an inequality is shown;-2\sqrt{2}<x<125

Question

which two values make it true

0.63
27/20
pi
-sqrt(10)
-pi/2

Answer 1

To determine which two values satisfy the inequality \(-2\sqrt{2} < x < 125\), we first need to evaluate the boundaries of the inequality.

1. Calculate \(-2\sqrt{2}\):
   • \(\sqrt{2} \approx 1.414\)
   • Therefore, \(-2\sqrt{2} \approx -2 \times 1.414 \approx -2.828\)

Now we have the inequality: \[ -2.828 < x < 125 \]

Now let's check the provided values against this inequality:

1. 0.63:

   • \(-2.828 < 0.63 < 125\) ⇒ True

2. 27/20 (which is 1.35):

   • \(-2.828 < 1.35 < 125\) ⇒ True

3. \(\pi\) (approximately 3.14):

   • \(-2.828 < 3.14 < 125\) ⇒ True

4. \(-\sqrt{10}\) (which is approximately -3.16):

   • \(-2.828 < -3.16 < 125\) ⇒ False (since -3.16 is less than -2.828)

5. \(-\pi/2\) (approximately -1.57):

   • \(-2.828 < -1.57 < 125\) ⇒ True

Thus, the values that satisfy the inequality are:

• 0.63
• 27/20
• \(\pi\)
• \(-\pi/2\)

However, we are looking for two values, so the pairs that work are:

• 0.63 and 27/20 (the smallest two values), or any combination with \(\pi\) or \(-\pi/2\).

Overall, possible selections of two values from the provided list that satisfy the inequality are:

• 0.63 and 27/20
• 0.63 and \(\pi\)
• 27/20 and \(\pi\)
• 0.63 and \(-\pi/2\)
• 27/20 and \(-\pi/2\)
• \(\pi\) and \(-\pi/2\)

However, if strictly selecting just two from the options:

• 0.63 and 27/20 would be good candidates.