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Given AD is the median of ΔABC and E is the midpoint of AD
Through D, draw DG || BF
In ΔADG, E is the midpoint of AD and EF || DG
By converse of midpoint theorem we have
F is midpoint of AG and AF = FG → (1)
Similarly, in ΔBCF
D is the midpoint of BC and DG || BF
G is midpoint of CF and FG = GC → (2)
From equations (1) and (2), we get
AF = FG = GC → (3)
From the figure we have, AF + FG + GC = AC
AF + AF + AF = AC [from (3)]
3 AF = AC
AF = (1/3) AC

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If u r talking about lightning then here is your answers:-

lightning is produce by the position and negative charge particles when ever very little AIR PASSED between the CHARGES ,, positive and negative charge GET contact with each other which GIVE the lightning bolt

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If angle b = angle c
then , AB = AC
ab/2 = ac/2
then , MN = BC

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LET the present AGE of father be x
and the present age of son be y

• The SUM of the ages of a father and his son is 50 years

x + y = 50

x = 50 - y ........ ( i )

• Five Years ago their age will be

Father's age :- ( x - 5 ) years
Son's age :- ( y - 5 ) years

° Five years ago the product of their ages was 175.

( x - 5 ) ( y - 5 ) = 175

XY - 5x - 5y + 25 = 175

xy - 5x - 5y = 175 - 25

xy - 5x - 5y = 150 .... ( ii )


Putting value of x from ( i ) in ( ii )

xy - 5x - 5y = 150

( 50 - y ) y - 5 ( 50 - y ) - 5y = 150

50y - y² - 250 + 5y - 5y = 150

- y² + 50y - 250 = 150

- y² + 50y = 150 + 250

- y² + 50y = 400

y² - 50y + 400 = 0

y² - 40y - 10y + 400 = 0

y ( y - 40 ) - 10 ( y - 40 ) = 0

( y - 10 ) ( y - 40 ) = 0


• ( y - 10 ) = 0

y = 10

• ( y - 40 ) = 0

y = 40
[ neglected as the age of Son can't be more than his own father ]


Putting the value of y as 10 in the ( i ) Equation

x = 50 - y

x = 50 - 10

x = 40


So,
the present age of Father is ( x ) :- 40 years
and the present age of son is ( y ) :- 10years

The no is -1 because the required condition - that the no and its sq are at EQUAL DISTANCES from 0 - is FULFILLED in case of -1 only...

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Mai COPY pe karke batata hu OK

If the van can't CARRY beyond 800g, then how it will carry even a SINGLE box WEIGHING 4kg 500G, which is greater than 800g. The van can't carry any box

Let the number pf persons be 'n'
n*(n-1)/2 = 66
n*(n-1) = 132
n*(n-1) = 12*11
Hence, n = 12 [COMPARING above]
No: of PEOPLE in the room = 12
[formula CHECK: Let there be 3 people namely, A, B & C. Handshakes-- A-B, A-C, B-C..3 nos. formula: 3*2/2 = 3.... Let us consider 4 people, A, B, C, D. Handshakes-- A-B, A-C, A-D, B-C, B-D, C-D..6 nos. formula: 4*3/2 = 6..verified]
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Y =67 first of all SEND 5 on RHS and MULTIPLY with 14 and then SUBTRACT 3 from the result

2.101001000010000010000001

1/2 - 2/3 = 1/3
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==================================

Let the original PRICE be X

According to the QUESTION,

After increasing the price by 12%
Price BECOME Rs. 896

X + X × (12/100) = 896

X + 12X/100 = 896

(100X+12X)/100 = 896

112X = 89600

X = 89600/112

X = 800

Hence,

The original price of suit is Rs. 800

Notebooks=1/3×300 
=$100 
MONEY left =200$ 
stationary=1/4×200 
=$50 
money left = 200-50 
=$150 

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The PRIME FACTORS of 5005 are 5,7,11 and 13.

Hi ,

Let x = 0.053777...---( 1 )

multiply EQUATION ( 1 ) , with 1000 ,

1000X = 53.777...---( 2 )

multiply equation ( 2 ) with 10 ,

10000x = 537.777...( 3 )

subtract ( 2 ) from ( 3 ), we get

9000x = 537 - 53

9000x = 484

x = 484/ 9000

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Let the age of son be a years

Age of FATHER = 2a + 20

According to QUESTION,

a + 2a + 20 = 65

=> 3a + 20 = 65

=> 3a = 45

=> a = 15

Son's age = 15 years

Father's age = 50 years

The QUADRATIC EQUATION is

X^2 - X - 12 .....

If these are in AP then a+c= 2B

What are some examples of the commutative property?

Simply PUT, it says that the numbers can be added in any order, and you will still get the same ANSWER. For example, if you are adding one and two together, the commutative property of ADDITION says that you will get the same answer whether you are adding 1 + 2 or 2 + 1. This also works for more than two numbers.

__________________________________

In MATHEMATICS, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it.

Prime factorization of 1234 = 2 * 617

Prime factorization of 432 = 2 * 2 * 2 * 2 * 3 * 3 * 3 

LCM(1234,432) = 2 * 2 * 2 * 2 * 3 * 3 * 3 * 617

                          = 266544.


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Let , and be mutually INDEPENDENT normal random variables havingmean and variance . CONSIDER the random variable What distributiondoes have? The random variable can be written as where , and are mutually independent standard normal random variables. ... Therefore has a Gamma distribution with parameters and .

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