Question
Question 1
Solve each problem on a piece of paper. Make sure to show your steps and submit a picture of your work.(2 points)
1. Rearrange the slope formula y=mx+b
for the quantity of interest m
.
2. Daisy received a $100 gift card and needs new sweaters for fall. The sweaters cost $28.50 each.
Write an equation, then solve the equation to determine how many sweaters she can buy.
sweaters
Question 2
If you are unable to submit your work in the box below, text or webmail a picture of your work to your teacher.(2 points)
Solve each problem on a piece of paper. Make sure to show your steps and submit a picture of your work.(2 points)
1. Rearrange the slope formula y=mx+b
for the quantity of interest m
.
2. Daisy received a $100 gift card and needs new sweaters for fall. The sweaters cost $28.50 each.
Write an equation, then solve the equation to determine how many sweaters she can buy.
sweaters
Question 2
If you are unable to submit your work in the box below, text or webmail a picture of your work to your teacher.(2 points)
Answers
GPT-4o mini
Sure! Let's go through each problem step-by-step.
### Question 1
1. **Rearranging the slope formula:**
The slope formula is given as:
\[
y = mx + b
\]
To solve for \( m \):
- Start by isolating the term \( mx \):
\[
y - b = mx
\]
- Now, divide both sides by \( x \) to isolate \( m \):
\[
m = \frac{y - b}{x}
\]
Thus, the rearranged formula for \( m \) is:
\[
m = \frac{y - b}{x}
\]
2. **Calculating how many sweaters Daisy can buy:**
Let \( x \) equal the number of sweaters Daisy can buy.
The cost of each sweater is $28.50. Therefore, the total cost for \( x \) sweaters is:
\[
28.50x
\]
This total cost cannot exceed Daisy's gift card limit of $100, so we set up the inequality:
\[
28.50x \leq 100
\]
To find \( x \), solve the equation:
\[
x \leq \frac{100}{28.50}
\]
Now, perform the calculation:
\[
x \leq 3.50877
\]
Since Daisy cannot buy a fraction of a sweater, we round down to the nearest whole number. Thus, the maximum number of sweaters Daisy can buy is:
\[
x = 3
\]
### Summary of Answers:
1. Rearranged slope formula for \( m \):
\[
m = \frac{y - b}{x}
\]
2. Daisy can buy a maximum of **3 sweaters**.
If you need to submit a picture of your work, you can write this step-by-step solution on paper, take a clear photo, and submit it as requested. Let me know if you have any other questions!
### Question 1
1. **Rearranging the slope formula:**
The slope formula is given as:
\[
y = mx + b
\]
To solve for \( m \):
- Start by isolating the term \( mx \):
\[
y - b = mx
\]
- Now, divide both sides by \( x \) to isolate \( m \):
\[
m = \frac{y - b}{x}
\]
Thus, the rearranged formula for \( m \) is:
\[
m = \frac{y - b}{x}
\]
2. **Calculating how many sweaters Daisy can buy:**
Let \( x \) equal the number of sweaters Daisy can buy.
The cost of each sweater is $28.50. Therefore, the total cost for \( x \) sweaters is:
\[
28.50x
\]
This total cost cannot exceed Daisy's gift card limit of $100, so we set up the inequality:
\[
28.50x \leq 100
\]
To find \( x \), solve the equation:
\[
x \leq \frac{100}{28.50}
\]
Now, perform the calculation:
\[
x \leq 3.50877
\]
Since Daisy cannot buy a fraction of a sweater, we round down to the nearest whole number. Thus, the maximum number of sweaters Daisy can buy is:
\[
x = 3
\]
### Summary of Answers:
1. Rearranged slope formula for \( m \):
\[
m = \frac{y - b}{x}
\]
2. Daisy can buy a maximum of **3 sweaters**.
If you need to submit a picture of your work, you can write this step-by-step solution on paper, take a clear photo, and submit it as requested. Let me know if you have any other questions!