Solve for x: y=-3x+6
2 answers:
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Answer:
(a)
(b) 10
(c)
(d) 0
(e) 1024
Step-by-step explanation:
(a)
A = {x ∈ Z | 0 < x, x² ≤ 100}
We need to find all the elements of given set.
The given conditions are
... (1)
Taking square root on both sides.
.... (2)
Using (1) and (2) we get
Since x ∈ Z,
(b)
We need to find the value of | {x ∈ Z | 0 < x, x² ≤ 100}| or |A|. It means have to find the number of elements in set A.
| {x ∈ Z | 0 < x, x² ≤ 100}| = 10
(c)
B = {x ∈ Z | x > 10, x² ≤ 100}
We need to find all the elements of given set.
The given conditions are
... (3)
It means
.... (4)
Inequality (3) and (4) have no common solution, so B is null set or empty set.
(d)
We need to find the value of |{x ∈ Z | x > 10, x² ≤ 100}| or |B|. It means have to find the number of elements in set B.
|{x ∈ Z | x > 10, x² ≤ 100}| = 0
(e)
We need to find the value of | P(A) |. P(A) is the power set of set A.
Number of elements of a power set is
where, n is the number of elements of set A.
We know that the number of elements of set is 10. So the value of |P(A)| is
Therefore |P(A)|=1024.
Answer:
(1) y=C,
(2) x=C
(1) y=0
Step-by-step explanation:
For the linear equation, the power on the solitary variable must be 1.
When the graph of a function crosses/ touches the x-axis than the equation has solution/solutions otherwise it does not has a solution.
When it touches/cresses the x-axis for infinite times then it will have an infinite number of solutions.
(1) The linear equation y-C=0, where y is a variable and C is a non-zero constant, , has the graph parallel to the x-axis. It has no solution as the graph will never cross/touch the x-axis.
Algebraically, in linear equation y-C=0, is independent of x, so there is no value of x for the solution to be exist.
(2) The linear equation x-C=0, where x is a variable and C is a constant, has one solution.
The solution for the equation is
x-C=0
, where
.
(3) The linear equation y=0, where y is a variable, has the graph coinciding with the x-axis. So, it has infinitely many solutions.
Algebraically, in linear equation y=0, is independent of x, so for all value of x, the given equation is zero. Hence, there are infinitely many solutions.