Answer:
(a) Theorem 9
Step-by-step explanation:
Any of the given theorems can be used to prove lines are parallel. We need to find the one that is applicable to the given geometry.
<h3>Analysis</h3>
The marked angles are between the parallel lines (interior) and on opposite sides of the transversal (alternate).
Theorem 9 applies to congruent alternate interior angles.
When you have something like this, all you need to do is substitute the values, the last is for what value of x
For the first one;
((x^2+1)+(x-2))(2)
(x^2+x-1)(2)
(2)^2+(2)-1
4+2-1
5
For the second one;
((x^2+1)-(x-2))(3)
(x^2-x+3)(3)
(3)^2-(3)+3
9-3+3
9
For the last one;
3(x^2+1)(7)+2(x-2)(3)
3((7)^2+7)+2((3)-2)
3(49+7)+2(3-2)
3(56)+2(1)
168+2
170
Answer:
2/11
Step-by-step explanation:
Let's say our fraction is x = 0.1818181818...
The trick is to multiply x by 10²=100 in this case, since there are two repeating digits, and then subtract the original x.
So, in fact you are subtracting 0.181818 from 18.181818 which effectively cancels the entire bit after the decimal point.
You get:
100x - x = 18
Which you can solve:
99x = 18
x = 18/99 = 2/11
