Question

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Explanation:

Problem 6

Step1: Calculate numerator first

$5^2 + 4 = 25 + 4 = 29$

Step2: Calculate denominator (PEMDAS)

$5(10 - 8 \div 2) = 5(10 - 4) = 5 \times 6 = 30$

Step3: Divide numerator by denominator

$\frac{29}{30}$

Problem 12

Step1: Multiply numerators and denominators

$\frac{4}{9} \cdot \frac{7}{10} = \frac{4 \times 7}{9 \times 10} = \frac{28}{90}$

Step2: Simplify the fraction

$\frac{28 \div 2}{90 \div 2} = \frac{14}{45}$

Problem 13

Step1: Factor 72 into perfect square

$\sqrt{72} = \sqrt{36 \times 2}$

Step2: Simplify the square root

$\sqrt{36} \times \sqrt{2} = 6\sqrt{2}$

Problem 14

Step1: Write as fraction and simplify

$\frac{12}{16} = \frac{12 \div 4}{16 \div 4} = \frac{3}{4}$

Problem 19

Step1: Distribute the coefficients

$5(y - 3) - 7(3 - 4y) = 5y - 15 - 21 + 28y$

Step2: Combine like terms

$5y + 28y - 15 - 21 = 33y - 36$

Problem 24

Step1: Cross-multiply to solve for $w$

$5w = 3 \times 8$

Step2: Calculate and isolate $w$

$5w = 24 \implies w = \frac{24}{5} = 4.8$

Answer:

Problem 6: $\frac{29}{30}$
Problem 12: $\frac{14}{45}$
Problem 13: $6\sqrt{2}$
Problem 14: $\frac{3}{4}$
Problem 19: $33y - 36$
Problem 24: $\frac{24}{5}$ (or $4.8$)