Abus company took a tour on the ferry when there were 30 people aboard. the very charge the bus company $180. the following week the bus and 50 people on board and the ferry charge them $220. how much is the base rate for the empty bus? how much does each person cost?

$2 variable per person, 120 base fee

Step-by-step explanation:

the delta are 20 persons and $40

therefore variable cost are $2 per person

base fee: 180-30*2=120

Base rate is $ 120 and each person costs $ 2.

Step-by-step explanation:

Let the equation that shows the total charges for x persons,

y = ax + b

Where,

a = cost per person,

b = base rate of empty bus,

According to the question,

if x = 30, y = $ 180,

180 = 30a + b (1),

if x = 50, y = $ 220,

220 = 50a + b (2),

Equation (2) - equation (1),

40 = 20a

⇒ a = 2,

From equation (1),

180 = 30(2) + b

180 = 60 + b

⇒ b = 120

Hence, base rate for empty bus = $ 120

And, each person costs $ 2.

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct