Question

Please solve this question​

Answer 1

Answer:

${3}^{2 \times{n + 6} } \times {9}^{2n - 7} \div {27}^{2n}$

answer is 1/9

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Answer 2

Step-by-step explanation:

6.

a. 36 = 1 + 3 + 5 + 7 + 9 + 11

{ \sqrt{36} = 6

36

=6 So, 36 is the sum of first 6 consecutive odd numbers}

b . 64 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15

{ \sqrt{64} = 8

64

=8 So, 64 is the sum of first 8 consecutive odd numbers}

c . 81 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17

{ \sqrt{81} = 9

81

=9 So, 81 is the sum of first 9 consecutive odd numbers}

d. 144 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

{ \sqrt{144} = 12

144

=12 So, 144 is the sum of first 12 consecutive odd numbers}

7.

Pythagorean triplets are of the form 2m , m²-1 and m²+1

a. 14

2m = 14 ⇒ m = 14÷2 = 7

m²-1 = 7² - 1 = 49 - 1 = 48

m²+1 = 7² + 1 = 49 + 1 = 50

So, 14, 48 and 50 are Pythagorean triplets.

b. 10

2m = 10 ⇒ m = 10÷2 = 5

m²-1 = 5² - 1 = 25 - 1 = 24

m²+1 = 5² + 1 = 25 + 1 = 26

So, 10, 24 and 26 are Pythagorean triplets.

c. 16

2m = 16 ⇒ m = 16÷2 = 8

m²-1 = 8² - 1 = 64 - 1 = 63

m²+1 = 8² + 1 = 64 + 1 = 65

So, 16, 63 and 65 are Pythagorean triplets.

d. 22

2m = 22 ⇒ m = 22÷2 = 11

m²-1 = 11² - 1 = 121 - 1 = 120

m²+1 = 11² + 1 = 121 + 1 = 122

So, 22, 120 and 122 are Pythagorean triplets.