Question

1. select all of the expressions equivalent to $(-\frac{1}{3})^{2}+\sqrt{2^{2}+9}$. $\frac{1}{9}$ $\frac{11}{9}$ $-\frac{1}{9}+\sqrt{25}$ $\frac{1}{9}+\sqrt{25}$ $-\frac{1}{9}+5$ $\frac{1}{9}+5$ 17. match the equivalent expressions. 18. which list orders the numbers from least to greatest? a $\sqrt{19}, 4.3,3.\overline{6}, \sqrt{13}, \pi$ b $\pi, 3.\overline{6}, 4.3, \sqrt{13}, \sqrt{19}$ c $\sqrt{19}, 3.\overline{6}, 4.3, \sqrt{13}, \pi$ d $\pi, \sqrt{13}, 3.\overline{6}, 4.3, \sqrt{19}$ 19. the mass of a human cell is 0.0000000000001 kilograms. what is the mass of a human cell in scientific notation, in kilograms? $\square \times 10^{\square}$ 20. what is the common monomial factor of the expression $16 m^{2} n^{2}-12 m n^{3}$? a $4 m^{2} n$ b $4 m n^{2}$ c $8 m^{2} n$ d $8 m n^{2}$

Explanation:

Problem 16

Step1: Simplify \((-\frac{1}{3})^{2}+\sqrt{x^{2}+9}\) (assuming \(x = 0\) for simplicity, since no value of \(x\) is given, and we just check the structure)

\((-\frac{1}{3})^{2}+\sqrt{0 + 9}=\frac{1}{9}+3=\frac{1 + 27}{9}=\frac{28}{9}\)

Step2: Check \(\frac{28}{9}\)

\(\frac{28}{9}\) is one of the options.

Step3: Check \(-\frac{1}{9}+\sqrt{25}\)

\(-\frac{1}{9}+5=\frac{- 1+45}{9}=\frac{44}{9}
eq\frac{28}{9}\)

Step4: Check \(\frac{1}{9}+\sqrt{25}\)

\(\frac{1}{9}+5=\frac{1 + 45}{9}=\frac{46}{9}
eq\frac{28}{9}\)

Step5: Check \(-\frac{1}{9}+5\)

\(-\frac{1}{9}+5=\frac{-1 + 45}{9}=\frac{44}{9}
eq\frac{28}{9}\)

Step6: Check \(\frac{1}{9}+5\)

\(\frac{1}{9}+5=\frac{1+45}{9}=\frac{46}{9}
eq\frac{28}{9}\)

Step1: Approximate the values

\(\sqrt{13}\approx3.61\), \(\sqrt{19}\approx4.36\), \(\pi\approx3.14\), \(3.\overline{6}\approx3.67\), \(4.3 = 4.3\)

Step2: Compare the values

\(\pi\approx3.14<\sqrt{13}\approx3.61<3.\overline{6}\approx3.67<4.3<\sqrt{19}\approx4.36\)

Step1: Write in scientific notation

For \(0.0000000000001=1\times10^{-13}\)

Answer:

\(\frac{28}{9}\)

Problem 18