3 functions f and a are defined by these equations:
$f(x) = 80 - 15x$ $a(x) = 25 + 10x$
which function has a greater value when x is 2.5?

4 an equilateral triangle has three sides of equal length. function p gives the perimeter of an equilateral triangle of side length s.
a. find $p(2)$
b. find $p(10)$
c. find $p(s)$

5 from unit 5, lesson 1
imagine a situation in which a person is using a garden hose to fill a child’s pool. think of two quantities that are related in this situation and that can be seen as a function.
a. define the function using a statement of the form “______ is a function of ______.” be sure to consider the units of measurement.
b. sketch a possible graph of the function. be sure to label the axes.
then, identify the coordinates of one point on the graph, and explain its meaning.

Question

3 functions f and a are defined by these equations:
$f(x) = 80 - 15x$  $a(x) = 25 + 10x$
which function has a greater value when x is 2.5?

4 an equilateral triangle has three sides of equal length. function p gives the perimeter of an equilateral triangle of side length s.
 a. find $p(2)$
 b. find $p(10)$
 c. find $p(s)$

5 from unit 5, lesson 1
imagine a situation in which a person is using a garden hose to fill a child’s pool. think of two quantities that are related in this situation and that can be seen as a function.
 a. define the function using a statement of the form “______ is a function of ______.” be sure to consider the units of measurement.
 b. sketch a possible graph of the function. be sure to label the axes.
then, identify the coordinates of one point on the graph, and explain its meaning.

Accepted Answer

### Problem 3
# Explanation:
## Step1: Calculate $ f(2.5) $
Substitute $ x = 2.5 $ into $ f(x)=80 - 15x $.
$ f(2.5)=80-15\times2.5 $
$ =80 - 37.5 $
$ = 42.5 $

## Step2: Calculate $ A(2.5) $
Substitute $ x = 2.5 $ into $ A(x)=25 + 10x $.
$ A(2.5)=25+10\times2.5 $
$ =25 + 25 $
$ = 50 $

## Step3: Compare the two values
Since $ 42.5<50 $, $ A(x) $ has a greater value.

# Answer: $ A(x) $

### Problem 4
#### Part a
# Explanation:
## Step1: Recall the perimeter formula for equilateral triangle
The perimeter $ P $ of an equilateral triangle with side length $ s $ is $ P(s)=3s $ (because all three sides are equal, so perimeter = 3×side length).

## Step2: Substitute $ s = 2 $ into $ P(s) $
$ P(2)=3\times2=6 $

# Answer: 6

#### Part b
# Explanation:
## Step1: Use the perimeter formula $ P(s)=3s $
## Step2: Substitute $ s = 10 $ into $ P(s) $
$ P(10)=3\times10 = 30 $

# Answer: 30

#### Part c
# Explanation:
## Step1: Define the perimeter function for equilateral triangle
For an equilateral triangle, perimeter $ P $ is three times the side length $ s $. So $ P(s)=3s $.

# Answer: $ P(s) = 3s $

### Problem 5
#### Part a
# Brief Explanations:
One possible pair of quantities: The volume of water in the pool (in liters) is a function of time (in minutes). As time passes, the volume of water increases because the hose is filling the pool. The function can be stated as "Volume of water (in liters) is a function of time (in minutes)". Another example: The height of water in the pool (in centimeters) is a function of time (in minutes), since as time increases, the height of water rises as the pool is being filled.

# Answer: For example, "Volume of water (in liters) is a function of time (in minutes)" (or other valid pairs like height of water and time, etc.)

#### Part b
# Brief Explanations:
- **Axes Labeling**: The x - axis should be labeled as "Time (minutes)" and the y - axis as "Volume of Water (liters)" (or the other quantity you chose, e.g., "Height of Water (cm)").
- **Graph Shape**: Since the hose is filling the pool at a (presumably) constant rate, the graph will be a straight line with a positive slope. It starts at the origin (0,0) because at time 0, the pool has no water (assuming it was empty initially).
- **Point Explanation**: For example, if we take the point (5, 10) (assuming the hose fills the pool at a rate of 2 liters per minute), this means that after 5 minutes, the volume of water in the pool is 10 liters.

# Answer:
- **Axes**: x - axis: Time (minutes), y - axis: Volume of Water (liters) (or relevant quantity).
- **Graph**: A straight line starting at (0,0) with a positive slope.
- **Point Example**: (5, 10) means after 5 minutes, the volume of water is 10 liters (explanation depends on the rate assumed).

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QUESTION IMAGE

Question

Explanation:

Problem 3

Step1: Calculate \( f(2.5) \)

Step2: Calculate \( A(2.5) \)

Step3: Compare the two values

Step1: Recall the perimeter formula for equilateral triangle

Step2: Substitute \( s = 2 \) into \( P(s) \)

Step1: Use the perimeter formula \( P(s)=3s \)

Step2: Substitute \( s = 10 \) into \( P(s) \)

Answer:

Problem 4

Part a