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angle ACD = sum of interior angles ( CAB +ABC) angle ACD = 75+45 = 120°

(6x*x+9x)/3(x*x-4x)=3x(2x+3)/3x(x-4)=(2x+3)/(x-4)

x^3 - 6x^2 + 12x - 35

= (x^3 - 5x^2) + (-x^2 + 5x) + (7x - 35)

= x^2(x - 5) - x(x - 5) + 7(x - 5)

= (x - 5)(x^2 - x + 7)

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sinθ = cosθtanθ= 1So,θ= 45°So,2tanθ+ cos²θ2tan(45°) + cos²(45°)2 × 1 + 1/(√2)²2 + 1/25/2

Answer C)2Explanation

if three points are in collinear then area of these points will be 0.here x1=4, y1= 2, x2=7, y2=5, x3=9,y3=7area =1/2[x1 (y2-y3)+x2 (y3-y1)+x3 (y1-y2)]=1/2[4(5-7)+7(7-2)+9(2-5)]=1/2[-8+35-27]=1/2[35-35]=0so these points are in collinear.

According to question AP=PQ=QBhence P divide AB 1:2ratio now use section formulap (x, y)x=(1 x (-7)+2 x 2)/(2+1)=-3/3=-1y=(1 x4+2 x (-2)) /(2+1)=0p (-1,0)now Q divide line AB 2:1ratiouse again section formulaQ (r, u)r=(2 x (-7)+1 x 2)/(2+1)=-12/3=-4u=(2 x4+1 x (-2))/(2+1)=2Q (-4,2)

2(i+b)=2(125/3+93/5)=2(725×273)/15=2(998)/15=1996/15=516

Consider a set of two numbers, if they have no positive integer that can divide both, other than 1, the pair of numbers is co-prime.Ex 1: 21 and 2221 and 22:

The factors of 21 are 1, 3, 7 and 21.

The factors of 22 are 1, 2, 11 and 22.

Here 21 and 22 have only one common factor that is 1.Hence their HCF is 1 and are co-prime.Ex 2: 21 and 2721 and 27:

The factors of 21 are 1, 3, 7 and 21.

The factors of 27 are 1, 2, 3, 9 and 27.

Here 21 and 27 have two common factors they are 1 and 3. HCF is 3 and they are not co-prime.

The answer is 1, cause they don't have any common factor other than 1.

HCF of coprime numbers is 1

1 is the correct answer of the given question

factors of 21 & 23; Factors 21=1,3,7,; 27=1,3,9; hcf=1,3

5x+√3y= 12Here 5 is rational and √3 is irrational

The formula to find the distance between points (x1,y1) (x2,y2) isd=√(x1-x2)^2+(y1-y2)^2 Sod=√(-7-2)^2+(9-6)^2d=√(-9)^2+(3)^2d=√81+9d=√90

Length of the vertical pole = 6m (Given)

Shadow of the pole = 4 m (Given)

Let Height of tower =hm

Length of shadow of the tower = 28 m (Given)

In ΔABC and ΔDEF,

∠C = ∠E (angular elevation of sum)

∠B = ∠F = 90°

∴ ΔABC ~ ΔDEF (By AA similarity criterion)

∴ AB/DF = BC/EF (If two triangles are similar corresponding sides are proportional)

∴ 6/h= 4/28

⇒h= 6×28/4

⇒h=6 × 7

⇒h= 42 m

Hence, the height of the tower is 42 m.

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ur ans. is right but I didn't understand it .. n there may be use of formula also right?

Okay.I will explain.

Length and shadow are directly proportional that means for any object (Length of the object ÷ shadow of the object) = constant.

But in ur ans their is no use of Theorem 6.6 ?

Please post the theorem to be used.

The process is general one.If you want it to be done using theorem please post that theorem here.

this may be the theorem that has to be use or . there is so many other theorem also

How that two triangles becomes similar without any method

Using the concept of similar triangles.....we find the height of tower = 42 mtrs.