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If -2 is the root of the EQUATION x² + 7X + k = 0; then
(-2)² + 7×(-2) + k = 0
⇒ 4 - 14 + k = 0
⇒ -10 + k = 0
⇒ k = 10

the equation is x² + 7x + 10 = 0. 
let the other root is β.
we know that sum of ROOTS is -b/a, that is -7/1 = -7.
⇒ β + (-2) = -7
⇒ β - 2 = -7
⇒ β = -7 + 2 
⇒ β = -5
So other root is -5.

3 x + 2 is factor of  P(x)  = 6 x³ + 7 x² - x - 2  ??

   If  3 (x + 2/3)  is a factor of  the expression, P(x = - 2/3)  should be 0.
       Reminder of division of P(x) by (x+2/3) is  P( - 2/3)
     P(2/3) = -48/27  + 28/9 + 2/3 - 2 = 0
As the reminder is  zero,  (x + 2/3) is a factor. 
 
 Hence,  6 x³ + 7 x² - x - 2 = 3 (x + 2/3)  ( a x² + b x + c) +  0

 COMPARING coefficients of x³ on both sides, 3 a = 6  => a = 2
     coefficients of the constant terms:    -2 = 2 c    => c = -1
           finding coefficient of x² term:  7 = 2 a + 3 b    =>  b = 1

             quotient :  2 x² + x - 1
==========================================

3 x + 2  )  6 x³  + 7 x² - x - 2  (  2 x²  + x  - 1
               6 x³  + 4 x²
           ============
                       3 x² - x
                       3 x² + 2 x
                     ===========
                               - 3 x - 2
                               - 3 x - 2
                             =======
                               0

The answer will be 60
60x60=3600
the easiest way is that u can TAKE out the LCM of 3600 and then MAKE the pair of the numbers and multiply them...
as for 3600 is concerned, the LCM will be 2x2x2x2x5x5x3x3
now take the pair out i.e; 2x2x5x3
you will GET 60..

As, ΔABC is isosceles
angle B = angle C
But BCED is a cyclic QUADRILATERAL with base ANGLES B and C are equal.
⇒ angle B = angle E
But angle B + angle E = 180 degrees (OPP angles of cyclic quadrilateral are supplementary)
⇒ angle C + angle E = 180 degrees
Therefore, DE is PARALLEL to BC

The LEAST number is 5 children. Since each girl must have another SISTER, the MINIMUM number of GIRLS there can be are 2 girls. And since each BOY must have at least 2 brothers, the minimum number of boys there can be are just 3 boys.
So, in total
3 boys + 2 girls = 5 children.

Dimension of FLAT surface = 6m×4m or 600cm×400cm
height of RAINFALL = 2cm
volume of water = 600×400×2 cm³

radius of CYLINDER = 20cm
let height of water = h
volume = πr²h 



Height of water is 382cm (to the NEAREST whole NUMBER.)

Equation of sphere => (x-1)²(y-1)²(z-1)² = 3²
centre of sphere is (1,1,1)
radius = 3
if plane touches the sphere then perpendicular DISTANCE from centre of sphere to the plane is equal to the radius of sphere
equation of plane is x+y+z-a = 0 
|(1+1+1-a)/√(1²+1²+1²)| = 3
|(3-a)/√3| = 3
(3-a)/√3 = +3 or -3
3-a = 3√3
a = 3(1-√3)
or 
3-a = -3√3
a = 3(1+√3)

The above CONDITION with the given SET of numbers is not possible. Because, when we add any two odd numbers, the resultant NUMBER is always an even number. Hence, even if we repeat a SINGLE number again, the solution cannot be obtained.

Area=100 cm²
a²=100
a=√100=10
side= 10 CM

Let number of STUDENTS be "N"
and number of BENCHES be"n"
so 3 students on each benches student left will be 1
3n+1=N
4n-4=N
or
3n-N=-1.....1
4n-N=4.............2
subtracting 1 and 2 we GET 
n=5
putting n=5
in in 1
15-N=-1
N=16
so number of student are 16 and number of benches are  5

No its not possible as NUMBER of blanks are odd in number and DIGITS to be filled are odd too.....
and odd TIMES odd is an odd number only but we know that 30 is an even number

Sin(45)=1/
COS(45)=1/
 sin(45)/cos(45)=1
*this FORMULA is only VALID when A=(45)

3 men or women can do the WORK in 12 days.
1 man or WOMAN can do the work = 12×3 = 36 days.
1 man or women will do in 1 DAY = 1/36 of the work.

6 men in 1 day will day do =  of work
5 women in 1 day will day do =  of work

together they can do in 1 day =  of the work

They will complete in =  days

No it can't be possible as number of BOXES are odd and number to be filled are ALSO odd so no possibiliies COZ odd times odd is odd but 30 is an EVEN number

1.Because rectangle is a PARALLELOGRAM too. 

2. Because Parallelogram has two pairs of equal parallel sides which a rectangle ALSO has. Rectangle is special parallelogram in which the angles are 90 degree.

(b+c)(b-c) + a(a+2b)
b^2-c^2+a^2+2ab
(a+b)^2-c^2
c^2-c^2
0

LET rabbit=r,dog=d,cat=c,

ACCORDING to the question,

r+c=10

d+r=20

d+c=24

On adding the above three EQUATIONS;

r+c+d+r+d=c=10+20+24

2(d+c+r)=54

d+c+r=54/2

d+c+r=27

Thus,weight of dog+weight of cat+weight of rabbit=27 kg

Hope I helped!

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I am class 9 TH student. All theorems mentioned in the NCERT BOOK are important for all chapters. And if it is a geometry chapter most questions will be from the NCERT itself . So, be WELL prepared with NCERT. If u want proof u can also CONSULT RD Sharma that's a good book TOOO

Radius of QUADRANT of circle, R = 8.4cm
PERIMETER of quadrant = 

Perimeter of quadrant = Perimeter of BASE of cone
let radius of cone = r

SLANT HEIGHT of cone is R, so slant height is 8.4cm.

The quadrilateral can be divided into two triangles- ΔABC and ΔADC.
Now find the areas of the triangles and add them.

In ΔABC, AB= 28, BC = 26, AC = 30
s = (28+26+30)/2 = 84 / 2 = 42


Similarly in ΔADC. AD = 40, CD = 50, AC = 30
s = (30+40+50)/2 = 60
applying same formula, 


Total area = 300+600 = 900 cm²

X^2-2x+K )     x^4  - 6 x^3  - 16 x^2  + 25  x  + 10 ( x^2 - 4 x  - (24+k)
                    x^4  - 2x^3 + k x^2
                   ===================
                          - 4 x^3  -(16+k) x^2  + 25 x
                          - 4 x^3  + 8 x^2  - 4 k x
                         =====================
                                     - (16 + k + 8) x^2  + (25+4k) x   + 10
                                     -(24 +k) x^2 + 2(24+k) x - (24+k) k
                                    ============================
                                                 (-23 + 2 k) x + (k^2+ 24 k +10)
 -23 + 2 k = 1       =>  k = 12
 k^2 + 24 k + 10 =  a      =>    a = 442
  REMINDER = x + 442


verification
 ========================================
 x^2 - 2x + 12  )  x^4  - 6 x^3  - 16 x^2 + 25 x + 10 (  x^2  - 4 x - 36
                              x^4 - 2 x^3  + 12 x^2
                             ====================
                                     - 4 x^3 - 28 x^2  + 25 x
                                     - 4 x^3  + 8 x^2  - 48 x
                                         ===============
                                              - 36 x^2  + 73 x  + 10
                                             - 36 x^2 + 72 x   - 432
                                     =========================
                                                                1 x  +  442

============================================

Right ANGLE =90
1/3of 90=30
THEREFORE,2/5 of 30=12

the ANSWER is therefore 12
so the COMPLEMENT of 12 is 78

It is a CIRCLE with RADIUS a.
Area is πa².

3a² - 2b³ = 6 LOG z
⇒ 3 log X - 2 log y = 6 log z
⇒ log x³ - log y² = log z⁶
⇒ log (x³/y²) = log z⁶
⇒ x³/y² = z⁶
⇒ y² = z⁶/x³
⇒ 

ABC is a RIGHT TRIANGLE
Area of right triangle = 1/2 × base × HEIGHT
 
                                  = 1/2 × AB × AC
 
1/2 × (x) × (x+5) = 150

x(x+5) = 300

x² + 5x - 300 = 0

(x+20)(x-15) = 0

x = 15 

Sides AB = 15 cm and AC = 15 + 5 = 20 cm

Hypotenuse BC = 

                          = 

                          = 

                          = 

Here's the GRAPH for the EQUATION:

4x+7=x+2
4x-x=2-7
3x=-5
x=-5÷3
x=-1.666666666666666

14 is the ANSWER  I have a SMALL DOUBT...

The QUESTION should be

4x^2 + 24x + 20.


Refer to the attachment above for your SOLUTION



HOPE it HELPS! ! ! ! ! ! !