Explanation

Given:

4x/6 = 2

Multiplying both sides by 6/4:

x = 2 × 6/4

x = 12/4

x = 3

Explanation

1 milligram (mg) = 10⁻⁶ kilograms (kg)

So, 20 milligrams equals:

20 mg = 20 × 10⁻⁶ kg

Which simplifies to:

2 × 10⁻⁵ kg

Explanation

Given cos θ = 4/5 and θ lies in the 4th quadrant.

In the 4th quadrant, cosine is positive, and sine is negative.

We know that sin² θ + cos² θ = 1

sin² θ = 1 - cos² θ

= 1 - (4/5)²

= 1 - 16/25

= 9/25

sin θ = ±√(9/25)

= ±3/5

Since θ lies in the 4th quadrant, sin θ is negative:

sin θ = -3/5

Explanation

Given:

a² + b² + c² = 12

a + b + c = 5

We know that:

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

Expanding the equation:

5² = 12 + 2(ab + bc + ca)

25 = 12 + 2(ab + bc + ca)

Subtract 12 from both sides:

13 = 2(ab + bc + ca)

Divide by 2:

ab + bc + ca = 13/2

Explanation

The LCM of 8 and 24 is 24 (since 24 is a multiple of 8).

The common multiples are: 24, 48, 72, 96 (4th common multiple).