business charges $22 per t-shirt that is custom made.

Question

Another business charges $16 per t-shirt plus a $15 set up fee for custom made t-shirts.

Answer 1

To compare the costs of the two businesses based on the number of t-shirts ordered, we can create a cost equation for each.

1. Business A charges $22 per t-shirt.

   • Cost for \( n \) t-shirts: \[ \text{Cost}_A = 22n \]

2. Business B charges $16 per t-shirt plus a $15 setup fee.

   • Cost for \( n \) t-shirts: \[ \text{Cost}_B = 16n + 15 \]

To find when the costs are equal:

Set the two costs equal to each other: \[ 22n = 16n + 15 \]

Solve for \( n \):

1. Subtract \( 16n \) from both sides: \[ 22n - 16n = 15 \] \[ 6n = 15 \]

2. Divide by 6: \[ n = \frac{15}{6} = 2.5 \]

Since you can't order half a t-shirt, we evaluate the costs for whole numbers.

Cost Comparison:

• For \( n = 2 \):

  • Cost for Business A: \[ 22 \times 2 = 44 \]
  • Cost for Business B: \[ 16 \times 2 + 15 = 32 + 15 = 47 \]

  Business A is cheaper.

• For \( n = 3 \):

  • Cost for Business A: \[ 22 \times 3 = 66 \]
  • Cost for Business B: \[ 16 \times 3 + 15 = 48 + 15 = 63 \]

  Business B is cheaper.

Summary:

• For 2 t-shirts, Business A ($44) is cheaper than Business B ($47).
• For 3 t-shirts, Business B ($63) is cheaper than Business A ($66).

Thus, if you order 2 t-shirts or fewer, Business A is more cost-effective. If you order 3 t-shirts or more, Business B becomes the better option.

Answer 2

How would you transform the first graph to make it become a non proportional graph with the same y-intercept as the second graph?

Answer 3

To transform the first graph (which represents a proportional relationship) into a non-proportional graph while maintaining the same y-intercept as the second graph, you can follow these steps:

Understanding the Graphs

1. First Graph: The equation for the first graph, based on the information you provided, is \( y = 22x \). This is a proportional relationship, meaning it goes through the origin (0,0), and has a y-intercept of 0.

2. Second Graph: The equation for the second graph is \( y = 16x + 15 \). This is a non-proportional relationship because it has a constant term (the y-intercept is 15).

Transformation Steps

1. Change the Equation: To create a non-proportional graph from the first equation, we can add a constant term to its original equation. For instance, you can modify the equation to include a y-intercept of 15 (the same as in the second graph).

   • Start with the equation of the first graph: \[ y = 22x \]
   • Then, add a constant \( k \): \[ y = 22x + k \]
   • To achieve the desired y-intercept of 15, set \( k = 15 \): \[ y = 22x + 15 \]

2. Resulting Equation: Now, the transformed equation is: \[ y = 22x + 15 \]

Final Graph Characteristics

• Non-Proportional: The transformed graph is non-proportional because it does not pass through the origin. It has a defined y-intercept at \( (0, 15) \), which corresponds to the value when \( x = 0 \).
• Same Y-Intercept: The new equation has the same y-intercept as the second graph, which is \( 15 \).

Summary

To transform the first graph into a non-proportional graph with the same y-intercept as the second graph, adjust the equation of the first graph by adding a constant term (in this case, \( 15 \)). The new graph would be represented by \( y = 22x + 15 \).

Answer 4

up 4

up 15

right 4

down 15

left 15

Answer 5

Let's break down the sequence of movements you provided:

1. Up 4: Move 4 units in the positive y-direction.
2. Up 15: Move an additional 15 units in the positive y-direction.
3. Right 4: Move 4 units in the positive x-direction.
4. Down 15: Move 15 units in the negative y-direction.
5. Left 15: Move 15 units in the negative x-direction.

Let's summarize and calculate the final position:

Assuming you start at the origin (0,0):

1. Starting Position: (0, 0)
2. After Up 4:
   • New Position: (0, 0 + 4) = (0, 4)
3. After Up 15:
   • New Position: (0, 4 + 15) = (0, 19)
4. After Right 4:
   • New Position: (0 + 4, 19) = (4, 19)
5. After Down 15:
   • New Position: (4, 19 - 15) = (4, 4)
6. After Left 15:
   • New Position: (4 - 15, 4) = (-11, 4)

Final Position:

After performing all the given movements, the final position is (-11, 4).

Answer 6

which one

Answer 7

It seems like your question might be incomplete or lacking context. If you're referring to a choice between two options, the movements, or something specific that's not mentioned, please provide a bit more detail so that I can assist you better.

If you're asking to confirm which position is the final one after the movements you listed, the final position after executing the movements "up 4, up 15, right 4, down 15, left 15" starting from (0, 0) is:

Final Position: (-11, 4)

If you meant something else, please clarify!

Answer 8

up 4
up 15

right 4

down 15

left 15 which one is correct

Answer 9

To determine which of the movements you provided is "correct," we need to follow the sequence accurately and see how they affect the position. Assuming we're starting from the origin point (0, 0), let's go through the movements once more step by step:

1. Start at (0, 0).

2. Up 4: This means moving 4 units in the positive y-direction.

   • New Position: \( (0, 0 + 4) = (0, 4) \)

3. Up 15: Move an additional 15 units in the positive y-direction.

   • New Position: \( (0, 4 + 15) = (0, 19) \)

4. Right 4: Move 4 units in the positive x-direction.

   • New Position: \( (0 + 4, 19) = (4, 19) \)

5. Down 15: Move 15 units in the negative y-direction.

   • New Position: \( (4, 19 - 15) = (4, 4) \)

6. Left 15: Move 15 units in the negative x-direction.

   • New Position: \( (4 - 15, 4) = (-11, 4) \)

Summary of the Movements:

• Final position after executing all moves from (0, 0): (-11, 4).

Conclusion

If you meant to ask which of the movements themselves (up, down, left, right) was "correct" in terms of being accurately executed, all movements were executed as they were described. The final position after all the movements, however, is (-11, 4).

If you have a specific question about the moves or if there's a specific option you're asking about (for example, selecting the correct movement based on context), please provide more information!