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x^2 + 12 x - 45 = 0

=> x^2 + 12x =45

add (6)^2 both side

=> x^2 + 12x + (6)^2 = 45 + (6)^2

=> x^2 + 2. (6).x + (6)^2 = 81 =(9)^2

=>(x + 6)^2 = (9)^2

=> (x + 6)^2 -(9)^2 = 0use formula, a^2 - b^2 = (a - b)(a + b)

now,=>(x + 6 -9)(x + 6 + 9)=0

=> x=3 , -15 , hence roots of equation is 3 and -15

the term in the denominator can be replaced by x

so, x = 1/1+(2/x) => x = x/x+2 => x²+2x = x => x²+x = 0 so, x(x+1) = 0 or , x = -1, 0.

π/15 = 180/15 = 12° , let angle C = 90°

so, difference between acute angle = A-B = 12°..(1)

in RT ∆ , sum of angle A+B +C = 180°=> A+B +90 = 180=> A+B = 90.......(2)

so, adding both (1) and (2) => 2A = 90+12 = 102 => A = 102/2 = 51° and B = 51-12 = 39°

smallest angle = 39°

Cipla Limited is an Indian multinational pharmaceutical and biotechnology company, headquartered in Mumbai, India. Cipla primarily develops medicines to treat respiratory, cardiovascular disease, arthritis, diabetes, weight control and depression; other medical conditions.

36 and 60 is right answer

36 and 60 are the correct answer to this question

36 and 60 are the right answer.

the answer is 36 and 60

36 & 60 is the correct answer

third part of a is 12 - a)3/12

third part of a is 12-a)3/12

what is the question

Total part=100%

part to naresh=1/3of 100% =33.33%

part to mukesh=2/3of 100% =66.66%

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CP of 1st pen = Rs 20Gain= 5%SP= 20+20(5/100)= 20+20(1/20)=21RsCP of 2nd pen = Rs 2Loss=5%SP= 20-20(5/100)= 20-20(1/20)=19RsTotal CP= 40RsTotal SP=40Rs So neither profit nor loss

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Thanks, please see my other question

16)

17)

19) Area of triangle=1/2*base *height

formula of distance

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The circumference is directly proportional to the radius of the circle

And the area is directly proportional to the square of the radii

∴Ratio of their areas =4²:5²=16:25

Option (a) is correct.

It's a linear polynomial as the power of x is one

linearbecause it have no power

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Principal (P) = Rs 10, 800

Rate (R) 12 1/2% = 25/2% ( annual )

Number of years (n) = 3

Amount, A = p( 1 + R/100 )n

= Rs [10800 (1 + 25/200)3]

= Rs [10800(225/200)3]

= Rs ( 10800 x 225/200 x 225/200 x 225/200 )

= Rs 15377.34375

= Rs 15377.34 (approximately)

C.I. = A − P = Rs (15377.34 − 10800) = Rs 4,577.34

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please like my answer if you find it useful

please like my answer if you find it useful

opposite angles of parallelogram are equal

and adjacent angles add up to 180°

so, the value of opposite angle is

=> x+x = 140°=> 2x = 140° => x = 70°

so other angle will be 180-70 = 110°

original area cow is grazing=(area of whole circle of radius 12 m)= π*r^2=π*144=144*π sq. m

new area cow is grazing=(area of circle of radius 23 m)=π*R^2=π*529=529*π sq. m

increased area=(529*π-144*π)sq. m=(529–144)*π sq. m

=385*π sq.m=1210 sq. m

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Savings per month = 1200*20/100

= 240 rupees

Savings per year = 240*12

= Rs.2880

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6+4 =10 ,18+2=20 ,24+6=30,14+6=20

This is a sequence and series based sum. Hence we are using the concept of Arithmetic Progression for solving it.

As all numbers divisible by 6 must be divisible by 2. So numbers divisible by 6 are only even numbers.

First Term ( a ) = 102

Common Difference ( d ) = 6

Number of terms = ?

Last term ( l ) = 996

So Using the formula below, we get,

l = a + ( n - 1 ) d

=> 996 = 102 + ( n - 1 ) 6

=> 996 - 102 = 6 ( n - 1 )

=> 894 = 6 ( n - 1 )

=> 894 / 6 = ( n - 1 )

=> 149 = ( n - 1 )

=> n = 149 + 1 = 150 terms

Hence Sum of all terms can be found out by applying the formula:

S ( n ) = n / 2 [ a + l ]

=> S ( 150 ) = 150 / 2 [ 102 + 996]

=> S ( 150 ) = 75(1098)

=> S ( 150 ) = 82350

Hence the sum of all even integers divisible by 6 present between 100 and 1000 is 82350.

Let length of model be xLet length of ship be 200x

Now, length of model = 4 cmThen, length of ship = 200*4 = 800 cm

Area of deck of ship = 160000Let length of deck be ss^2 = 160000s = 400 cm

Now, length of deck of model = 400/200 = 2 cmArea of deck of model= 2*2 = 4 cm^2

Ship and its model are similar figures.

∴1/200 = 4/length of ship

(by the property of similarity)

⇒ Length of the ship = 800 cm.

area of model/area of ship = (1/200)²

⇒area of model = 16000/40000

area of model = 0.4 m

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We know that power,P = I^2 *RSo P = 1*1*200 = 200 Watts

Energy = P*tSo, E = 200*5 = 1000 Watt hour = 1 kWh

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Volume =πr^2h22/7*9*2=396/7radius=2772*7/396 *3=147cmheight=49*2=98cm

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Sol:Radii of the concentric circles = 21 cm and 42 cm

Area between the circles = π R2- r2= (22/7) (422- 212) = 4158 cm2

Angle subtended by the arc in the inner circle = 60°

Area of the sector in the inner circle = (60° / 360°) x π r2= (60° / 360°) x (22/7) x (21)2= 231 cm2

Angle subtended by the arc in the outer circle = 60°

Area of the sector in the inner circle = (60° / 360°) x π R2= (60° / 360°) x (22/7) x (42)2= 924 cm2

Area of the portion of the sector in between the circles = 924 - 231 = 693 cm2Area of the shaded portion = (Area between the circles) - (Area of the portion of the sector in between the circles) =4158-693 = 3465Therefore, the area of the shaded region is 3465 cm2.