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Mathematics

1 answer:

pentagon [3]2 years ago

7 0

The option that represents the answers for 6, 8, 10, and 14 is the second option- 31, 41, 51, 71

<h3>Sequence and Series </h3>

From the question, we are to determine the option that represents the answer for pictures 6, 8, 10, and 14

In the given diagram,

The first picture requires 6 matches

The 2nd picture requires additional 5 matches

the 3rd picture requires additional 5 matches

and so on

That is

1 → 6

2 → 6 + 5 = 11

3 → 11 + 5 = 16

4 → 16 + 5 = 21

5 → 21 + 5 = 26

6 → 26 + 5 = 31

7 → 31 + 5 = 36

8 → 36 + 5 = 41

9 → 41 + 5 = 46

10 → 46 + 5 = 51

11 → 51 + 5 = 56

12 → 56 + 5 = 61

13 → 61 + 5 = 66

14 → 66 + 5 = 71

Hence, the option that represents the answers for 6, 8, 10, and 14 is the second option- 31, 41, 51, 71

Learn more on Sequence and Series here: brainly.com/question/10321751

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In a 30cm by 25cm rectangle, a quadrant of a circle of radius 7cm has been cut away from each corner. What is the perimeter of t

lidiya [134]

Answer:

Perimeter = 98 cm

Area = 596 $cm^{2}$

Step-by-step explanation:

Please refer to the attached image for the resultant figure when a quadrant of circle with radius 7 cm is cut from a rectangle of sides 30 cm and 25 cm.

Perimeter of a figure = Sum of all its sides + Perimeter of circle

Quadrant of a circle is one fourth of a circle and there are 4 such quadrant of a circle, so eventually there is one complete circle in this figure.

The sides of this resultant figure = 30 - 14 = 16 cm

and 25 - 14 = 11 cm

So perimeter of this figure = 16 + 11 + 16 + 11 + Perimeter of circle

$\Rightarrow 54 + 2 \pi r\\\Rightarrow 54 + 2 \times \dfrac{22}{7} \times 7\\\Rightarrow 54 + 44 = 98 cm$