We have the expression:
When we have rational functions, where the denominator is a function of x, we have a restriction for the domain for any value of x that makes the denominator equal to 0.
That is because if the denominator is 0, then we have a function f(x) that is a division by zero and is undefined.
If we have a value that makes f(x) to be undefined, then this value of x does not belong to the domain of f(x).
Expression:
Answer: There is no restriction for x in the expression.
Answer:
Step-by-step explanation:
<u>Linear Modeling</u>
Some events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.
The linear function can be expressed in the slope-intercept format:
For the problem at hand, we must pick the adequate variables according to the data provided.
The question states the charge for renting a car is a function of the mileage. It also provides two points from which we can build our model. Let's set the following variables:
c = the charge for renting a car in dollars
x = the distance driven by the businessman in miles
Representing the ordered pair as (x,c), we have the points: (150,79) and (65,63.70). Our model will be expressed as:
We must find the values of m and b with the data provided. Substituting the first point:
Substituting the second point:
Both equations form the following system:
Subtracting both equations:
Note the variable b was canceled out in the operation, leaving only the variable m to solve. Joining like terms:
Solving:
From the first equation
Solving for b:
The model for the problem is:
Now we need to calculate how many miles (x) could be driven for c=$100. From the equation above, substitute c=100
Solve for x:
Rounding to the closest integer:
✪ Both triangles will be proven similar by AA theorem i.e. Angle-Angle theorem.
✪ The symbol for similarity is ~.
✪ The symbol for congruency is ≅.
