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=25
x2=64
x2=−16
x3=125
Responses:
+4
No real solution
+8 and -8
-5
-8
+5
+8
+5 and -5
Infinite solutions
+4 and -4
-4

Answer 1

To match the equations with their solutions, we can solve each equation step-by-step:

1. \(x^3 = -64\)

   • The cube root of -64 is -4.
   • Solution: -4

2. \(x^2 = 25\)

   • The square roots of 25 are +5 and -5.
   • Solution: +5 and -5

3. \(x^2 = 64\)

   • The square roots of 64 are +8 and -8.
   • Solution: +8 and -8

4. \(x^2 = -16\)

   • There are no real solutions since the square of a real number cannot be negative.
   • Solution: No real solution

5. \(x^3 = 125\)

   • The cube root of 125 is +5.
   • Solution: +5

Now, we can summarize the matches:

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

Arranging these solutions according to the equations, we get:

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

You can now place these answers in the correct inputs for your question.