This question has two parts.
Danielle's phone plan charges her $30 per month for the first 200 minutes and then $0.10 per minute for each subsequent minute.
1. Which of the following functions takes an input of any whole number value of x is greater than or equal to 200 and outputs the value for f(x) as the amount of dollars Danielle would pay for x minutes of phone usage?
A. f(x) = 0.1x + 10
B. f(x) = 0.1x + 20
C. f(x) = 0.1x + 30
D. f(x) = 0.1x + 200
E. f(x) = 0.1x + 230
2. If Danielle paid exactly $100 last month, how many minutes did she use?
F. 700
G. 800
H. 900
J. 1,000
K. 1,200
whats the answer?
1. The function that represents the amount of dollars Danielle would pay for x minutes of phone usage given that x is greater than or equal to 200 is:
C. f(x) = 0.1x + 30
This is because the phone plan charges Danielle $30 per month for the first 200 minutes and then $0.10 per minute for each subsequent minute. The equation 0.1x represents the additional cost for each minute beyond the first 200 minutes, and the constant term 30 represents the fixed cost for the first 200 minutes.
2. To find out how many minutes Danielle used if she paid exactly $100 last month, we need to solve the equation:
f(x) = 0.1x + 30
Given that Danielle paid $100, we set f(x) equal to 100:
0.1x + 30 = 100
Subtracting 30 from both sides:
0.1x = 70
Dividing both sides by 0.1:
x = 700
Therefore, Danielle used 700 minutes.
The answer is F. 700
To answer the first question, let's break down Danielle's phone plan charges. She is charged $30 per month for the first 200 minutes. So for any x greater than or equal to 200, the initial cost would be $30.
For any subsequent minute after the first 200 minutes, she is charged $0.10 per minute. So, the additional cost for subsequent minutes is 0.1 * (x - 200), where (x - 200) represents the number of minutes beyond the first 200.
To find the total cost for x minutes of phone usage, we need to add the initial cost of $30 to the additional cost of 0.1 * (x - 200).
Therefore, the function that represents the amount of dollars Danielle would pay for x minutes of phone usage is:
f(x) = 30 + 0.1 * (x - 200)
Now, let's solve the second question. We know that Danielle paid exactly $100 last month. We can set up the equation:
100 = 30 + 0.1 * (x - 200)
Simplifying the equation, we have:
70 = 0.1 * (x - 200)
Dividing both sides by 0.1, we get:
700 = x - 200
Adding 200 to both sides, we have:
x = 700 + 200
x = 900
Therefore, Danielle used 900 minutes of phone usage last month.
So the answers are:
1. C. f(x) = 0.1x + 30
2. H. 900
1. ) = 30 + 0.1(x-200)
F(x) = 30 + 0.1x - 20
The above Eq is valid for all real
values of X that are equal to or greater
than 200: X => 200.
When x = 200 minutes, the cost would be
$30.
None of the given choices meets this
requirement.
2. Cost = 30 + 0.1x - 20 = $100
0.1x = 100-10 = 90
X = 900 Minutes.