Math / Algebra

QuestionProblem 3 The functions $f(x)$ and $g(x)$ are defined by these equations. - $f(x)=-15 x+80$ - $g(x)=10 x+25$
Which is greater: $f(2)$ or $g(2)$ ? f(2) $g(2)$

Studdy Solution

STEP 1

What is this asking? We're comparing the values of two functions, $f(x)$ and $g(x)$ , when $x = 2$ .
Which one is bigger? Watch out! Don't mix up the functions!
Make sure you plug $x = 2$ into the correct formula each time.

STEP 2

1. Calculate $f(2)$
2. Calculate $g(2)$
3. Compare the results

STEP 3

We're given the function $f(x) = -15x + 80$ .
We want to find $f(2)$ , so we'll substitute $x = 2$ into the equation.
It's like putting a 2 in the $x$ -shaped slot!

STEP 4

$f(2) = -15 \cdot 2 + 80$ Remember, we're multiplying $-15$ by 2 first!

STEP 5

$f(2) = -30 + 80$ Great! Now, we just add $-30$ and $80$ .

STEP 6

$f(2) = 50$ So, $f(2) = 50$ !

STEP 7

Now, let's do the same thing for $g(x)$ .
We know $g(x) = 10x + 25$ , and we want to find $g(2)$ .
Let's plug in $x = 2$ !

STEP 8

$g(2) = 10 \cdot 2 + 25$ Multiply $10$ by 2!

STEP 9

$g(2) = 20 + 25$ Almost there!
Add $20$ and $25$ .

STEP 10

$g(2) = 45$ Awesome! We found that $g(2) = 45$ .

STEP 11

We found that $f(2) = 50$ and $g(2) = 45$ .
Now, we just need to see which one is bigger.

STEP 12

Since $50$ is greater than $45$ , we know that $f(2)$ is greater than $g(2)$ !

STEP 13

$f(2)$ is greater than $g(2)$ .

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QuestionProblem 3 The functions $f(x)$ and $g(x)$ are defined by these equations. - $f(x)=-15 x+80$ - $g(x)=10 x+25$
Which is greater: $f(2)$ or $g(2)$ ? f(2) $g(2)$

Studdy Solution

STEP 1

What is this asking? We're comparing the values of two functions, $f(x)$ and $g(x)$ , when $x = 2$ .
Which one is bigger? Watch out! Don't mix up the functions!
Make sure you plug $x = 2$ into the correct formula each time.

STEP 2

1. Calculate $f(2)$
2. Calculate $g(2)$
3. Compare the results

STEP 3

We're given the function $f(x) = -15x + 80$ .
We want to find $f(2)$ , so we'll substitute $x = 2$ into the equation.
It's like putting a 2 in the $x$ -shaped slot!

STEP 4

$f(2) = -15 \cdot 2 + 80$ Remember, we're multiplying $-15$ by 2 first!

STEP 5

$f(2) = -30 + 80$ Great! Now, we just add $-30$ and $80$ .

STEP 6

$f(2) = 50$ So, $f(2) = 50$ !

STEP 7

Now, let's do the same thing for $g(x)$ .
We know $g(x) = 10x + 25$ , and we want to find $g(2)$ .
Let's plug in $x = 2$ !

STEP 8

$g(2) = 10 \cdot 2 + 25$ Multiply $10$ by 2!

STEP 9

$g(2) = 20 + 25$ Almost there!
Add $20$ and $25$ .

STEP 10

$g(2) = 45$ Awesome! We found that $g(2) = 45$ .

STEP 11

We found that $f(2) = 50$ and $g(2) = 45$ .
Now, we just need to see which one is bigger.

STEP 12

Since $50$ is greater than $45$ , we know that $f(2)$ is greater than $g(2)$ !

STEP 13

$f(2)$ is greater than $g(2)$ .

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QuestionProblem 3 The functions f(x)f(x)f(x) and g(x)g(x)g(x) are defined by these equations. - f(x)=−15x+80f(x)=-15 x+80f(x)=−15x+80 - g(x)=10x+25g(x)=10 x+25g(x)=10x+25Which is greater: f(2)f(2)f(2) or g(2)g(2)g(2) ? f(2) g(2)g(2)g(2)

Studdy Solution

STEP 1

What is this asking? We're comparing the values of two functions, f(x)f(x)f(x) and g(x)g(x)g(x), when x=2x = 2x=2.Which one is bigger? Watch out! Don't mix up the functions!Make sure you plug x=2x = 2x=2 into the correct formula each time.

STEP 2

1. Calculate f(2)f(2)f(2)2. Calculate g(2)g(2)g(2)3. Compare the results

STEP 3

We're given the function f(x)=−15x+80f(x) = -15x + 80f(x)=−15x+80.We want to find f(2)f(2)f(2), so we'll **substitute** x=2x = 2x=2 into the equation.It's like putting a **2** in the xxx-shaped slot!

STEP 4

f(2)=−15⋅2+80f(2) = -15 \cdot 2 + 80f(2)=−15⋅2+80 Remember, we're multiplying −15-15−15 by **2** first!

STEP 5

f(2)=−30+80f(2) = -30 + 80f(2)=−30+80 Great! Now, we just add −30-30−30 and 808080.

STEP 6

f(2)=50f(2) = 50f(2)=50 So, f(2)=50f(2) = 50f(2)=50!

STEP 7

Now, let's do the same thing for g(x)g(x)g(x).We know g(x)=10x+25g(x) = 10x + 25g(x)=10x+25, and we want to find g(2)g(2)g(2).Let's **plug in** x=2x = 2x=2!

STEP 8

g(2)=10⋅2+25g(2) = 10 \cdot 2 + 25g(2)=10⋅2+25 Multiply 101010 by **2**!

STEP 9

g(2)=20+25g(2) = 20 + 25g(2)=20+25 Almost there!Add 202020 and 252525.

STEP 10

g(2)=45g(2) = 45g(2)=45 Awesome! We found that g(2)=45g(2) = 45g(2)=45.

STEP 11

We found that f(2)=50f(2) = 50f(2)=50 and g(2)=45g(2) = 45g(2)=45.Now, we just need to see which one is bigger.

STEP 12

Since 505050 is greater than 454545, we know that f(2)f(2)f(2) is greater than g(2)g(2)g(2)!

STEP 13

f(2)f(2)f(2) is greater than g(2)g(2)g(2).

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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.

QuestionProblem 3 The functions $f(x)$ and $g(x)$ are defined by these equations. - $f(x)=-15 x+80$ - $g(x)=10 x+25$
Which is greater: $f(2)$ or $g(2)$ ? f(2) $g(2)$

What is this asking? We're comparing the values of two functions, $f(x)$ and $g(x)$ , when $x = 2$ .
Which one is bigger? Watch out! Don't mix up the functions!
Make sure you plug $x = 2$ into the correct formula each time.

1. Calculate $f(2)$
2. Calculate $g(2)$
3. Compare the results

We're given the function $f(x) = -15x + 80$ .
We want to find $f(2)$ , so we'll substitute $x = 2$ into the equation.
It's like putting a 2 in the $x$ -shaped slot!

$f(2) = -15 \cdot 2 + 80$ Remember, we're multiplying $-15$ by 2 first!

$f(2) = -30 + 80$ Great! Now, we just add $-30$ and $80$ .

$f(2) = 50$ So, $f(2) = 50$ !

Now, let's do the same thing for $g(x)$ .
We know $g(x) = 10x + 25$ , and we want to find $g(2)$ .
Let's plug in $x = 2$ !

$g(2) = 10 \cdot 2 + 25$ Multiply $10$ by 2!

$g(2) = 20 + 25$ Almost there!
Add $20$ and $25$ .

$g(2) = 45$ Awesome! We found that $g(2) = 45$ .

We found that $f(2) = 50$ and $g(2) = 45$ .
Now, we just need to see which one is bigger.

Since $50$ is greater than $45$ , we know that $f(2)$ is greater than $g(2)$ !

$f(2)$ is greater than $g(2)$ .