1. The cost in dollars of an "n" mile trip with the Supreme Taxi Service is given by 1.5 + 1.75n. The cost of an "n" mile trip using Twon Taxi Service is given by 1.9 + 1.6n. For rides between 1 and 10 miles, which service would you choose? Explain.

2. Peach = 35 calories
Banana = 105 calories
Bacon Slice = 37 calories
Bread Slice = 65 calories
Egg = 75 calories

Use this information to write an expression for the number of calories in each situation.

a) "p" peaches and" n" bananas
b) two slices of bread, "b" slicers of bacon, and one egg

3. A hot air balloon is at a height of 2,250 feet. It descends 150 feet each minute. Find it's height after six, eight, and ten minutes. Make a table to show the pattern of heights. Write an expression for the balloon's height at "m" minutes.

1. To compare the costs for rides between 1 and 10 miles using the Supreme Taxi Service and the Twon Taxi Service, we can substitute the values of n from 1 to 10 into the cost functions and compare the results.

For Supreme Taxi Service:
Cost = 1.5 + 1.75n

For Twon Taxi Service:
Cost = 1.9 + 1.6n

Let's calculate the costs for rides of different distances:

For 1 mile ride:
Supreme Taxi Service: Cost = 1.5 + 1.75(1) = 3.25 dollars
Twon Taxi Service: Cost = 1.9 + 1.6(1) = 3.5 dollars

For 2 mile ride:
Supreme Taxi Service: Cost = 1.5 + 1.75(2) = 4.25 dollars
Twon Taxi Service: Cost = 1.9 + 1.6(2) = 4.1 dollars

For 3 mile ride:
Supreme Taxi Service: Cost = 1.5 + 1.75(3) = 5 dollars
Twon Taxi Service: Cost = 1.9 + 1.6(3) = 4.7 dollars

Continue this calculation up to 10 miles, and then compare the costs for each distance.

By comparing the costs for each distance, we can determine which service would be more affordable for rides between 1 and 10 miles.

2. Expression for the number of calories in each situation:

a) "p" peaches and "n" bananas:
Total calories = (35 * p) + (105 * n)

b) Two slices of bread, "b" slices of bacon, and one egg:
Total calories = (65 * 2) + (37 * b) + 75

3. The initial height of the hot air balloon is 2,250 feet.
The height decreases by 150 feet each minute.

After 6 minutes:
Height = 2,250 - (150 * 6) = 2,250 - 900 = 1,350 feet

After 8 minutes:
Height = 2,250 - (150 * 8) = 2,250 - 1,200 = 1,050 feet

After 10 minutes:
Height = 2,250 - (150 * 10) = 2,250 - 1,500 = 750 feet

The pattern of heights can be represented in a table:

| Minutes | Height (feet) |
|---------|--------------|
| 0 | 2,250 |
| 1 | 2,100 |
| 2 | 1,950 |
| 3 | 1,800 |
| 4 | 1,650 |
| 5 | 1,500 |
| 6 | 1,350 |
| 7 | 1,200 |
| 8 | 1,050 |
| 9 | 900 |
| 10 | 750 |

Expression for the balloon's height at "m" minutes:
Height = 2,250 - (150 * m)

1. To compare the cost of the two taxi services for rides between 1 and 10 miles, we can simply substitute the values of n into the given expressions and compare the results.

For the Supreme Taxi Service, the cost of an "n" mile trip is given by 1.5 + 1.75n.
For example, for a 1-mile trip:
Cost = 1.5 + 1.75(1) = 1.5 + 1.75 = 3.25 dollars.
Similarly, for a 2-mile trip:
Cost = 1.5 + 1.75(2) = 1.5 + 3.5 = 5 dollars.

For the Twon Taxi Service, the cost of an "n" mile trip is given by 1.9 + 1.6n.
For a 1-mile trip:
Cost = 1.9 + 1.6(1) = 1.9 + 1.6 = 3.5 dollars.
For a 2-mile trip:
Cost = 1.9 + 1.6(2) = 1.9 + 3.2 = 5.1 dollars.

By comparing the costs for trips between 1 and 10 miles using the given expressions, we can see that for all distances within this range, the Supreme Taxi Service is cheaper. Therefore, for rides between 1 and 10 miles, we should choose the Supreme Taxi Service.

2. To calculate the number of calories in different situations, we can multiply the number of each item by its respective calorie value.

a) The number of calories in "p" peaches and "n" bananas is given by:
Calories = (Number of peaches × Calories per peach) + (Number of bananas × Calories per banana)
Calories = p × 35 + n × 105

b) The number of calories in two slices of bread, "b" slices of bacon, and one egg is given by:
Calories = (2 × Calories per bread slice) + (b × Calories per bacon slice) + (1 × Calories per egg)
Calories = 2 × 65 + b × 37 + 1 × 75
Calories = 130 + 37b + 75

3. To find the balloon's height after six, eight, and ten minutes, we can subtract the descent distance per minute from the initial height each time.

Let's analyze the pattern:
- After 1 minute: Initial height - Descent per minute (2250 - 150)
- After 2 minutes: (2250 - 150) - (150 × 2)
- After 3 minutes: (2250 - 150) - (150 × 3)
- ...
- After m minutes: Initial height - (150 × m)

Using this pattern, we can write the expression for the balloon's height at "m" minutes as:
Height = Initial height - (150 × m)

Here is a table showing the pattern of heights after 6, 8, and 10 minutes:
| Time (in minutes) | Height (in feet) |
|-------------------|-----------------|
| 6 | 1350 |
| 8 | 1050 |
| 10 | 750 |

By substituting the values of "m" into the expression for the balloon's height, we can calculate the height at any given time.