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Liono4ka [1.6K]
3 years ago
7

How many subsets are there of the set N = {1, 42, 65, 12, 31, 27}?

Mathematics
1 answer:
lutik1710 [3]3 years ago
4 0

Answer:

\boxed{ \bold{  \huge{ \boxed{ \sf{64}}}}}

Step-by-step explanation:

If ' n ' is the cardinal number of a set, the number of subsets of a given set can be obtained by using the formula 2ⁿ

Given,

N = { 1 , 42 , 65 , 12 , 31 , 27 }

where n ( total number of elements ) = 6

So, the number of possible subsets of set N :

= 2ⁿ

= 2⁶

= 2 × 2 × 2 × 2 × 2 × 2

= 64

Hope I helped!

Best regards!!

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11. If triangle ABC is an isosceles triangle and triangle DBE is an equilateral triangle, find each missing
Ann [662]

Answer:

∠1 = 43°, ∠2 = 17°, ∠3 = 120°, ∠4 = ∠5 = ∠6 =  60°, ∠7 = 17°, ∠8 = 120°, ∠9 = 43°.

Step-by-step explanation:

I found the figure for this problem.

It is provided that ΔABC is isosceles and ΔDBE is equilateral.

Isosceles Triangle:

According to the definition the length of two sides are equal and hence the two base angles are equal.

Equilateral Triangle:

All the sides are of equal length and can also be defined as equiangular  with all the angles of measure 60°

CALCULATION:

For any triangle the sum of interior angles is always 180°.

ΔABC: ∠1+ (∠2 + ∠5 + ∠7)+∠9= 180°,

where, (∠2 + ∠5 + ∠7) is the total angle ∠ABC

ΔABC is isosceles so,

∠1 = ∠9,

4x+3 = 9x-47,

50 = 5x ⇒ x=10,

Putting the value of x in ∠1 we get,

∠1 = 4*(10)+3 = 43°,

∠1 = 43°.

ΔABD: ∠1+ ∠2+∠3= 180°

Now in order to find ∠2, firstly we have to find ∠3 in  ΔABD.

According to the exterior angle property, the exterior angle of an equilateral triangle is always 120°. Since ∠3 is an exterior angle for the equilateral triangle ΔDBE therefore,

∠3 =  120°,

furthermore,

∠2 = 180° - ∠3 - ∠1,

⇒ ∠2 = 180° - 120° - 43°

∠2 = 17°.

ΔDBE: ∠4+ ∠5+∠6= 180°,

Also, ΔDBE is equilateral ⇒ ∠4 = ∠5 = ∠6 =  60°.

Now from ∠1+ (∠2 + ∠5 + ∠7)+∠9= 180°

we can find ∠7,

⇒ ∠1+ (∠2 + ∠5 + ∠7)+∠9= 180°

∠7 =  180° - (∠2 + ∠5 + ∠1+∠9),

∠7 =  180° - (17° + 60° + 43° + 43°),

∠7 =  180° - (163°)  

∠7 = 17°.

Similarly, ∠8 is an exterior angle for the equilateral triangle ΔDBE therefore,

∠8 =  120°,

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