Ask a New Question
Menu

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

1 answer

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!