1. Tommy the cat is constantly stealing hair ties. At the start of the week, he had already stolen 5 hair ties. Each day, Tommy steals 3 more hair ties.

Question

Part A: Write a linear equation that represents the total number of hair ties (h) based on the number of days that have passed (d).

h(d)=

Part B:  Tommy would have stolen 
 hair ties after 9 days.

2. Penny earned a monetary reward for returning a lost puppy. She decides to spend $12 from the reward each week on treats for her own pets. After 4 weeks Penny has $134 left.

Part A: What is the slope and what is one point that we know?

m=

a point that we know is 
 (write your response as an ordered pair)
Part B: Write a linear equation that models the total money left, y, from her reward after x weeks.

y=
 
 (Write your answer in slope y-intercept form:y=mx+b
)

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GPT-4o mini · Answer

Let's solve the problems step by step. ### Problem 1: Tommy the Cat **Part A:** Start with the information given. At the start of the week (day 0), Tommy has stolen 5 hair ties, and he steals 3 more each day. We can write the linear equation: - Initial amount of hair ties = 5 - Daily increase = 3 hair ties per day The total number of hair ties after $d$ days can be represented by: $$ h(d) = 5 + 3d $$ **Part B:** To find out how many hair ties Tommy has stolen after 9 days: $$ h(9) = 5 + 3(9) = 5 + 27 = 32 $$ So, Tommy would have stolen **32 hair ties** after 9 days. --- ### Problem 2: Penny and the Reward **Part A:** Penny spends $12 each week, and after 4 weeks she has $134 left. 1. The slope $m$ of the linear function indicating how much money she has left can be described as the negative amount she spends per week. Therefore: $$ m = -12 $$ 2. One point we know is the amount she has after 4 weeks, which is given as (4, 134). **Part B:** To write a linear equation that models the total money left $y$ after $x$ weeks, we start with the slope-intercept form $y = mx + b$. Given: - Slope $m = -12$ - After 4 weeks, she has $134 left, so we need to find the y-intercept $b$. Using the point (4, 134): $$ 134 = -12(4) + b $$ $$ 134 = -48 + b $$ $$ b = 134 + 48 = 182 $$ So, the equation becomes: $$ y = -12x + 182 $$ ### Final Answers 1. **Tommy the Cat:** - Part A: $ h(d) = 5 + 3d $ - Part B: **32** hair ties after 9 days. 2. **Penny and the Reward:** - Part A: - $ m = -12 $ - A point that we know is $ (4, 134) $ - Part B: $ y = -12x + 182 $

Answer

y= (Write your answer in slope y-intercept form:y=mx+b )

GPT-4o mini · Answer

For the linear equation in slope-intercept form (y = mx + b) that models Penny's total money left after x weeks, we already established:

The slope $ m $ is $-12$, which represents the amount of money she spends each week.
The y-intercept $ b $ is $ 182$, which is the amount she started with before spending any money.

Thus, the complete equation is:

\[ y = -12x + 182 \]

This equation represents the total amount of money $ y $ that Penny has left after $ x $ weeks.

Answer

part a of tommy the cat is wrong

GPT-4o mini · Answer

Let's reevaluate Part A of Tommy's problem.

Tommy initially had 5 hair ties at the start of the week (day 0), and he steals 3 more hair ties each day.

So the total number of hair ties he has stolen after $d$ days would be:

Initial amount of hair ties: 5
Hair ties stolen each day: 3

The total number of hair ties after $d$ days can be represented by the equation:

\[ h(d) = 3d + 5 \]

This means that after $d$ days, Tommy has stolen a total of $5$ hair ties plus $3$ hair ties for each day that has passed.

Summary of Correct Equation

Correct Linear Equation: \[ h(d) = 3d + 5 \]

If there's anything more specific you would like to address regarding this problem, please let me know!