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maksim [4K]
2 years ago
6

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}

3 0
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

8 0
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.

4 0
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

6 0
3 years ago
Read 2 more answers
Please answer please answer please answer
serg [7]
For number 1 A: 2,8 B: 1,3 C: 6,6 D: 4,0 E: 8,2 for number 2 A: 7,9 B: 9,7 C: 0,6 D: 3,8 E: 7,5
7 0
3 years ago
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