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5x-3x = 12-2

2x = 10

x = 5

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64 cm is the least length that can be measured by any of the tapes exactly.

Area of rectangle=length*breadth

a. 5.8*3.5=20.3cm²b. 63*9.5=598.5 cm²

2520 ke jagah par 280

Area of circle=πr^2628=3.14*r^2r=14.14diameter=28.28cm

what is your question

30=3×2×560=3×2×2×515is HCF

Given series is 4 , 8 , 28 , 80 , 244 , __

We have find out pattern between the numbers.

i ) 3 ^1 + 1 = 3 + 1 = 4

ii ) 3 ^2 - 1 = 3 × 3 - 1 = 9 - 1 = 8

iii ) 3 ^3 + 1 = 3 × 3 × 3 + 1 = 27 +1 = 28

iv ) 3 ^ 4 - 1 = 3 × 3 × 3 × 3 - 1 = 81 - 1 = 80

v ) 3 ^5 + 1 = 3 × 3 × 3 × 3 × 3 + 1 = 243 + 1 = 244

vi ) 3 ^6 - 1 = 3 × 3 × 3 × 3 × 3 × 3 - 1 = 729 -1 = 728

Required next number in the series = 728

diameter of the sphere ( d ) = 6cm

radius of the sphere ( r ) = d/2 = 6/2 = 3cm

diameter of the cylindrical vessel ( D ) = 12 cm

radius of the cylindrical vessel ( R ) = 12/2 = 6 cm

level of water raised = h cm

according to the problem given ,

volume of the water raised in the vessel = volume of the sphere

πR²h = 4/3×πr³

h = ( 4× r³ ) / ( 3× R² )

h = ( 4× 3× 3× 3 ) / ( 3× 6× 6 )

h = 1 cm

Therefore ,

level of water raised in the vessel = h = 1 cm

4x^2+4root(3)x+3 =4x^2+2root(3)x+2root(3)x+3=2x(2x+root(3))+root(3)(2x+root(3))=(2x+root(3))^2

We know that, D = b^2 - 4 * a * c

Then, For equation 4x^2 + 4sqrt(3)x + 3 D = (4sqrt3)^2 - 4 * 4 * 3

= 16 * 3 - 48

= 48 - 48

= 0

So, given quadratic equation has equal real roots.

the give equation has equal roots.

For finding nature Here D= 0 so equal roots

PA, QB, RC,& SD are perpendicular on line l.

To find: PQ, QR & RS

Construction: produce SP & l to meet each other at E.

Proof: InΔEDS,AP║ BQ║DS║CR [ given]

∴ PQ : QR: RS = AB:BC:CD

PQ : QR: RS = 6:9:12

let PQ= 6x , QR= 9x RS= 12x

PS = PQ+QR+RS

∴ PQ+QR+RS=36 [PS=36cm]

6x+9x+12x=36

27x=36

x= 36/27= 3/4

x=3/4

∴ PQ= 6x = 6× 4/3= 8cm

QR= 9x = 9× 4/3= 12cm

RS= 12x= 12× 4/3= 16 cm

Theleastangle a protector can measure is calledleast countof aprotractor. It is 1 degree in normalprotractors(as there are 10 divisions after every 10 degrees).

If two linear equations have infinitely many solutions means

a1/a2 = b1/b2 = c1/c2

here two linear equations are

3x+4y=12 and (m+n)x + 2(m-n)y = (5m-1)

So we can write,

3/(m+n)= 4/2(m-n) = 12/(5m-1)

From this we get, 3/(m+n) = 4/[2(m-n)]

6(m-n)=4(m+n)

6m - 6n = 4m -4n

2m - 10n = 0 --------------(1)

similarly 3/(m+n) = 12/(5m-1)

3m - 12n = 3 -------------------(2)

(1) ⇒ 6m - 30n=0 -------(3)

(2) ⇒ 6m - 24n = 6 ------(4)

(4) - (2) ⇒ 6n = 6

n = 1

substituting the value of n in (1)

then (1) becomes 2m - 10 =0

m=5

Therefore m= 5 and n=1

Total Number of Families (N) = 10,000a) Number of families which buy Newspaper A = 40%*N +5%N + 4%N +2%N = 40/100*10000 + 5/100*10000 + 4*100*10000 + 2/100*10000 = 10000/100(40+5+4+2) = 100(51) = 5100

b) Number of Families which doesn't buy Any NewsPaper = (100 - (40+20+10+5+3+4+2))%N = (100 - 84)%N = 16%N = 16/100*10000 = 16*100= 1600

184/11 *11/4=184/4=46 rod

Longest rod=length of diagnal of roomFirst of all, diagonal of floor=(12^2+9^2)^(1/2)=(144+81)^(1/2)=15mHeight of room=8mDiagonal of room, diagonal of floor and height of room forms triangle.Therefore, length of rod=(15^2+8^2)^(1/2)=(225+64)^(1/2)=17m

I don't know plz study by your own

(40/(100-40)*100= (40/60)*100=66.67

(40/60) *100=4000/60=200/3=66.67

thank you very much

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i¹⁰=(i²)⁵=(-1)⁵=-1i¹⁰⁰=(i²)⁵⁰=(-1)⁵⁰=1i¹⁰⁰⁰=(i²)⁵⁰⁰=(-1)⁵⁰⁰=11+i¹⁰+i¹⁰⁰+i¹⁰⁰⁰=1-1+1+1=2