Question

identify whether the relationship is proportional or non - proportional:
a gym charges $15 per class plus a $10 monthly membership fee.
this relationship is ______.

○ non - proportional
○ proportional

question 11
1 pts
a blueprint uses a scale of 1 cm = 2.5 ft.
if a room measures 6.8 cm on the blueprint, what is the actual length?

○ 17 ft
○ 14 ft
○ 10 ft
○ 20 ft

Explanation:

First Question (Proportional/Non - proportional Relationship)

A proportional relationship can be represented in the form \(y = kx\) (where \(k\) is a constant), meaning the graph passes through the origin \((0,0)\). For the gym charges, let \(y\) be the total cost and \(x\) be the number of classes. The cost function is \(y=15x + 10\). When \(x = 0\) (no classes), \(y=10
eq0\), so it does not pass through the origin. Thus, the relationship is non - proportional.

Step 1: Understand the scale

The scale is \(1\space\text{cm}=2.5\space\text{ft}\). This means that for every centimeter on the blueprint, the actual length is \(2.5\) feet.

Step 2: Calculate the actual length

If the length on the blueprint is \(6.8\space\text{cm}\), we multiply the blueprint length by the scale factor. So the actual length \(L=6.8\times2.5\)
\[6.8\times2.5=(7 - 0.2)\times2.5=7\times2.5-0.2\times2.5 = 17.5 - 0.5=17\space\text{ft}\]

Answer:

non - proportional

Second Question (Scale Conversion)