Elect the relationship between each pair of quantities that are proportional. a A small pizza costs $9.00 and each additional topping costs $0.75 b A health club charges $45 per month. c A bike rental store charges $20 as a flat fee, plus $5 per hour. d A car travels 60 miles in 1 hour, 120 miles in 2 hours, and 180 miles in 3 hours. e A student earns $12 for each hour she tutors.

B, D, E

Step-by-step explanation:

As we know that a pair of quantities that are proportional when they can be expressed in the general form y = kx, where k is the constant of proportionality.

A.  A small pizza costs $9.00 and each additional topping costs $0.75  

=> the cost to buy the number of pizzas is: y = 0.75x + 9

It is not proportional

B. A health club charges $45 per month

=> The cost for health club y = 45x

It is not proportional

C. A bike rental store charges $20 as a flat fee, plus $5 per hour

=> the cost to rent the bike: y = 5x + 20

It is not proportional

D. A car travels 60 miles in 1 hour, 120 miles in 2 hours, and 180 miles in 3 hours

=> The distance the car travel is: y = 60x

It is proportional

E A student earns $12 for each hour she tutors.

=> The income the student get: y = 12x

It is proportional  

Hence, answer B, D, E are correct

Step-by-step explanation:

Proportionality constant is given by the formula,

y = kx

Where,

y is the dependent factor

x is the independent factor

A. A small pizza costs $9.00 and each additional topping costs $0.75

Let pizza be x, toppings be c and cost = y

y = x + c - linear form

B. A health club charges $45 per month.

Let charges be y, cost be c and months be x

y = c/x - inverse relationship

C. A bike rental store charges $20 as a flat fee, plus $5 per hour.

Let charges be y, flat fee be c, charge rate be t and hour be x

y = c + (t × x) - linear form

D. A car travels 60 miles in 1 hour, 120 miles in 2 hours, and 180 miles in 3 hours.

Let distance be y and hours of travel be x

y = 60 × x

E. A student earns $12 for each hour she tutors.

Let earnings be y and hours be x

y = 12 × x

Note: All proportional functions are linear, but not all linear functions are proportional.

From the above,

A, C, D, E Are all proportional.

step-by-step explanation:

the true statements are:

r = set of real numbers

n = set of natural numbers, 1,2,

w = n u{0} = {0,1,}