Math, asked by praveenraj39, 1 year ago

answer question and explain 99 103 104 105

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Answered by shadowsabers03
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99)


If a number is divisible by 11, then the difference between the sum of alternate digits of that number will be divisible by 11.


E. g.: Check whether 54763786 is a multiple of 11.


First take the sum of alternate digits of the number.


54763786:

5 + 7 + 3 + 8 = 23

4 + 6 + 7 + 6 = 23


Then take the difference of the sums obtained. The difference can be the value of all integers, including 0 and negatives.


23 - 23 = 0


Here, 0 is got. ∴ 54763786 is a multiple of 11.


Okay, let's have a look at 1372x413.


Sum of alternate digits is to be taken first.


1372x413:

1 + 7 + x + 1 = x + 9

3 + 2 + 4 + 3 = 12


Here, 12 - (x + 9) is a multiple of 11.


12 - (x + 9)

= 12 - x - 9

= 3 - x


∴ 3 - x is a multiple of 11.


If x = 3, 3 - x = 3 - 3 = 0 is a multiple of 11.

If x = 14, 3 - x = 3 - 14 = -11 is a multiple of 11. But x can't be 14 as x is a digit of 1372x413 and 14 is a two-digit number.


∴ The answer is 3, i. e., option (D).


103)


The diagonals of any square makes the angles on either sides of the diagonal 45°. That's a feature of a square.


Here, BD is a diagonal.


∴∠CDB = ∠DBA = ∠ADB = ∠DBC = 45°


Let the point where x° is located be P. The point is not marked in the question. So I suggested a name for the point.


Here, ∠DOC = ∠POB = 85° (Alternate angles)


Found that ∠DBA = 45°


By considering ΔPOB,


∠POB = 85°

∠DBA (Or ∠OBP for better) = 45°

∴ ∠BPO = 180° - (85° + 45°) = 180° - 130° = 50°


∠APC and ∠BPC (i. e., ∠BPO) are linear pairs.


∴ ∠APC = x° = 180° - ∠BPC = 180° - 50° = 130°


130° is the answer.


104)


∠EOS = ∠BOT = 50° (Alternate angles)


In any rectangle, the diagonals have equal length and bisect each other.


∴ OB = OE = OS = OT


In ΔBOT,

∠BOT = 50°

OB = OT

∴ ∠OTB = ∠OBT


∠OTB + ∠OBT = 180° - ∠BOT = 180° - 50° = 130°


∠OTB = ∠OBT = 130° ÷ 2 = 65°


65° is the answer.


105)


Let the sides be 4x and 5x.


Perimeter = 2(l + b) = 90 cm

= 2(4x + 5x) = 90 cm

= 2 × 9x = 90 cm

= 18x = 90

x = 90 ÷ 18 = 5

4x = 4 × 5 = 20 cm

5x = 5 × 5 = 25 cm


∴ Sides are 20, 25.


Hope these may be helpful.


Please mark my answer as the brainliest if these may be helpful.


Thank you. Have a nice day.


#adithyasajeevan

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