Answer:
If A ⊆ B, then A ⊂ B.
If A = B, then A ⊆ B.
If A = B, then A ⊂ B.
Step-by-step explanation:
In set theory '⊂' is the symbol of proper subset and '⊆' is the symbol of subset of a set.
In option (a),
If A ⊆ B
⇒ A ⊂ B or A = B
Thus, If A ⊆ B, then A ⊂ B.
Option a is true.
(b) If A ⊂ B
⇒ A is the subset of B
That is, all elements of A are also the element of B,
But we can not say A = B
Thus, option b is not true.
(c) If A = B
⇒ A ⊂ B and A ⊃ B or A ⊆ B and B ⊆ A ( Because every set is the subset of itself )
⇒ A ⊆ B.
Option c is true.
(d) If A = B,
⇒ A ⊂ B
Option d is true.
(e) If A ⊂ B,
Then we can not say that,
A = B or A ≠ B
Thus, option e is not correct.
Answer: y+9=-2(x-9)
Step-by-step explanation:
The point-slope equation is
. All we have to do is fill in all the values except for y and x.
To find m, you use
. Since we are given 2 points, we cna plug them in.
. Now that we have our slope m, we can fill in the point slope equation.


Let
x---------> the length of the rectangle
y--------> the width of the rectangle
we know that
A=84 ft²
[area of rectangle]=x*y-----> 84=x*y-----> equation 1
x=y-5------> equation 2
substitute 2 in 1
84=[y-5]*y-----> 84=y²-5y---------> y²-5y-84=0
using a graph tool-----> to resolve the second order equation
see the attached figure
the solution is
y=12
x=y-5-----> x=12-5-----> x=7
the answer isthe length of the rectangle is 7 ftthe width of the rectangle is 12 ft