4) Jerry cuts a piece of paper from one corner to the other, as shown. How long is the cut edge (look at photo)
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This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality. The value of x is 6.
<h3>What are directly proportional and inversely proportional relationships?</h3>Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called the constant of proportionality.
This directly proportional relationship between p and q is written as
p ∝ q where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n be two variables.
Then m and n are said to be inversely proportional to each other if
(both are equal)
where c is a constant number called the constant of proportionality.
This inversely proportional relationship is denoted by
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
Let the days to set up with entries be represented by a, while the number of concerts is represented by b. Now, It is known that the days to set up with entries and the number of the concert are in a relationship. Therefore, we can write the relationship as,
a ∝ b
a = k b
Now, if we substitute the values from the first row, we will get,
1.5 = k × 1
1.5 = k
Thus, the value of k is 1.5.
Now, if we substitute the entries from the 4th row, we will get,
a = k × b
x = 1.5 × 4
x = 6
Hence, the value of x is 6.
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