Math / Algebra

QuestionA hardware store rents vacuum cleaners that customers may use for part of a day before returning. The function $f(x)=6 x+14$ models the total rental cost of a vacuum cleaner.
What is the flat fee that the store charges? \\square$

Studdy Solution

STEP 1

What is this asking? What's the base price to rent a vacuum, before even starting to use it? Watch out! Don't get tricked into thinking the number multiplied by $x$ is the flat fee!

STEP 2

1. Define the function
2. Analyze the function
3. Calculate the flat fee

STEP 3

Alright, so we've got this super cool function, $f(x) = 6 \cdot x + 14$ , that tells us the total cost to rent a vacuum cleaner.
Here, $x$ is the amount of time the vacuum is rented for, and $f(x)$ spits out the total cost.

STEP 4

Let's break down this function piece by piece.
We've got two parts here: $6 \cdot x$ and $+ 14$ .
The $6 \cdot x$ part changes depending on how long we rent the vacuum.
This means $\$6$ is the rate we're charged for each unit of time.

STEP 5

Now, the $+ 14$ part is super interesting!
This part doesn't change, no matter how long we rent the vacuum for.
This is our flat fee!
It's what we pay just for the privilege of using the vacuum, even if we rent it for zero time!

STEP 6

So, to find the flat fee, we need to figure out what $f(x)$ would be if $x = 0$ , meaning zero rental time.
Let's plug that into our function: $f(0) = 6 \cdot 0 + 14$

STEP 7

Anything multiplied by zero is zero, so $6 \cdot 0 = 0$ .
Now we have: $f(0) = 0 + 14$

STEP 8

Adding zero to a number doesn't change the number, so $0 + 14 = 14$ .
This gives us: $f(0) = 14$

STEP 9

So, the flat fee is $\$14$ !

STEP 10

The flat fee is $\$14$ .

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QuestionA hardware store rents vacuum cleaners that customers may use for part of a day before returning. The function $f(x)=6 x+14$ models the total rental cost of a vacuum cleaner.
What is the flat fee that the store charges? \\square$

Studdy Solution

STEP 1

What is this asking? What's the base price to rent a vacuum, before even starting to use it? Watch out! Don't get tricked into thinking the number multiplied by $x$ is the flat fee!

STEP 2

1. Define the function
2. Analyze the function
3. Calculate the flat fee

STEP 3

Alright, so we've got this super cool function, $f(x) = 6 \cdot x + 14$ , that tells us the total cost to rent a vacuum cleaner.
Here, $x$ is the amount of time the vacuum is rented for, and $f(x)$ spits out the total cost.

STEP 4

Let's break down this function piece by piece.
We've got two parts here: $6 \cdot x$ and $+ 14$ .
The $6 \cdot x$ part changes depending on how long we rent the vacuum.
This means $\$6$ is the rate we're charged for each unit of time.

STEP 5

Now, the $+ 14$ part is super interesting!
This part doesn't change, no matter how long we rent the vacuum for.
This is our flat fee!
It's what we pay just for the privilege of using the vacuum, even if we rent it for zero time!

STEP 6

So, to find the flat fee, we need to figure out what $f(x)$ would be if $x = 0$ , meaning zero rental time.
Let's plug that into our function: $f(0) = 6 \cdot 0 + 14$

STEP 7

Anything multiplied by zero is zero, so $6 \cdot 0 = 0$ .
Now we have: $f(0) = 0 + 14$

STEP 8

Adding zero to a number doesn't change the number, so $0 + 14 = 14$ .
This gives us: $f(0) = 14$

STEP 9

So, the flat fee is $\$14$ !

STEP 10

The flat fee is $\$14$ .

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QuestionA hardware store rents vacuum cleaners that customers may use for part of a day before returning. The function f(x)=6x+14f(x)=6 x+14f(x)=6x+14 models the total rental cost of a vacuum cleaner.What is the flat fee that the store charges? \ \square$

Studdy Solution

STEP 1

What is this asking? What's the base price to rent a vacuum, before even starting to use it? Watch out! Don't get tricked into thinking the number multiplied by xxx is the flat fee!

STEP 2

1. Define the function2. Analyze the function3. Calculate the flat fee

STEP 3

Alright, so we've got this super cool function, f(x)=6⋅x+14f(x) = 6 \cdot x + 14f(x)=6⋅x+14, that tells us the *total* cost to rent a vacuum cleaner.Here, xxx is the amount of time the vacuum is rented for, and f(x)f(x)f(x) spits out the total cost.

STEP 4

Let's break down this function piece by piece.We've got two parts here: 6⋅x6 \cdot x6⋅x and +14+ 14+14.The 6⋅x6 \cdot x6⋅x part changes depending on how long we rent the vacuum.This means $6\$6$6 is the *rate* we're charged for each unit of time.

STEP 5

Now, the +14+ 14+14 part is super interesting!This part *doesn't* change, no matter how long we rent the vacuum for.This is our **flat fee**!It's what we pay just for the privilege of using the vacuum, even if we rent it for zero time!

STEP 6

So, to find the flat fee, we need to figure out what f(x)f(x)f(x) would be if x=0x = 0x=0, meaning zero rental time.Let's plug that into our function: f(0)=6⋅0+14f(0) = 6 \cdot 0 + 14f(0)=6⋅0+14

STEP 7

Anything multiplied by zero is zero, so 6⋅0=06 \cdot 0 = 06⋅0=0.Now we have: f(0)=0+14f(0) = 0 + 14f(0)=0+14

STEP 8

Adding zero to a number doesn't change the number, so 0+14=140 + 14 = 140+14=14.This gives us: f(0)=14f(0) = 14f(0)=14

STEP 9

So, the **flat fee** is $14\$14$14!

STEP 10

The flat fee is $14\$14$14.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionA hardware store rents vacuum cleaners that customers may use for part of a day before returning. The function $f(x)=6 x+14$ models the total rental cost of a vacuum cleaner.
What is the flat fee that the store charges? \\square$

What is this asking? What's the base price to rent a vacuum, before even starting to use it? Watch out! Don't get tricked into thinking the number multiplied by $x$ is the flat fee!

1. Define the function
2. Analyze the function
3. Calculate the flat fee

Alright, so we've got this super cool function, $f(x) = 6 \cdot x + 14$ , that tells us the total cost to rent a vacuum cleaner.
Here, $x$ is the amount of time the vacuum is rented for, and $f(x)$ spits out the total cost.

Let's break down this function piece by piece.
We've got two parts here: $6 \cdot x$ and $+ 14$ .
The $6 \cdot x$ part changes depending on how long we rent the vacuum.
This means $\$6$ is the rate we're charged for each unit of time.

Now, the $+ 14$ part is super interesting!
This part doesn't change, no matter how long we rent the vacuum for.
This is our flat fee!
It's what we pay just for the privilege of using the vacuum, even if we rent it for zero time!

So, to find the flat fee, we need to figure out what $f(x)$ would be if $x = 0$ , meaning zero rental time.
Let's plug that into our function: $f(0) = 6 \cdot 0 + 14$

Anything multiplied by zero is zero, so $6 \cdot 0 = 0$ .
Now we have: $f(0) = 0 + 14$

Adding zero to a number doesn't change the number, so $0 + 14 = 14$ .
This gives us: $f(0) = 14$

So, the flat fee is $\$14$ !

The flat fee is $\$14$ .