Answer:
3 gallons of diesel weight = <u>22.2 pounds </u>
The constant of variation = <u>7.4</u>
The quantities vary <u>directly</u>
Step-by-step explanation:
Given:
5 gallons of gas weights = 37 pounds
To find
a) the weight of 3 gallons of gas.
b) if the quantities vary directly or inversely.
c) the constant of variation.
Solution:
Applying unitary method to find weight of 3 gallons of gas.
If 5 gallons weight = 37 pounds
Then, 1 gallon will weight = =7.4 pounds
Thus, 3 gallons will weight = = 22.2 pounds
Listing out the data we have:
1 gallon = 7.4 pounds
3 gallons = 22.2 pounds
5 gallons = 37 pounds
From the data, we find out that as the number of gallons of gas increases the weight of gas also increases. This shows that these quantities are directly proportional to each other.
<em>The unit rate of the quantities is called the constant of variation.</em>
<em>Unit rate: 7.4 pounds per gallon</em>
Thus, the constant of variation = 7.4
Given 12−(−2) over a line 12−6÷2
We can use PEMDAS rule and solve the expression in the order as given below:-
1. Parentheses
2. Exponents
3. Multiplication
4. Division
5. Addition
6. Subtraction
Now solving for given expression:-
So final answer is 14/9 i.e. 14 over 9.
If a function can be written in y = mx + b form, it is linear.
The function given:
Taking "5" to the right hand side, we get:
This is in the form y = mx + b, with m = 5 and b = 5.
This is a linear function.