If x+y = 5, y+z = 7and z+x = 12, what is the value of x+y+z?
⇒ x+y+z = 12
2 (x + y + z) = 24
How many auxiliary formulae can be formed from the expression in the box?
3 formulae with the three unknowns can be formed from the given expression.
What is the difference between 3a + 2b and −2a − 5b?
(3a + 2b) − (−2a − 5b)
= 3a + 2b + 2a + 5b = 5a + 7b
The length and breadth of a rectangular plot are I and b. Two rectangular paths each of width W run inside the plot one parallel to the length and the other parallel to the breadth. What is the total area of the paths?
Area of the path along length = l×w
Area of the path along breadth = l×w
The common area of the paths = w2
∴ Total area of the path = lw+lw−w2 = (l+b−w)w
In a two digit number, the units digit is x and tens digit is (x+3). What is the sum of the digits in the number?
Sum of units digit (x) and tens digit (x + 3) is x + x + 3 = 2x+3.
A and B are polynomials and each is the additive inverse of the other. What does it mean?
When a certain number, 'm' is divided by 5 and added to 8, the result is equal to thrice the number subtracted from 4. What is the value of 'm?
5 added to thrice a number is equal to 12 added to twice the number. What is the number?
In the figure given what is the perimeter, in cm, of the triangle?
If , find the value of x.
⇒ C(x−b) = x−a
⇒ x =
Match the following.
Which of the following is true?
If x = 3, a = (−1) and b= (−2), what is the value of 2−6x + 4a−3b?
For what value of 'm' is 9 − 5m = (−1)?
Simplify x2y3 −1.5x2y3+1.4x2y3.
What is the value of(a3−2a2+4a−5)−(−a3−8a+2a2+5)?
a3−2a2 + 4a − 5 −(−a3 − 8a + 2a2+5)=a3 − 2a2 + 4a − 5 + a3 + 8a - 2a2-5
=2a3 − 4a2 + 12a − 10
By how much is x4−4x2y2+y4 less than x4+8x2y2+y4?
What is the sum of ; and a2+b3+c3?
+ (a2 + b3 + c3)
Match the following.
Substitute the given values in the expressions and evaluate.
a3−b3 = 33−23 = 9−8 =1
z3−3 (z−10) =103−3(10−10)
=103 − 0 =1000
x2+2x+1 = (−1)2 + 2(1)+1
= 1−2+1 = 0
Simplify the following expression.x(y−z)−y(z−x)−z(x−y)
x(y−z) − y(z−x) − z(x−y)
= xy − xz − yz + xy − zx + yz
= 2xy − 2zx = 2x(y−z)