Answer:
80/100
Step-by-step explanation:
this is simplified ones
8/10
4/5
Answer:
Step-by-step explanation:
<u>slope-intercept </u><u>form</u>
y= mx +c, where m is the slope and c is the y-intercept
Given line: y= 2x +2
slope= 2
The product of the slopes of perpendicular lines is -1. Let the slope of the unknown line be m.
m(2)= -1
m= -1 ÷2
m= -½
Substitute the value of m into the equation:
y= -½x +c
To find the value of c, substitute a pair of coordinates.
When x= 4, y= 3,
3= -½(4) +c
3= -2 +c
c= 3 +2
c= 5
Thus, the equation of the line is y= -½x +5.
I will try to solve your system of equations.
3
x
−
4
y
=
2
;
9
x
−
12
y
=
6
Step: Solve
3
x
−
4
y
=
2
for x:
3
x
−
4
y
+
4
y
=
2
+
4
y
(Add 4y to both sides)
3
x
=
4
y
+
2
3
x
3
=
4
y
+
2
3
(Divide both sides by 3)
x
=
4
3
y
+
2
3
Step: Substitute
4
3
y
+
2
3
for
x
in
9
x
−
12
y
=
6
:
9
x
−
12
y
=
6
9
(
4
3
y
+
2
3
)
−
12
y
=
6
6
=
6
(Simplify both sides of the equation)
6
+
−
6
=
6
+
−
6
(Add -6 to both sides)
0
=
0
Answer:
Infinitely many solutions.
Only two real numbers satisfy x² = 23, so A is the set {-√23, √23}. B is the set of all non-negative real numbers. Then you can write the intersection in various ways, like
(i) A ∩ B = {√23} = {x ∈ R | x = √23} = {x ∈ R | x² = 23 and x > 0}
√23 is positive and so is already contained in B, so the union with A adds -√23 to the set B. Then
(ii) A U B = {-√23} U B = {x ∈ R | (x² = 23 and x < 0) or x ≥ 0}
A - B is the complement of B in A; that is, all elements of A not belonging to B. This means we remove √23 from A, so that
(iii) A - B = {-√23} = {x ∈ R | x² = 23 and x < 0}
I'm not entirely sure what you mean by "for µ = R" - possibly µ is used to mean "universal set"? If so, then
(iv.a) Aᶜ = {x ∈ R | x² ≠ 23} and Bᶜ = {x ∈ R | x < 0}.
N is a subset of B, so
(iv.b) N - B = N = {1, 2, 3, ...}
