Question

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

1 + π
-2√2.2
-π
1 - π
-5π/4
2 - √2.2

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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 \(-2\sqrt{2.2}\)

\(\sqrt{2.2}\approx1.483\), then \(-2\sqrt{2.2}\approx-2\times1.483 = - 2.966\), 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 \(-\frac{5\pi}{4}\)

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

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

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

Answer:

\(-2\sqrt{2.2}\) (value \(\approx - 2.966\) between \(-3\) and \(-2\)), \(1 - \pi\) (value \(\approx - 2.14\) between \(-3\) and \(-2\))