Question

select the two correct answers.
which expressions have a value between −3 and −2?

1 + π
−2√2.2
−π
1 − π
−\\(\frac{5\pi}{4}\\)
2 − √2.2

reset next

Explanation:

Step1: Analyze \(1 + \pi\)

\(\pi\approx3.14\), so \(1+\pi\approx1 + 3.14 = 4.14\), which is not between \(-3\) and \(-2\).

Step2: Analyze \(-2\sqrt{2.2}\)

\(\sqrt{2.2}\approx1.483\), so \(-2\sqrt{2.2}\approx - 2\times1.483=-2.966\), which is between \(-3\) and \(-2\).

Step3: Analyze \(-\pi\)

\(\pi\approx3.14\), so \(-\pi\approx - 3.14\), which is less than \(-3\), not between \(-3\) and \(-2\).

Step4: Analyze \(1-\pi\)

\(\pi\approx3.14\), so \(1 - \pi\approx1-3.14=-2.14\), which is between \(-3\) and \(-2\).

Step5: Analyze \(-\frac{5\pi}{4}\)

\(\pi\approx3.14\), so \(-\frac{5\pi}{4}\approx-\frac{5\times3.14}{4}\approx - 3.925\), which is less than \(-3\), not between \(-3\) and \(-2\).

Step6: Analyze \(2-\sqrt{2.2}\)

\(\sqrt{2.2}\approx1.483\), so \(2-\sqrt{2.2}\approx2 - 1.483 = 0.517\), which is positive, not between \(-3\) and \(-2\).

Answer:

\(-2\sqrt{2.2}\), \(1 - \pi\) (i.e., the options with \(-2\sqrt{2.2}\) and \(1 - \pi\))