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What is the solution of equation 4 x z equals 28?
4 x z = 28 z = 28/4 z = 7
What is an example of inverse variation?
for variables x and y and constanat k -
What are the different properties of a rational number?
The set of rational numbers is a mathematical field. This requires that if x, y and z are any rational numbers then their properties are as follows:x + y is rational : [closure of addition];(x + y) + z = x + (y + z) : [addition is associative];there is a rational number, denoted by 0, such that x + 0 = x = 0 + x : [existence of additive identity];there is a rational number denoted by -x, such that x + (-x) = 0 = (-x) + x : [existence of additive inverse];x + y = y + x : [addition is commutative];x * y is rational : [closure of multiplication];(x * y) * z = x * (y * z) : [multiplication is associative];there is a rational number, denoted by 1, such that x * 1 = x = 1 * x : [existence of multiplicative identity];for every non-zero x, there is a rational number denoted by 1/x, such that x * (1/x) = 1 = (1/x) * x : [existence of multiplicative inverse];x * y = y * x : [multiplication is commutative];x * (y + z) = x * y + x * z : [multiplication is distributive over addition].
What does real number mean?
It is a number which satisfies all the conditions that are given below:For any three real numbers x, y and z and the operations of addition and multiplication,• x + y belongs to R (closure under addition)• (x + y) + z = x + (y + z) (associative property of addition)• There is an element, 0, in R, such that x + 0 = 0 + x = x (existence of additive identity)• There is an element, -x, in R, such that x + (-x) = (-x) + x = 0 (existence of additive inverse)• x + y = y + x (Abelian or commutative property of addition)• x * y belongs to R (closure under multiplication)• (x * y) * z = x * (y * z) (associative property of multiplication)• There is an element, 1, in R, such that x * 1 = 1 * x = x (existence of multiplicative identity)• For every non-zero x, there is an element, 1/x, in R, such that x * 1/x = 1/x * x = 1 (existence of multiplicative inverse)• x * (y + z) = x*y + x * z (distributive property of multiplication over addition)
Justify that if x plus y equals x plus z then y equals z?
The requirements are that the operation of addition is associative, the existence of an additive identity and additive inverses. Associativity: a + (b + c) = (a + b) + c = a + b + c Identity: The set contains a unique element, called the additive identity and often denoted by 0 with the property that a + 0 = 0 + a = a for all a in the set. Inverse: For each element in the set, x, there exists an element which is its additive inverse. For addition, this is denoted by -x, and has the property that -x + x = 0. x + y = x + z Add the inverse of x to both sides: -x + (x + y) = -x + (x + z) By associativity: (-x + x) + y = (-x + x) + z -x is additive inverse of x, so: 0 + y = 0 + z 0 is additive identity, so y = z
