16,42 greatest common factor

1 answer:

7 0

2

42 ÷ 2 = 21
16 ÷ 2 = 8

Let's try the other factors of 42...

42 ÷ 6 = 7
16 ÷ 6 = 2.66
No...

42 ÷ 7 = 6
16 ÷ 7 = 2 2/7
No...

42 ÷ 14 = 3
16 ÷ 14 = 1.1428
No...

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The diagram shows a hexagon-shaped tile used for flooring. Each hexagon tile has an area of 18/3 in 2 Find x.

mylen [45]

Answer:

x = 12

Step-by-step explanation:

The hexagonal tile given here is made up of 6 triangles with equal bases and heights.

So, area of hexagonal tile will be equal to 6 times the area of one triangle.

Therefore,

$18 \sqrt{3} = 6 \times \frac{1}{2} \times 2 {( \sqrt{3)} }^{ \frac{x}{12} } . {( \sqrt{3)} }^{ \frac{x}{6} } \\ \\ 18 \sqrt{3} = 6 {( \sqrt{3)} }^{ \frac{x}{12} } . {( \sqrt{3)} }^{ \frac{2x}{12} } \\ \\ \frac{18 \sqrt{3} }{6} = {( \sqrt{3)} }^{ \frac{x}{12} + \frac{2x}{12} } \\ \\ 3 \sqrt{3} = {( \sqrt{3)} }^{ \frac{3x}{12} } \\ \\ 3. {3}^{ \frac{1}{2} } = {3}^{ \frac{3x}{24} } \\ \\ {3}^{1 + \frac{1}{2} } = {3}^{ \frac{x}{8} } \\ \\ {3}^{ \frac{3}{2} } = {3}^{ \frac{x}{8} } \\ (bases \: are \: equal \: so \: exponents \: \\ will \: also \: be \: equal) \\ \implies \frac{3}{2} = \frac{x}{8} \\ \\ x = \frac{3 \times 8}{2} \\ \\ x = 3 \times 4 \\ \\ x = 12$