Find the 10th term of the sequence defined by the given rule.

f(1) = 2; f(n) = f(n-1) + 7

f(2) = (2-1) + 7 = 1 + 7 =8

f(3) = (8-1) + 7 = 7 + 7 =14

f(4) = (14-1) + 7 = 13 + 7 =20

f(5) = (20-1) + 7 = 19 + 7 =26

and so on...so it's increase by 6

f(6) = 26 + 6 = 32

f(7) = 32 + 6 = 38

f(8) = 38 + 6 = 44

f(9) = 44 +6 = 50

f(10) = 50 + 6 = 56

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!