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I joined o and c In ΔOPA and ΔOCA, OP = OC (Radii of the same circle) AP = AC (Tangents from point A) AO = AO (Common side) ∴ ΔOPA ≅ ΔOCA (SSS congruence criterion) ⇒ ∠POA = ∠COA … (i) Similarly, ΔOQB ≅ ΔOCB ∠QOB = ∠COB … (ii) Since POQ is a diameter of the circle, it is a straight line. ∴ ∠POA + ∠COA + ∠COB + ∠QOB = 180 º From equations (i) and (ii), 2∠COA + 2∠COB = 180º ⇒ ∠COA + ∠COB = 90º ⇒ ∠AOB = 90°

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(xy+4)×(xy-4)=(xy)²-4²= x²y² - 16

we know,

let us suppose two roots as x1 & x2

ATQ, x1=(-x2)

sum of roots,

x1+x2=(-b/a)

=(8k-8)/4=2k-1. (x1=-x2)

now, 2k-1=0

k=1/2(ans)

So, the other equation isx^2 + 3x -18=0x^2 + 6x - 3x - 18=0x(x+6)-3(x+6)=0(x-3)(x+6)=0x=3,-6

Let the son's age be x. So, mother's age =x+25After 8 years,Son's age= x+8Mother's age =x+25+8=x+33 Sons age / Mother's age = 4/9x+8/x+33 = 4/99(x+8) = 4(x+33) 9x+72 = 4x+ 1325x=60x=12 So the son's age is 12 years.

Let t = the time to the fill the tank

t/30 + t/40 + t/60= 1

40X60t +30X60t +30X40t = 30X40X60

24t.+18t + 12t = 120X6

4t+ 3t + 2t = 120

9t= 120

t =120/9

t =13 minutes and 3/9*60

= 13minutes and 20 seconds

Let t = the time to the fill the tank

t/30 + t/40 + t/60= 1

40X60t +30X60t +30X40t = 30X40X60

24t.+18t + 12t = 120X6

4t+ 3t + 2t = 120

9t= 120

t =120/9

t =13 minutes and 3/9*60

= 13minutes and 20 seconds

but the ans is 4 hours 30 minutes

here we find percentage of students getting A grade.Mary's class= (6/25)*100=24%John's class=(5/20)*100=25%so, John's class has a better record.

suppose number is xso 7/3x=1/6x+13so (14-1)/6*x=13so 13x=6×13so x=6

t^3 - 3t^2 + 2

= t^3 - 2t^2 - t^2 + 2

= t^2(

Let the volume of the cistern be V.

Together two pipes take 3 1/13 mins = 40/13

Rate of both the pipes together = V/(40/13)

Let pipes be A and B,

Time taken by A = t mins , So rate = V/t

Time taken by B = t+3 mins, So rate = V/(t+3)

Combined rate = V/t + V/(t+3)

We already know that combined rate = V/(40/13)

Equating both ,

V/t + V/(t+3) = V/(40/13)

1/t + 1/(t+3) = 13/40

(t+3+t) / t(t+3) = 13/40

(2t + 3)/ (t^2+3t) = 13/40

80t + 120 = 13t^2 + 39t

13t^2 - 41t - 120 = 0

The quadratic equation yields two roots :

5 and -1.846 , since time cannot be negative

Time taken by pipe A = 5 mins

Time taken by pipe B = 5+3 = 8 mins

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n9

19500×3= 585003 month =1950012 month =19500×3= 58500

yearly income = 19500×4 = 78000 is the right answer

78000 is right answer

78000 is the correct answer of the given question

Answer:Given; circle with centre O in which chords AB and CD intersect at M.To Prove: AM = DM and CM = BM

In ΔAOM and ΔDOMOA = OD (radii)OM = OM (common side)So, ΔAOM ≈ Δ DOMHence, AM = DM provedIt is given that AB = CDSo, AB – AM = CD – DMOr, CM = BM provedplease like the solution 👍 ✔️

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(1/5)/2= (1/10) piecesif (1/5) piece is cut into 1/2 we get (1/10) pieces

1 piece cut into 4 =1/4 pieces 1/4 pieces cut into1/2 =1/8 pieces so 1/5 pieces cut into 1/2 pieces =1/10 pieces 1/5 ×1/2= 1/10 pieces

Perimeter of rectangular park=2(l+b)=2(350+250) m=2*600 m=1200 m

Cost of fencing 1m=₹18.50Cost of fencing 1m=₹18.50×1200=₹22,200

Area = length × breadth = 350 × 275 = 96250 sq meter 26 per sq meter so total cost = 26 × 96250 = 1502500 Rs.

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Area = 350*200

= 70000 m²

Cost = 72*70000

= 5040000 rupees

thank you

As 2017 is not leap year hence there are 28 days.Hence total earnings will be 350*28=9800rupees

Speed =distance /timeSpeed =350/28=12.5 m/secNow in km/ hr =12.5*3600/1000*1045 km per hour

Conversion:1km =1000m

Distance=3250mTherefore, distance=3250/1000km=3.25 kmHence the distance between Radha 's home and her school is 3.25 km

what is the meaning of what

150km=₹25501km=₹2550/150=₹17124km=17×124=₹2108

charge for 150km.=2550rs.then,charge for 1 km.=2550÷150 =17rs.so,charge for 124km.=124×17 =2108rs.

150km=2550rsthen .1km=2550×150so124=124÷17=2108rs

charge for 150km=2550rs.then,charge for 1km,=2550÷150 =17rs.so,charge for 124km.=124×17 =2108rs.

Given -

Speed of water = 15km/hr

Distance travelled upstream and downstream = 30 km

Let, speed of stream be x km/hr

So, time taken to travel 30km upstream = 30/15-x

and, time taken to travel 30km downstream = 30/15+x

Time taken to travel 30km upstream and 30km downstream = 4 hour 30 min or 9/2 hours

So, the equation formed will be

30/15-x + 30/15+x = 9/2

=> 30(1/15-x + 1/15+x) = 9/2

=> 1/15-x + 1/15+x = 9/2*30 = 3/20

=> (15+x+15-x)/225 - x2= 3/20

=> 30/225-x2= 3/20

=> 225-x2= 30*20/3

=>225-x2= 200

=> x2= 225-200

=> x2= 25

=>x = 5

But, x = speed of stream

So, speed of the stream = 5 km/hr

InΔPAC andΔQBC∠PCA =∠QCB∠PAC =∠QBC

ΔPAC congurent toΔQBCPA/QB = AC/BCx/y = AB/BCy/x = BC/AC

InΔRCA andΔQBA∠RAC =∠QAB∠RCA =∠QBAΔRCA is congruent toΔQBARC/QB = AC/AB

z/y= AC/ABy/z= AB/AC

adding both eqy/z + y/z = BC + AC/ AC = 1

y/z + y/z = 1

multiplying both sides by y

1/x + 1/z = 1/y

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Its wrong answer

x-10x/100= 1800x-0. 1x= 18000.9x= 1800x= 1800/0.92000plants

Let son age be x so mother age will be x + 25

According to question after 8 years

x + 8 4-------- = -----x+33 9

9(x + 8) = 4 ( x + 33)

9x + 72 = 4x + 132

5x = 132 - 72

5x = 60

x = 12

Son age after 8 year is 20

Let present age of son be X years.

Age of mother = ( X + 25 ) years.

After 8 years age of son= ( X + 8 ) years.

After 8 years age of mother = ( X + 25 + 8 ) = ( X + 33 ) years.

According to the question,

X+ 8 / X + 33 = 4/9

9 ( X + 8 ) = 4 ( X + 33 )

9X + 72 = 4X + 132

9X - 4X = 132 - 72

5X = 60

X = 60/5

X = 12 years.

Present age of son = X = 12 Years.

And,

Present age of mother = X + 25 = 12 + 25 = 37 years.

ok

Let son age be xThen mother age = x + 25

After 8 yearsSon age = x + 8Mother age = x + 25 + 8

As per given condition(x + 8)/(x + 33) = 4/99(x + 8) = 4(x + 33)9x + 72 = 4x + 1329x - 4x = 132 - 725x = 60x = 60/5 = 12

Son's age = 12 years

Let present age of son = xThen present age of mother = x + 25

After 8 years,Age of son = x + 8Age of mother = x + 25 + 8

As per given condition x + 8/x + 33 = 4/99x + 72 = 4x + 1325x = 132 - 72 = 50x = 50/5 = 10

Therefore, son present age = 10 years

perimeter of rectangle is 2(L+B)2(L+B) = 34L+B = 17 L = 17 - 5L = 12 so dignonal is 12² + 5 ² = D²144+ 25 = D² 169 = D ² D = 13