Math / Algebra

Question7 AM Sat Dec 14 < <> S Savvas EasyBridge AA MATHEMATICS, GR 8 (FULL)-1(A)-24-25 3.4 MathXL (5 problems) savvasrealize.com S Savvas Realize DUE Savvas Realize Nov 18-11:59 pm Late A car moving at a constant speed passed a timing device at t=0. After 7 seconds, the car has traveled 588 ft. Write a linear function rule to model the distance in feet d the car has traveled any number of seconds t after passing the timing device. The linear function rule is d = ☐ -

Studdy Solution

STEP 1

What is this asking? We need to find an equation that tells us how far a car travels given how long it's been driving, knowing it goes 588 ft in 7 seconds. Watch out! Make sure to use the correct units (feet and seconds) and remember that the car starts at the timing device at $t = 0$ .

STEP 2

1. Find the speed.
2. Write the equation.

STEP 3

Alright, so the car is moving at a constant speed, which is super important!
This means we can use the good ol' formula: $\text{speed} = \frac{\text{distance}}{\text{time}}$ .

STEP 4

We know the car traveled 588 ft in 7 seconds.
So, plugging those numbers in, we get: $\text{speed} = \frac{588 \text{ ft}}{7 \text{ s}}$

STEP 5

Let's crunch those numbers! $\text{speed} = 84 \frac{\text{ft}}{\text{s}}$ So, the car's speed is 84 feet per second!

STEP 6

Now, we need to write a linear equation.
A linear equation looks like this: $y = mx + b$ , where $m$ is the rate of change (or slope) and $b$ is the initial value (or y-intercept).

STEP 7

In our case, the distance $d$ depends on the time $t$ .
So, our equation will look like $d = mt + b$ .

STEP 8

We already figured out the rate of change – it's the car's speed, which is $\mathbf{84 \frac{ft}{s}}$ .
So, $m = 84$ .

STEP 9

The initial value is the distance the car has traveled at $t = 0$ .
Since the car passed the timing device at $t = 0$ , the initial distance is 0 ft.
So, $b = 0$ .

STEP 10

Putting it all together, our equation is: $d = 84t + 0$ Or simply: $d = 84t$

STEP 11

The linear function rule is $d = 84t$ .

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Studdy Solution

STEP 1

What is this asking? We need to find an equation that tells us how far a car travels given how long it's been driving, knowing it goes 588 ft in 7 seconds. Watch out! Make sure to use the correct units (feet and seconds) and remember that the car starts at the timing device at $t = 0$ .

STEP 2

1. Find the speed.
2. Write the equation.

STEP 3

Alright, so the car is moving at a constant speed, which is super important!
This means we can use the good ol' formula: $\text{speed} = \frac{\text{distance}}{\text{time}}$ .

STEP 4

We know the car traveled 588 ft in 7 seconds.
So, plugging those numbers in, we get: $\text{speed} = \frac{588 \text{ ft}}{7 \text{ s}}$

STEP 5

Let's crunch those numbers! $\text{speed} = 84 \frac{\text{ft}}{\text{s}}$ So, the car's speed is 84 feet per second!

STEP 6

Now, we need to write a linear equation.
A linear equation looks like this: $y = mx + b$ , where $m$ is the rate of change (or slope) and $b$ is the initial value (or y-intercept).

STEP 7

In our case, the distance $d$ depends on the time $t$ .
So, our equation will look like $d = mt + b$ .

STEP 8

We already figured out the rate of change – it's the car's speed, which is $\mathbf{84 \frac{ft}{s}}$ .
So, $m = 84$ .

STEP 9

The initial value is the distance the car has traveled at $t = 0$ .
Since the car passed the timing device at $t = 0$ , the initial distance is 0 ft.
So, $b = 0$ .

STEP 10

Putting it all together, our equation is: $d = 84t + 0$ Or simply: $d = 84t$

STEP 11

The linear function rule is $d = 84t$ .

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Studdy Solution

STEP 1

What is this asking? We need to find an equation that tells us how far a car travels given how long it's been driving, knowing it goes 588 ft in 7 seconds. Watch out! Make sure to use the correct units (feet and seconds) and remember that the car starts at the timing device at t=0t = 0t=0.

STEP 2

1. Find the speed.2. Write the equation.

STEP 3

Alright, so the car is moving at a **constant speed**, which is super important!This means we can use the good ol' formula: speed=distancetime\text{speed} = \frac{\text{distance}}{\text{time}}speed=timedistance​.

STEP 4

We know the car traveled **588 ft** in **7 seconds**.So, plugging those numbers in, we get: speed=588 ft7 s \text{speed} = \frac{588 \text{ ft}}{7 \text{ s}} speed=7 s588 ft​

STEP 5

Let's crunch those numbers! speed=84fts \text{speed} = 84 \frac{\text{ft}}{\text{s}} speed=84sft​ So, the car's speed is **84 feet per second**!

STEP 6

Now, we need to write a linear equation.A linear equation looks like this: y=mx+by = mx + by=mx+b, where mmm is the **rate of change** (or slope) and bbb is the **initial value** (or y-intercept).

STEP 7

In our case, the distance ddd depends on the time ttt.So, our equation will look like d=mt+bd = mt + bd=mt+b.

STEP 8

We already figured out the **rate of change** – it's the car's speed, which is 84fts\mathbf{84 \frac{ft}{s}}84sft​.So, m=84m = 84m=84.

STEP 9

The **initial value** is the distance the car has traveled at t=0t = 0t=0.Since the car passed the timing device at t=0t = 0t=0, the initial distance is **0 ft**.So, b=0b = 0b=0.

STEP 10

Putting it all together, our equation is: d=84t+0 d = 84t + 0 d=84t+0 Or simply: d=84t d = 84t d=84t

STEP 11

The linear function rule is d=84td = 84td=84t.

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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.

What is this asking? We need to find an equation that tells us how far a car travels given how long it's been driving, knowing it goes 588 ft in 7 seconds. Watch out! Make sure to use the correct units (feet and seconds) and remember that the car starts at the timing device at $t = 0$ .

1. Find the speed.
2. Write the equation.

Alright, so the car is moving at a constant speed, which is super important!
This means we can use the good ol' formula: $\text{speed} = \frac{\text{distance}}{\text{time}}$ .

We know the car traveled 588 ft in 7 seconds.
So, plugging those numbers in, we get: $\text{speed} = \frac{588 \text{ ft}}{7 \text{ s}}$

Let's crunch those numbers! $\text{speed} = 84 \frac{\text{ft}}{\text{s}}$ So, the car's speed is 84 feet per second!

Now, we need to write a linear equation.
A linear equation looks like this: $y = mx + b$ , where $m$ is the rate of change (or slope) and $b$ is the initial value (or y-intercept).

In our case, the distance $d$ depends on the time $t$ .
So, our equation will look like $d = mt + b$ .

We already figured out the rate of change – it's the car's speed, which is $\mathbf{84 \frac{ft}{s}}$ .
So, $m = 84$ .

The initial value is the distance the car has traveled at $t = 0$ .
Since the car passed the timing device at $t = 0$ , the initial distance is 0 ft.
So, $b = 0$ .

Putting it all together, our equation is: $d = 84t + 0$ Or simply: $d = 84t$

The linear function rule is $d = 84t$ .