Answer: One of them is the set {1,2,3,4,5,6}itself; one is the empty set, containing no elements. “Proper subset of a set ” usually denotes a subset in which at least one element of the original set is missing; so one of the subsets - the original set iitself - is not a proper subset. Therefore the answer is 63.
Step-by-step explanation:
Answer:

Step-by-step explanation:
Please refer to the image attached with this answer. Assuming our triangle to be ΔABC and Line AD meeting BC at D.
As we are given that side b = side c
The angle subtended by them ∠B and ∠C must be equal . Let us assume them to be x each . hence
x + x + 52° +31° = 180°
2x + 73° = 180°
2x = 180°- 73°
2x = 107 °
x = 53.5°
Hence in ΔACD
x+ 31°+∠2= 180°
53.5°+31°+ ∠2 = 180°
∠2=180°-84.5°
∠2=95.5°
Also
∠1 + ∠2 = 180°
∠1 + 95.5° = 180°
∠1 = 180°-95.5°
∠1 =84.5°
Now applying Sine rule in ΔABD




Hence we have c as 15.14
as we are given that side c = side b , b=15.14
The properties of any triangle says that the sum of two sides of any triangle is always greater than the third side. Hence
a<b+c
12+2x-6<15.14+15.14
6+2x<30.28
2x<30.28-6
2x<24.28
x<12.14
also side a must be greater than 0
12+2x-6>0
6+2x>0
2x>-6
x>-3
Hence the range of x will be
-3 <x < 12.14
D. X=10 all you have to do is pick an answer and plug it in
Answer:
4/33
Step-by-step explanation:
We seek to find the repeating decimal 0.121212... in the form of a fraction.
First, set x equal to this decimal:
x = 0.121212...
Multiply both sides by 100:
100x = 12.121212....
Now, let's subtract the original equation from this new one:
100x = 12.121212....
- x = 0.121212....
We realize that since the repeating decimal part goes on forever, we can simply cancel it out when we subtract. So we're left with:
100x - x = 12 - 0
99x = 12
Divide both sides by 99:
x = 12/99 = 4/33
The answer is 4/33.
<em>~ an aesthetics lover</em>
We know that
the area of a rectangle=length*width
let
length=x-3
width=x+8
area=42 ft²
so
42=(x-3)*(x+8)----------> x²+8x-3x-24=42--------> x²+5x-66=0
using a graph tool-------> to resolve the second order equation
see the attached figure
the solution is
x=6
hence
length=x-3------> 6-3-----> 3 ft
width=x+8 ------> 6+8----> 14 ft
the answer is<span>
the dimensions of the rectangle are 3 ft x 14 ft</span>