Question
The function f(x) = 5x + 12 models
the amount of money, in dollars, Alex makes when mowing lawns for x hours. How much will Alex make for 3 hours of mowing?
5. The function d(x) = 0.4x + 2 models
the depth of water, in feet, in a storage tank after x hours.
After 1 hour, the depth is
0.4
1.4
feet.
2.4
3.4
After 6.5 hours, the depth is
2.6
4.6
feet.
6.9
8.9
6. Consider the function
d(x) = -2x2 + 4.
Determine whether each statement is true or false.
la
2. The function f(x) = -3.5x + 45 for
0 < x ≤ 12.5 models the length of a rectangle in terms of its width, x.
Find the length of the rectangle when its width is 9.5 units.
units
the amount of money, in dollars, Alex makes when mowing lawns for x hours. How much will Alex make for 3 hours of mowing?
5. The function d(x) = 0.4x + 2 models
the depth of water, in feet, in a storage tank after x hours.
After 1 hour, the depth is
0.4
1.4
feet.
2.4
3.4
After 6.5 hours, the depth is
2.6
4.6
feet.
6.9
8.9
6. Consider the function
d(x) = -2x2 + 4.
Determine whether each statement is true or false.
la
2. The function f(x) = -3.5x + 45 for
0 < x ≤ 12.5 models the length of a rectangle in terms of its width, x.
Find the length of the rectangle when its width is 9.5 units.
units
Answers
GPT-4o mini
Let's break this down step by step:
1. **Calculating Alex's Earnings for 3 Hours of Mowing:**
The function is given as \( f(x) = 5x + 12 \), where \( x \) is the number of hours. To find out how much Alex makes for 3 hours of mowing, we substitute \( x = 3 \) into the function:
\[
f(3) = 5(3) + 12 = 15 + 12 = 27
\]
So, Alex will make **$27** for 3 hours of mowing.
2. **Depth of Water in Storage Tank After 1 Hour:**
The function is \( d(x) = 0.4x + 2 \). To find the depth after 1 hour, substitute \( x = 1 \):
\[
d(1) = 0.4(1) + 2 = 0.4 + 2 = 2.4
\]
Therefore, the depth of water after 1 hour is **2.4 feet**.
3. **Depth of Water in Storage Tank After 6.5 Hours:**
Again using the function \( d(x) = 0.4x + 2 \) and substituting \( x = 6.5 \):
\[
d(6.5) = 0.4(6.5) + 2 = 2.6 + 2 = 4.6
\]
So, the depth of water after 6.5 hours is **4.6 feet**.
4. **Evaluating the Statement for d(x) = -2x² + 4:**
You mentioned determining if a statement regarding \( d(x) = -2x^2 + 4 \) is true or false, but did not provide the statements to evaluate. If you provide the statements, I can help determine their truth values.
5. **Finding the Length of the Rectangle When Width is 9.5 Units:**
The function given is \( f(x) = -3.5x + 45 \). To find the length when the width \( x = 9.5 \):
\[
f(9.5) = -3.5(9.5) + 45 = -33.25 + 45 = 11.75
\]
Thus, the length of the rectangle when its width is 9.5 units is **11.75 units**.
Feel free to ask further questions or clarify if you need more help!
1. **Calculating Alex's Earnings for 3 Hours of Mowing:**
The function is given as \( f(x) = 5x + 12 \), where \( x \) is the number of hours. To find out how much Alex makes for 3 hours of mowing, we substitute \( x = 3 \) into the function:
\[
f(3) = 5(3) + 12 = 15 + 12 = 27
\]
So, Alex will make **$27** for 3 hours of mowing.
2. **Depth of Water in Storage Tank After 1 Hour:**
The function is \( d(x) = 0.4x + 2 \). To find the depth after 1 hour, substitute \( x = 1 \):
\[
d(1) = 0.4(1) + 2 = 0.4 + 2 = 2.4
\]
Therefore, the depth of water after 1 hour is **2.4 feet**.
3. **Depth of Water in Storage Tank After 6.5 Hours:**
Again using the function \( d(x) = 0.4x + 2 \) and substituting \( x = 6.5 \):
\[
d(6.5) = 0.4(6.5) + 2 = 2.6 + 2 = 4.6
\]
So, the depth of water after 6.5 hours is **4.6 feet**.
4. **Evaluating the Statement for d(x) = -2x² + 4:**
You mentioned determining if a statement regarding \( d(x) = -2x^2 + 4 \) is true or false, but did not provide the statements to evaluate. If you provide the statements, I can help determine their truth values.
5. **Finding the Length of the Rectangle When Width is 9.5 Units:**
The function given is \( f(x) = -3.5x + 45 \). To find the length when the width \( x = 9.5 \):
\[
f(9.5) = -3.5(9.5) + 45 = -33.25 + 45 = 11.75
\]
Thus, the length of the rectangle when its width is 9.5 units is **11.75 units**.
Feel free to ask further questions or clarify if you need more help!