Applying parallel line postulate twice
36degree=3x degree +2y degree
126 degrees=12 x degree + 2y degree
So, the two equations are:
3x + 2y = 36
and
12x + 2y = 126
Eliminate x to solve for y
-(3x + 2y)= -(36)
-3x - 2y = -36
Combine the equations
(-3x - 2y)+ (12x + 2y) = (-36) + (126)
-3x -2y + 12x + 2y = -36 + 126
9x = 90
x = 10
Plug value of x back into to the equations to solve for y
3(10) + 2y = 36
30 + 2y = 36
2y =6
y = 3
Optional
Plug x into the other equation to check for error
12(10) +2y = 126
120 + 2y =126
2y = 6
y = 3
We can write this expression as 10 - 4 = 9 - x
10 - 4 = 9 - x
6 = 9 - x
6 - 9 = 9 - x - 9
-3 = -x
-3/-1 = -x/-1
3 = x
Hope This Helped! Good Luck!
Step-by-step explanation:
(You might need to draw the triangle on a piece of paper to follow)
First I tried to find the height in terms of<em> a</em>.
If you draw the height in, the triangle is cut in half. That half triangle is a right triangle.
Using the Pythagoras theorem you can find out the height. Since you know that the hypotenuse is also <em>a </em>(because it's an equilateral triangle) the equation would be:
(a/2)² + h² = a²
Assuming that h = height
(It's a/2 because when you cut the triangle in half, the base of the right triangle became a/2)
This equation is simplified:
a²/4 + h² = a²
a² + 4h = 4a²
4h = 3a²
h² = 3a²/4
Now, remeber that everything is squared so it should be
h = a√3/2
Now we have the height. To get the area we need to multiply it by the base, which is <em>a, </em>and then divide it by 2<em>.</em>
a√3/2 × a ÷ 2
a²√3/2 ÷ 2
a²√3/4
And there you go. Thats the area.
Answer:
a) True
b) False
c) True
d) False
e) Not a proposition
f) Not a proposition
Step-by-step explanation:
Proposition:
- It is a declarative statement that is either false or true.
- It cannot be both true or false.
a) Boston is the capital of Massachusetts.
The given statement is true. Hence, the given statement is a proposition.
b) Miami is the capital of Florida.
The given statement is false. Hence, the given statement is a proposition.
c) 2 + 3 = 5.
The given statement is true. Hence, the given statement is a proposition.
d) 5 + 7 = 10.
The given statement is false. Hence, the given statement is a proposition.
e) x + 2 = 11.
The given statement can neither be true or false. It depends on the value of x. Hence, it is not a proposition.
f ) Answer this question.
The given statement is not a declarative in nature. Hence, it is not a proposition.
