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2 years ago

Which expression represents the prime factorization of 108?

Mathematics

1 answer:

ankoles [38]2 years ago

4 0

Answer:

2×2×3×3×3

Step-by-step explanation:

●108=

•2×54

•2×27

•3×9

• 3×3

Writing the prime numbers;

108=2×2×3×3×3

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Kathi's order at the diner cost $12.75. She had<br> to pay 6% tax on the bill. How much is her tax?

Talja [164]

$\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6\% of 12.75}}{\left( \cfrac{6}{100} \right)12.75}\implies 0.765~~\approx 0.77~~\textit{about 77 cents}$

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2 years ago

Total surface area of a cube is 1014cm^2. It's volume will be :

Karolina [17]

Answer:

Option A (2197 cm³)

Step-by-step explanation:

For a cube with length of each side "a" , it's

Total Surface Area = 6a²
Volume = a³

_____________________________________________

According to the question ,

Total Surface Area = 1014 cm²

Let the length of each side of cube be 'a'.

Using the formula ,

$6a^{2} =1014$

$=> a^{2} =\frac{1014}{6} = 169$

$=> a = \sqrt{169} = +13 \: or -13$

But length can't be negative . So , length of each side = 13 cm

∴ Volume of cube = 13³ = 2197 cm³

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3 years ago

Mara is building a set of shelves supported by a diagonal brace, as shown in the diagram. Answer the questions to decide whether

Kazeer [188]

Answer:

Step-by-step explanation:

1). Since, m∠1 + m∠2 = 180° [Supplementary angles]

If m∠2 = 120°

m∠1 + 120° = 180°

m∠1 = 180° - 120°

m∠1 = 60°

2). If a transversal intersects two parallel lines on the top and middle,

∠1 and ∠5 will be corresponding angles.

3). Since, m∠1 = m∠5 = 60° (Corresponding angles)

Therefore, both the lines on top and middle will be parallel.

4). Since, m∠9 + m∠11 = 180° [Supplementary angles]

If m∠11 = 120°

m∠9 + 120° = 180°

m∠9 = 60°

Since, m∠1 = m∠9 = 60° [Corresponding angles]

Therefore, both the lines on the top and bottom shelves will be parallel.

5). Since, m∠5 = m∠9 = 60° [Corresponding angles]

Therefore, middle and bottom shelves will be parallel.

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3 years ago

A model of a car is 24 in. long. The actual car is 16 ft long. What is the ratio

kirill115 [55]

1 foot = 12 inches.

The model of the car is 24/12 = 2 feet long.

The ratio would be 2 ft/ 16 ft which can be reduced to 1/8

Answer 1/8

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serg [7]

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3 years ago

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