<u>Answer:</u>
Amount collected in 2012 = 3.49
and in 2013 = 3.35
<u>Explanation:</u>
Let x be the baggage fees collected in 2013 and
y be the baggage fees collected by airlines in 2012
From the given question we can obtain two equations as follows:
x + y = 6.84 $ - eq 1
and
y = 0.14 + x
as fees in 2012 exceeds that in 2013 by 0.14$
Now, solving these two equations by substitution,
we substitute y = 0.14 + x in eq 1
and solve for x,
which gives us x = 3.35 and
substituting this value in eq 1
we get y = 3.49
Answer:
420
Step-by-step explanation:
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.
