At a local movie theatre, members pay a $45 membership fee and pay $2 per movie. Nonmembers pay $3.50 per movie. For what number of movies will the cost for members and nonmembers be the same?

30 movies

Step-by-step explanation:

Let Number of movies = x

Member :

Membership fee + 2x

45 + 2x - - - (1)

Non members :

3.50x - - - (2)

Equate (1) and (2)

45 + 2x = 3.50x

45 = 3.50x - 2x

45 = 1.50x

x = 45 / 1.50

x = 30

30 movies

step-by-step explanation:

your mom

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°