Respuesta :
Answer:
(a) The cost if a person drives 160 miles is 77 dollars
(b) the person drive 375 miles
(c) the maximum number of miles the person can drive is 775 milles
(d) the implied domain of C is numbers bigger than zero
(e) the slope says how cost every mille that a person drive .
(f) the y- intercept says what is the minimum value of renting the truck even if a person doesn’t drive any mile.
Step-by-step explanation:
The Cost C is given by the function: C(x)=0.2*x+45
Then, for calculate the cost if a person drives 160 miles, we should replace x by 160 miles in the function, So:
C(x)=0.2*160+45
C(x)=77 dollars
For calculate how many miles did the person drive if the cost of renting is 120, we replace C(X) with 120 and solve for x as:
120=0.2*x+45
120-45=0.2*x
X=375 miles
For calculate the maximum number of miles the person can drive if that person wants the cost to be no more than $200, we replace C(X) with 200 and solve for x as:
200=0.2*x+45
200-45=0.2*x
X=775 miles
In this case, we know that the cost could be 200 or less then if the person drive 775 miles or less, the cost is always going to be less than 200.
The domain are the values that the variable x can take, so it make sense that a person can drive any value of miles that are bigger than zero.
The slope of the function is the number that is multiplied with the variable x, so this number say what is the cost of every mile that a person drive. This means that every mile driven cost 0.2 dollars
The y intercept is the value that doesn’t have a variable multiplying. this is the fixed cost of renting a car, so if a person drive zero miles the cost of renting is 45 dollars.
To solve the problem we will substitute the value of x and C in the given function.
Given to us
The cost C, in dollars, of renting a moving truck for a day C(x)=0.20x+45,
What is the cost if a person drives x=160 miles?
To find the cost if a person drives x=160 miles, simply substitute the value of x in the function of cost c,
[tex]C(x)=0.20x+45\\\\C(160)=0.20(160)+45\\\\C(160)=77[/tex]
Hence, the cost of the moving truck if a person drives x=160 miles is $77.
If the cost of renting the moving truck is $120, how many miles did the person drive?
To solve the problem substitute the value of C as 120 in the given function,
[tex]C(x)=0.20x+45\\\\120 = 0.20x+45\\\\x = 375\rm\ miles[/tex]
Hence, If the cost of renting the moving truck is $120, the person drives 375 miles.
Suppose that a person wants the cost to be no more than $200. What is the maximum number of miles the person can drive?
To solve the problem substitute the value of C as 200 in the given function,
[tex]C(x)=0.20x+45\\\\200 = 0.20x+45\\\\x = 775\rm\ miles[/tex]
Hence, if a person wants the cost to be no more than $200. The maximum number of miles a person can drive is 775.
What is the implied domain of C?
Implied Domain is the value of C for which it is defined, since even if the truck is not moving a single mile it will still be costing $45, to a person, therefore, the domain of C is [45, +∞].
What is the slope of the function?
If we look at the function it is a function of line therefore, the comparing the two equations,
[tex]y = mx+c\\C=0.20x+45[/tex]
we know that m is the slope of the function,
m = 0.20
therefore, the slope of the function is 0.20.
What is the y-intercept?
We know that the intercept of y is the value of y at which it intersect the y axis.
when we put the value of x=0, we get the value of y as 45, therefore, the intercept of y is 45.
Hence, the intercept of y is 45.
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