Question
Use drag and drop to place the two equations below that have the same solution.(1 point) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Response area has the same solution as Response area . x2+4=5x−10x2+4=5x−105x9=35x9=36x−10=506x−10=502(5x+4)=8x+282(5x+4)=8x+28
Answers
GPT-4o mini
To determine which two equations have the same solution, we can simplify or solve both pairs of equations.
1. **Equation 1:** \(x^2 + 4 = 5x - 10\)
- Rearranging gives us: \(x^2 - 5x + 14 = 0\)
2. **Equation 2:** \(5x^9 = 35\)
- Dividing both sides by 5 gives us: \(x^9 = 7\)
3. **Equation 3:** \(6x - 10 = 50\)
- Adding 10 to both sides gives us: \(6x = 60 \Rightarrow x = 10\)
4. **Equation 4:** \(2(5x + 4) = 8x + 28\)
- Distributing the left side gives us: \(10x + 8 = 8x + 28\)
- Rearranging gives us: \(2x = 20 \Rightarrow x = 10\)
From the calculations:
- **Equation 3** and **Equation 4** both simplify to \(x = 10\).
Thus, **the two equations that have the same solution** are:
- \(6x - 10 = 50\)
- \(2(5x + 4) = 8x + 28\)
You can arrange them in the response areas accordingly.
1. **Equation 1:** \(x^2 + 4 = 5x - 10\)
- Rearranging gives us: \(x^2 - 5x + 14 = 0\)
2. **Equation 2:** \(5x^9 = 35\)
- Dividing both sides by 5 gives us: \(x^9 = 7\)
3. **Equation 3:** \(6x - 10 = 50\)
- Adding 10 to both sides gives us: \(6x = 60 \Rightarrow x = 10\)
4. **Equation 4:** \(2(5x + 4) = 8x + 28\)
- Distributing the left side gives us: \(10x + 8 = 8x + 28\)
- Rearranging gives us: \(2x = 20 \Rightarrow x = 10\)
From the calculations:
- **Equation 3** and **Equation 4** both simplify to \(x = 10\).
Thus, **the two equations that have the same solution** are:
- \(6x - 10 = 50\)
- \(2(5x + 4) = 8x + 28\)
You can arrange them in the response areas accordingly.