Match the equations with the correct solution(s).(5 points)

Question

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.
x3=−64
x2=64
x2=25
x3=125
x2=−16
responces:
+5
+4
-5
+5 and -5
-4
+8
+8 and -8
no real solution
-8
infinite solutions

Answer 1

Let's solve each equation and match them with the correct responses:

1. Equation: \( x^3 = -64 \)
   Solution: \( x = -4 \)
   Response: -4

2. Equation: \( x^2 = 64 \)
   Solution: \( x = 8 \) and \( x = -8 \)
   Response: +8 and -8

3. Equation: \( x^2 = 25 \)
   Solution: \( x = 5 \) and \( x = -5 \)
   Response: +5 and -5

4. Equation: \( x^3 = 125 \)
   Solution: \( x = 5 \)
   Response: +5

5. Equation: \( x^2 = -16 \)
   Solution: No real solutions (as the square of a real number cannot be negative)
   Response: no real solution

Final matching would be:

• \( x^3 = -64 \) : -4
• \( x^2 = 64 \) : +8 and -8
• \( x^2 = 25 \) : +5 and -5
• \( x^3 = 125 \) : +5
• \( x^2 = -16 \) : no real solution