Answer:
An irrational number is a number that can not be written as the quotient of two integer numbers.
Then if we have:
A = a rational number
B = a irrational number.
Then we can write:
A = x/y
Then the product of A and B can be written as:
A*B = (x/y)*B
Now, let's assume that this product is a rational number, then the product can be written as the quotient between two integer numbers.
(x/y)*B = (m/n)
If we isolate B, we get:
B = (m/n)*(y/x)
We can rewrite this as:
B = (m*y)/(n*x)
Where m, n, y, and x are integer numbers, then:
m*y is an integer
n*x is an integer.
Then B can be written as the quotient of two integer numbers, but this contradicts the initial hypothesis where we assumed that B was an irrational number.
Then the product of an irrational number and a rational number different than zero is always an irrational number.
We need to add the fact that the rational number is different than zero because if:
B is an irrational number
And we multiply it by zero, we get:
B*0 = 0
Then the product of an irrational number and zero is zero, which is a rational number.
A:
1) Use difference of squares:
2) Use difference of squares:
B:
1) Factor out common terms in the first two terms, then in the last two terms.
Factor out the common term y-1
C:
1) Collect like terms
2) Simplify.
D:
a3 – a2 – ab + a + b – 1
= a3 – a2 – ab + b + a – 1
= a2 (a – 1) – b (a – 1) + 1 (a – 1)
= (a – 1) (a2 – b + 1)
|-3| is 3 because......
<u>Absolute Value:</u>
In mathematics, the absolute value or modulus |x| of a real number x is the non-negative value of x without regard to its sign. Namely, |x| = x for a positive x, |x| = −x for a negative x, and |0| = 0. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3.
Answer:
seven and eight hundred ninety-three ten-thousandths
Step-by-step explanation: