**Answer:**

B. High optical density, and light travels more slowly through it.

**Step-by-step explanation:**

Refractive index is the property of a material that describes the change in the initial path of light and the rate at which light travels through it. And optical density of a material describes its absorption ability to rays or beam of light passing through it.

As the index of refraction of a material increases, therefore its optical density would increase. This would cause light to travel through it slowly. Unless the light has a high frequency.

A material with a high index of refraction has a high optical density, and light travels more slowly through it.

**Answer:**

**1). Option B.**

**2). Option C.**

**3). Option A.**

**4). Option C.**

**5). Option D.**

**6). Option C.**

**Step-by-step explanation:**

**1).** Bisector of angle ABC is,

**Option (B). stack BD with rightwards arrow on top**.

**2).** Since GH = GI [Given]

3x = 5x - 10

5x - 3x = 10

2x = 10

x = 5

Therefore, GH = 3x

= 3(5)

= 15

**Option (C). is the answer.**

**3). **Since m∠ABD ≅ m∠DCB [Given]

and m∠DCB ≅ m∠CBE [Since GH ≅ GI]

Therefore, m∠ABD ≅ m∠CBE

10y = 8y + 4

10y - 8y = 4

2y = 4

y = 2

**Option (A). is the answer.**

**4). **m∠DBE = m∠DBC + m∠CBE

= 10y + (8y + 4)

= (18y + 4)°

By putting y = 2,

m∠DBE = 18×2 + 4

= 36 + 4

= 40°

**Option (C) will be the answer.**

**5). **m∠ABE = m∠ABD + m∠DBC + m∠CBE

= 10y + 10y + (8y + 4)

= 28y + 4

= 28×2 + 4

= 56 + 4

= **60°**

**Option (D) will be the answer.**

**6). **If m∠FBA = 7x + 6y

By putting x = 5 and y = 2

m∠FBA = 7(5) + 6(2)

= 35 + 12

= **47°**

**Option (C) will be the answer.**

**Answer:**

f(3) = 3

**Step-by-step explanation:**

(1) = 1

f(2)= 2

(f(n) = f(n − 2) + f(n-1)

f(3) =f(3 − 2) + f(3-1)

= f(1) + f(2)

= 1 + 2

= 3

3m-3.

basically since 6 and -9 don’t have any variables, you would ignore the 3m to combine them like 6-9, which would be -3 and then adding that onto the 3m you would get 3m-3