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An Axiom is a mathematical statement that is assumed to be true. There are five basic axioms of algebra. The axioms are the reflexive axiom, symmetric axiom, transitive axiom, additive axiom and multiplicative axiom. Reflexive Axiom: A number is equal to itelf. (e.g a = a). An axiom would refer to a self-evident assumption common to many areas of inquiry, while a postulate referred to a hypothesis specific to a certain line of inquiry, that was accepted without proof. As an example, in Euclid's Elements, you can compare "common notions" (axioms) with postulates.
Gaurav Seth 4 years, 2 months ago
Axioms or Postulate is defined as a statement that is accepted as true and correct, called as a theorem in mathematics. Axioms present itself as self-evident on which you can base any arguments or inference. These are universally accepted and general truth. 0 is a natural number, is an example of axiom.
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Gaurav Seth 4 years, 2 months ago
Field had shape of rectangle since has difference in length and width. The perimeter of rectangle can be expressed as:
P = 2 × (a + b)
If:
a = 100 m
b = 70 m
Then
P = 2 × (100 m + 70 m)
P = 2 × 170 m
P = 340 m.
If posts are on every 5 m, the number of needed posts is:
340 m ÷ 5 m = 68.
Thus, 68 posts are needed for the fence.
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Gaurav Seth 4 years, 2 months ago
A Rational Number can be made by dividing two integers. (An integer is a number with no fractional part.)
If a number is expressed in the form of p/q then it is a rational number. Here p and q are integers, and q is not equal to 0. A rational number should have a numerator and denominator. Examples: 10/2, 30/3, 100/5
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Gaurav Seth 4 years, 2 months ago
An equation is said to be linear equation in two variables if it is written in the form of ax+by+c=0, where a,b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
The solution for such an equation is a pair of values, one for x and one for y which further makes the two sides of an equation equal.
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5x-3y=3
put x = 0 and y = k
5 (0) - 3 (k) = 3
-3k = 3
k = 3/-3
k = -1
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Gaurav Seth 4 years, 2 months ago
Given equation is:
2x+y=7
For x = - 1, we get
−2+y=7
⇒y=9
∴ (-1, 9) is a solution.
For x = 0, we get
⇒0+y=7
⇒y=7
∴ (0, 7) is a solution.
For x = 1, we get
⇒2+y=7
⇒y=5
∴ (1, 5) is a solution.
For x = 2, we get
⇒4+y=7
⇒y=3
∴ (2, 3) is a solution.
Hence, we have four solution (−1,9),(0,7),(1,5)and(2,3)
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Gaurav Seth 4 years, 2 months ago
We know that,x3 - y3 = (x - y)(x² + xy + y²) ....(i)
Given that, x/y + y/x = -1
(x² + y²)/xy = -1
x² + y² = -xy
x² + y² + xy = 0
(x² + xy + y²) = 0
Multyplying by (x - y) on both sides we get,(x - y)(x² + xy + y²) = (x - y) × 0
x3 - y3 = 0 using (i)
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