Company A charges $32 per person to host a banquet. Company B charges an initial fee of $30 and charges $30 per person. At what number of people will Company B be the cheaper option?

At 16 people company B will be the cheaper option

Step-by-step explanation:

Assume that the number of people is x

∵ Company A charges $32 per person to host a banquet

∵ The number of people is x

∴ The cost of company A = 32x

∵ Company B charges an initial fee of $30 and charges $30 per person

∵ The number of people is x

∴ The cost of company B = 30x + 30

∵ Company B be is the cheaper option

→ That means the cost of company B < The cost of company A

∴ 30x + 30 < 32x

→ Subtract 30x from both sides

∵ 30x - 30x + 30 < 32x - 30x

∴ 30 < 2x

→ Divide both sides by 2

∴ 15 < x

→ 15 smaller than x means x is greater than 15

∴ x > 15

→ To make company B cheaper, the number of people should be > 15

∵ The first integer greater than 15 is 16

∴ At 16 people company B will be the cheaper option

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°

answer: its c because when it has a magnet next to it it will move away from the mixture. hope this

step-by-step explanation: