Question

1. select all of the expressions equivalent to $(-\frac{1}{3})^{2}+\sqrt{2^{2}+9}$. $\square \frac{1}{9}$ $\square \frac{11}{3}$ $\square -\frac{1}{9}+\sqrt{25}$ $\square \frac{1}{9}+\sqrt{25}$ $\square -\frac{1}{9}+5$ $\square \frac{1}{9}+5$ 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:

1. For problem 16 (Algebra - Step - by - Step Format):

• First, simplify \((-\frac{1}{3})^{2}+\sqrt{x^{2}+9}\) (assuming \(x = 0\) for simplicity, since the problem is about equivalent expressions in a general algebraic sense of simplification). \((-\frac{1}{3})^{2}=\frac{1}{9}\), and \(\sqrt{0 + 9}=3\), so the expression is \(\frac{1}{9}+3=\frac{1 + 27}{9}=\frac{28}{9}\).
• Check each option:
• Option 1: \(\frac{28}{9}\) (if this is the first - boxed option, it is equivalent).
• Option 2: \(\frac{11}{3}=\frac{33}{9}

eq\frac{28}{9}\).

• Option 3: \(-\frac{1}{9}+\sqrt{25}=-\frac{1}{9}+5=\frac{-1 + 45}{9}=\frac{44}{9}

eq\frac{28}{9}\).

• Option 4: \(\frac{1}{9}+\sqrt{25}=\frac{1+45}{9}=\frac{46}{9}

eq\frac{28}{9}\).

• Option 5: \(-\frac{1}{9}+5=\frac{-1 + 45}{9}=\frac{44}{9}

eq\frac{28}{9}\).

• Option 6: \(\frac{1}{9}+5=\frac{1 + 45}{9}=\frac{46}{9}

eq\frac{28}{9}\).

1. For problem 18 (Algebra - Step - by - Step Format):

• Calculate approximate values:
• \(\sqrt{13}\approx3.61\), \(\sqrt{19}\approx4.36\), \(\pi\approx3.14\), \(3.\overline{6}\approx3.67\), \(4.3\).
• Now compare the values:
• \(\pi\approx3.14\), \(\sqrt{13}\approx3.61\), \(3.\overline{6}\approx3.67\), \(4.3\), \(\sqrt{19}\approx4.36\).

1. For problem 19 (Algebra - Step - by - Step Format):

• For a number \(a\times10^{n}\) in scientific notation (\(1\leq a\lt10\)), for \(0.0000000000001 = 1\times10^{-13}\).

1. For problem 20 (Algebra - Step - by - Step Format):

• Factor \(16m^{2}n^{2}-12mn^{3}\):
• Find the GCF (Greatest Common Factor) of the coefficients \(16\) and \(12\). The GCF of \(16\) and \(12\) is \(4\).
• For the variables, for \(m\) terms: the GCF of \(m^{2}\) and \(m\) is \(m\). For \(n\) terms: the GCF of \(n^{2}\) and \(n^{3}\) is \(n^{2}\).
• \(16m^{2}n^{2}-12mn^{3}=4mn^{2}(4m - 3n)\).

Answer:

s:

• Problem 16: If the first option is \(\frac{28}{9}\), then the answer is the first - boxed option.
• Problem 18: D. \(\pi,\sqrt{13},3.\overline{6},4.3,\sqrt{19}\)
• Problem 19: \(1\times10^{-13}\)
• Problem 20: B. \(4mn^{2}\)