Answer:
x = 2
Step-by-step explanation:
logx + log(2x - 1) = log 6
Apply log rules,
x(2x - 1) = 6
2x^2 - 1x = 6
x = 2 (true) or x = -3/2 (False)
Answer:
angle 4 is a full angle because it is represented full 110
Answer:
Step-by-step explanation:
Given that:
Point 
is interior of 
.
To find:
Solution:
First of all, let us represent the given values in the form of a diagram.
Kindly refer to the attached image for the given points and values of angles.
We can clearly see that:
Putting all the values given in above equation, we get:
Answer:
Concert ticket now costs $79.
Step-by-step explanation:
21% is being removed from the original cost, in this case, that's $21. 100-21=79. Hope this helps ;)
If points A, E and C are colinear, then they lie on the same line. The same statement you can say about points B, F and D.
1. Consider triangles AOC and BOD. In these triangles:
- AO≅OB (given);
- CO≅OD (given);
- ∠AOC≅∠BOD (as vertical angles).
Thus, ΔAOC≅ΔBOD by SAS Postulate (If any two corresponding sides and their included angle are the same in both triangles, then the triangles are congruent). Corresponding parts of congruent triangles are congruent, then
- AC≅BD;
- ∠ACO≅∠BDO;
- ∠CAO≅∠DBO.
Since angles ACO and BDO are alternate interior angles between lines AE and BF with transversal CD and these angles are congruent, then lines AE and BF are parallel.
This gives you that
2. Consider triangles ECO and FDO. In these triangles
- ∠CEO≅∠OFD (previous proof);
- CO≅OD (given);
- ∠ECO≅∠ODF (previous proof).
Therefore, ΔECO≅ΔFDO by AAS Postulate (if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent). Then CE≅FD.
3. Note that
Since AC≅BD and CE≅DF, then AE=AC+CE=BD+DF=BF.
