Question

please answer 56,57,58

Answer 1

for 56 use empirical relationship

3median = mode + 2mean



next image is the answer for 58

Answer 2

ans 56: 3 median = mode + 2 mean

                               = 12 + 2(24)

                               =60

      ∴ median = 60/3 = 20

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ans 57:

given: ∠ CAB = ∠ CED  ;  CD = 8 cm  ;  CE = 10 cm  ;  BE = 2 cm  ; AB = 9 cm  ;  AD = b  ;  DE = a

to find : value of a + b

solution :

In Δ ABC and Δ EDC

∠ C = ∠ C ( common)

∠ A = ∠ E ( given)

∴ Δ ABC ≈ Δ EDC ( AA rule)

∴ AB/ED = BC/DC = AC/EC ( sides of similar triangles are equal)

substitute the values

9/a = 12/8 = (8+b)/10

9/a = 3/2

⇒ 18 = 3a

∴ a= 6

(8+b)/10 = 3/2

⇒ 16 + 2b = 30

⇒ 2b = 14

∴ b = 7

now, a + b = 6 + 7 = 13

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ans 58:  4/x + 5y = 7     (1)

              3/x + 4y = 5    (2)

let 1/x be 'a'

substitute value of a in (1) and (2) and solve them

4a + 5y = 7   (1)

3a + 4y = 5   (2)

(1) * 3 = 12a + 15y = 21

(2) * 4= 12a + 16y = 20

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                       -y = 1

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∴ y = -1

substitute y in (1)

4a + 5(-1) = 7

4a = 7 + 5

a = 3

but a = 1/x

∴ 1/x = 1/3

so the answer is option a: (1/3, -1)