Answered

Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Jessica is selling books during the summer to earn money for college. She earns a commission on each sale but has to pay for her own expenses.

After a month of driving from neighborhood to neighborhood and walking door-to-door, she figures out that her weekly earnings are approximately a linear function of the number of doors she knocks on.

She writes the equation of the function like this: [tex]E(x) = 7x - 25[/tex], where [tex]x[/tex] is the number of doors she knocks on during the week and [tex]E(x)[/tex] is her earnings for the week in dollars.

Which of the following are reasonable interpretations of the [tex]y[/tex]-intercept of Jessica's function? Check all that apply.

A. Her expenses are [tex]\$25[/tex] per week.
B. She can earn [tex]\$7[/tex] per week even if she does not knock on any doors.
C. If she does not knock on any doors at all during the week, she will lose [tex]\$25[/tex].
D. She will lose [tex]\$7[/tex] per week if she does not knock on any doors.

Sagot :

GinnyAnswer
To analyze Jessica's weekly earnings function [tex]\( E(x) = 7x - 25 \)[/tex], let's examine each interpretation of the [tex]$y$[/tex]-intercept step-by-step.

### Understanding the Equation
- E(x) represents Jessica’s weekly earnings in dollars.
- x represents the number of doors she knocks on during the week.
- The equation is [tex]\( E(x) = 7x - 25 \)[/tex].

### Interpreting the y-intercept
The y-intercept of the function, which is the value of [tex]\( E(x) \)[/tex] when [tex]\( x = 0 \)[/tex], is [tex]\( -25 \)[/tex]. This value [tex]\( -25 \)[/tex] provides insight into Jessica's fixed costs or fixed losses that do not depend on the number of doors she knocks on.

Now let's evaluate each interpretation:

#### Interpretation A: Her expenses are \[tex]$25 per week. - When \( x = 0 \), the earnings are \( E(0) = 7(0) - 25 = -25 \). This means Jessica has a negative earning of \$[/tex]25 when she doesn't knock on any doors, which can be interpreted as her weekly expenses. Therefore, this interpretation is true.

#### Interpretation B: She can earn \[tex]$7 per week even if she does not knock on any doors. - When \( x = 0 \), her earnings are \( -25 \). This means she does not earn anything if she doesn't knock on any doors; instead, she incurs a loss of \$[/tex]25. Thus, this interpretation is false.

#### Interpretation C: If she does not knock on any doors at all during the week, she will lose \[tex]$25. - Again, when \( x = 0 \), \( E(0) = -25 \). This directly means that Jessica incurs a loss of \$[/tex]25 if she does not knock on any doors. This interpretation is true.

#### Interpretation D: She will lose \[tex]$7 per week if she does not knock on any doors. - This interpretation is incorrect because the loss when she does not knock on any doors is \$[/tex]25, not \$7. So, this interpretation is false.

Combining our evaluations:

- A. True
- B. False
- C. True
- D. False

The final result, expressed as a tuple where 1 represents true and 0 represents false, is:
```
(1, 0, 1, 0)
```
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.