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A K47 5 years, 1 month ago
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Gaurav Seth 5 years, 1 month ago
CPCT Rules in Maths
The full form of CPCT is Corresponding parts of Congruent triangles. Congruency can be predicted without actually measuring the sides and angles of a triangle. Different rules of congruency are as follows.
- SSS (Side-Side-Side)
- SAS (Side-Angle-Side)
- ASA (Angle-Side-Angle)
- AAS (Angle-Angle-Side)
- RHS (Right angle-Hypotenuse-Side)
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Atul Kumar 5 years, 1 month ago
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Yogita Ingle 5 years, 1 month ago
Let, the speed of a boat in still water = x km/hr
and speed of the stream = y km/hr
→ Speed of a boat in upstream = (x - y) km/hr and
Speed of a boat in downstream = (x + y) km/hr
We know that,
Time = Distance /Speed
According to the conditions in the question, we get

Posted by Krishna Krishna 5 years, 1 month ago
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Keshav Gupta 5 years, 1 month ago
Posted by Haripriya Paradeshi 5 years, 1 month ago
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Yogita Ingle 5 years, 1 month ago
x²-4x-77 = 0
x²-11x+7x-77 = 0 (splitting the middle term)
x(x-11)+7(x-11) = 0
(x+7)(x-11) = 0
x + 7 = 0 and x - 11 = 0
x = -7 and x = 11
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Gaurav Seth 5 years, 1 month ago
Let’s assume the digit at unit’s place as x and ten’s place as y. Thus from the question, the number needed to be found is 10y + x.
From the question it’s told as, the two digits of the number are differing by 2. Thus, we can write
x – y = ±2………….. (i)
Now after reversing the order of the digits, the number becomes 10x + y.
Again from the question it’s given that, the sum of the numbers obtained by reversing the digits and the original number is 66. Thus, this can be written as;
(10x+ y) + (10y+x) = 66
⇒ 10x + y + 10y + x = 66
⇒ 11x +11y = 66
⇒ 11(x + y) = 66
⇒ x + y = 66/11
⇒ x + y = 6………….. (ii)
Now, we have two sets of systems of simultaneous equations
x – y = 2 and x + y = 6
x – y = -2 and x + y = 6
Let’s first solve the first set of system of equations;
x – y = 2 …………. (iii)
x + y = 6 ………….. (iv)
On adding the equations (iii) and (iv), we get;
(x – y) + (x + y) = 2+6
⇒ x – y + x + y = 8
⇒ 2x =8
⇒ x = 8/2
⇒ x = 4
Putting the value of x in equation (iii), we get
4 – y = 2
⇒ y = 4 – 2
⇒ y = 2
Hence, the required number is 10 × 2 +4 = 24
Now, let’s solve the second set of system of equations,
x – y = -2 …………. (v)
x + y = 6 ………….. (vi)
On adding the equations (v) and (vi), we get
(x – y)+(x + y )= -2 + 6
⇒ x – y + x + y = 4
⇒ 2x = 4
⇒ x = 4/2
⇒ x = 2
Putting the value of x in equation 5, we get;
2 – y = -2
⇒ y = 2+2
⇒ y = 4
Hence, the required number is 10×4+ 2 = 42
Therefore, there are two such possible numbers i.e, 24 and 42.
Posted by Abhishek Patil 5 years, 1 month ago
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: (ᵔᴥᵔ) ???? (ᵔᴥᵔ) 5 years, 1 month ago
Posted by Prakrathi Hebri 5 years, 1 month ago
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Gaurav Seth 5 years, 1 month ago
Given,
α and ß are the zeroes of polynomial x² - px + q.
In this quadratic equation,
Coefficient of x² ( a ) = 1
Coefficient of x( b ) = -p
Constant term ( c ) = q.
We have,
⇒ Sum of zeroes = -b/a
⇒ α + ß = - ( - p ) / 1
∴ α + ß = p.
⇒ Product of zeroes = c/a
⇒ αß = q/1 = q
Now,
⇒ ( α + ß )² = α² + ß² + 2 αß
⇒ ( p )² = α² + ß² + 2 q
⇒ p² = α² + ß² + 2 q
∴ α² + ß² = p² - 2q
Posted by Aditya Sharma 5 years, 1 month ago
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Posted by Sujit Singh 5 years, 1 month ago
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Gaurav Seth 5 years, 1 month ago
The values of k = 4.
Given:
Quadratic equation has equal roots.
To find:
The values of k
Explanation:
General format of quadratic equation is .
If the roots of quadratic equation is equal then,
Where,
a = coefficient of x²
b = coefficient of x
c = constant term.
b² - 4ac =0
Comparing the quadratic equation
b = k a=2 c=2
k² - 4×2×2 = 0
k² = 16
k =
k = 4
Therefore, the values of k = 4 if roots are equal.
Posted by Megha Jangir 5 years, 1 month ago
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Gaurav Seth 5 years, 1 month ago
4tan = 3 ⇒ tan = 3/4
we know, tan = perpendicular/base
so, after comparing , perpendicular = 3 and base = 4
∴ hypotenuse = √(3² + 4²) = 5
now, sin = perpendicular/hypotenuse = 3/5
cos = base/hypotenuse = 4/5
now, (4sin - cos + 1)/(4sin + cos - 1)
= (4 × 3/5 - 4/5 + 1)/(4 × 3/5 + 4/5 - 1)
= (12 - 4 + 5)/(12 + 4 - 5)
= 13/11
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Yogita Ingle 5 years, 1 month ago
In Mathematics, Composite numbers are the numbers which have more than two factors, unlike prime numbers which have only two factors, i.e. 1 and the number itself. These numbers are also called composites.
All the natural numbers which are not prime numbers are composite numbers as they can be divided by more than two numbers. For example, 6 is composite because it is divisible by 1, 2, 3 and even 6, such as:
- 6÷1 = 6
- 6÷2 = 3
- 6÷3 = 2
- 6÷6 = 1
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Chandu G 5 years, 1 month ago

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Paritosh Suman 5 years, 1 month ago
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