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4x^2-4ax+(a^2-b^2)=0

=> (4x^2-4ax+a^2)-b^2=0

=>(2x-a)^2-b^2=0

=>{2x-a-b}{2x-a+b}=0

=> x=(a+b)/2 , (a-b)/2

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If AD is the bisector of ∠A of triangle ABC, show that AB>DB.Given AD is the bisector of ∠A of triangle ABCHence ∠DAB=∠DAC∠BDA is the exterior angle of the ∆DACHence ∠BDA> ∠DACor ∠BDA > ∠DAB Since ∠DAC=∠DAB→ AB > BD In a triangle sides opposite to greater angle is greater.

Total number of alphabets=5vowels A and I i.e 2if the word begins with vowel then the number of arrangements=2*4*3*2*1=48if the word terminates with vowel then number of arrangements=4*3*2*1*2=48thus total number of arrangements=48+48=96

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sin (a + b) = sin a cos b + cos a sin b

then: Sin 50 ° cos 10 ° + cos 50 ° sin 10 ° = Sin (50 + 10) = sin 60 = 1/2 √3

by using sin (A+B)=sinAcosB+cosAsinB sin(50+10)=sin50cos10+cos10sin50 .. .sin (50+10)=sin 60 =root3/2

Let present age of Pragati be xThen,Pragati age two years ago = (x - 2)Pragati age years hence = (x + 3)

As per given condition(x-2)(x + 3) = 84x^2 + 3x - 2x - 6 = 84x^2 + x - 90 = 0x^2 + 10x - 9x - 90 = 0x(x + 10) - 9(x + 10) = 0(x - 9)(x + 10) = 0x = 9, - 10

Negative value not possible

Therefore, present age of Pragati = 9 years

Let present age of Pragati be xThen,Pragati age two years ago = (x - 2)Pragati age years hence = (x + 3)

As per given condition(x-2)(x + 3) = 84x^2 + 3x - 2x - 6 = 84x^2 + x - 90 = 0x^2 + 10x - 9x - 90 = 0x(x + 10) - 9(x + 10) = 0(x - 9)(x + 10) = 0x = 9, - 10

Negative value not possible

Therefore, present age of Pragati = 9 years

Thanks

Viru age is 5 ys

Let the total journey be x km, thenaccording to the question ;

(2/5) of x = by train

(1/3) of x = by taxi

(1/6) of x = by bus

Remaining = 10 km --> by foot

Remaining distance = x - [(2/5)x+(1/3)x+(1/6)x]

10 = x - [(12+10+5)/30]x10 = x - (27/30)x10 = x-(9/10)x(1/10)x = 10x = 10×10x = 100------------------------------------------------Hence the length of the total journey is 100km

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maths book

f(n) = n + (the product of the nonzero digits of n).

12 + (1 * 2) = 12 + 2 = 14,

14 + (1 * 4) = 14 + 4 = 18

18 + (1 * 8) = 18 + 8 = 26,

26 + (2 * 6) = 26 + 12 = 38,

38 + (3 * 8) = 38 + 24 = 62

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Tread usually implies stepping with force, but it can also simply mean placing your feet, one after the other, on the ground.

40^2=1600; and 41^2=1681

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(40)^2=40×40=1600(41)^2=41×41=1681

i) Dividing both sides by 41, (9/41)*cos(A) + (40/41)*sin(A) = 1

ii) This is of the form, cos(A)*cos(B) + sin(A)*sin(B) = 1, where cos(B) = 9/41 and sin(B) = 40/41

iii) So, cos(A - B) = 1 ==> A - B = 2nπ Hence A = 2nπ + B

iv) So, cos(A) = cos(2nπ + B) = cos(B) = 9/41 csc(A) = csc(2nπ + B) = csc(B) = 41/40

MICR(magnetic ink character recognition) is a technology used to verify the legitimacy or originality of paper documents, especially checks. Special ink, which is sensitive to magnetic fields, is used in the printing of certain characters on the original documents.

Let the current age of sonal be x and manoj be y

x/y = 7/5 => x= 7y/5

after 10 years => (x+10)/(y+10) = 9/7

=> 7(x+10) = 9(y+10)=> 7x-9y = 90-70=20

putting x = 7y/5 in the equation

=> 7(7y/5) -9y = 20=> (49-45)y = 20*5 = 100=> 4y = 100=> y = 100/4 = 25 years

and hence x = 7*25/5 = 35 years

present age of sonal be = 35 yearspresent age of manoj be = 20 years

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25683927-1230982=24452945+1409834=25862779so the present population of the city is 25862779

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1 is the correct answer

sin^250+cos^250=1since sin^2A +cos^2 A=1

1is the correct answer

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sin50cos10+ cos50sin10 = sin(50+10) = sin60 = √3/2

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so late

Let the breadth = b mlength l =(2b+1) marea =528m²

l*b= 528(2b+1)b-528=0

2b²+b-528=02b²+33b-32b-528=0b(2b+33)- 16(2b+33)=0(2b+33)(b-16)=02b+33=0 or b-16=0

b should not be zerothereforeb-16=0b=16

breadth = 16mlength l = 2b+1= 2*16+1= 32+1= 33m

Given,themeasures of diagonals16,30We know that diagonals of rhombus are perpendicular bisectors of each other.

db=16DO=DB/2DO=16/2DO=8cmsimilarly,AO=15cmby using pythogaras theorem,DO²+AO²=DA²8²+15²=DA²64+225=DA²289=DA²DA=17perimeter=DA×4 =17×4PEIMETER=68CM

Multiplying(1+i)(X+iy)=2-5i=x+iy+xi-y=2-5iComparing real and imaginary partsHencex-y=2y+X=-5Henceadd both equations2x=-3hencex=-3/2x-y=2-3/2-y=2y=-3/2-2y=-7/2

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what is the value of k

Let the breadth =b mlength = l =(2b+1)marea =528m²

l*b= 528(2b+1)b-528=0

2b²+b-528=02b²+33b-32b-528=0b(2b+33)- 16(2b+33)=0(2b+33)(b-16)=02b+33=0 or b-16=0

b should not be zerothereforeb-16=0b=16

breadth = 16mlength =l= 2b+1=2*16+1=32+1=33m

Let breadth of rectangular plot be bl = 2b +1

Area = l*b = (2b +1)b 2b^2 + b - 528 = 02b^2 + 33b - 32b - 528 = 0b(2b + 33) - 16(2b + 33) = 0(b-16)(2b+33)=0b = 16, - 33/2

Thank you sir

ACartesian systemis the one which specifies a point plotted uniquely on a planeby a pair of numerical coordinates, having a pre-defined distance from the two fixed perpendicularcoordinates, measured in the same unit of length

inHind

Area of Reactangle land= length * breadth= 4.6*4= 18.4 m^2

Area of 4 squares = 4*(1.5*1.5)= 9 m^2

Area of remaining land= 18.4 - 9= 9.4 m^2