A certain book had an original rating of 27 out of 30 points on a survey chart. Each month, the rating fell by 3 points. Express the number of points as a function of m, the number of months since the release. (A) f(m)=3m (B) f(m)=3m−27 (C) f(m)=30−3m (D) f(m)=27−3m (E) f(m)=3−27m

D.) f(m)=27−3m

Step-by-step explanation:

Given that:

Original rating = 27

Total possible rating points = 30

Drop in rating point per month = 3

m = number of months since release :

Hence,

F(m) = original rating - drop in rating per month * number of months since release

F(m) = 27 - 3(m)

F(m) = 27 - 3m

she drove 134 miles

step-by-step explanation:

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9