Answer:
Linear relationship always produces a straight line and are without exponential.
Lets check all the given options:
1. the total area, in square meters, y, of a square garden if the side length is x meters.
The area of a square is
Here, side is 'x' and area 'y' will be .
This is not linear.
2. the height, y, of a 6-foot tree that grows 0.2 feet per month for x months
The equation forms:
When x = 1
When x = 2
=>
When x = 3
=>
This is a linear relation.
3. the total cost, y, of a ski rental from a company that charges $15 plus an additional $8 per day rented for x days
The equation forms:
When x = 1
When x = 2
=>
When x = 3
=>
This is also linear.
4. the total miles, y, traveled by a car going 62 miles per hour in x hours
The equation forms:
When x = 1
When x = 2
=>
When y = 3
=>
This is also linear in nature.
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Exponential Function.
Plotting the graph using this table gives the first figure. An exponential function has this kind of graph.
Answer:
(a) The ones that are equivalent to the given fraction are: 
and 
(b) The one that is equivalent to the given fraction is: 
The height of the ladder on the building is 19.77 feet
<h3>How high does the ladder reach on the building?</h3>
Represent the height of the ladder on the building with h
So, the given parameters are:
Angle, x = 64 degrees
Length of ladder, l = 22 feet
The height of the ladder on the building is calculated using
sin(x) = h/l
Substitute the known values in the above equation
sin(64) = h/22
Multiply both sides by 22
h = 22 * sin(64)
Evaluate the product
h = 19.77
Hence, the height of the ladder on the building is 19.77 feet
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