Answer:
-16.3 ≥ q
Step-by-step explanation:
–5.3 ≥ 6.7 + 4.3 + q
Combine like terms
–5.3 ≥ 11 + q
Subtract 11 from each side
–5.3-11 ≥ 11-11 + q
-16.3 ≥ q
Let us denote the semi arcs as congruent angles. This means that angles FEJ and EFJ are congruent (That is, they have the same measure). Since angles FEJ and EFJ have the same measure, this implies that sides EJ and FJ are equal. Since angles EJK and FJH are supplementary angles to angle EJF, this implies that EJK and FJH have the same measure.
Using the Angle Side Angle (SAS) criteria, we determine that triangles EKJ and triangle FJH are congruent. This implies that sides EK and FH are equal and that angles EKJ and FHJ are congruent. Note that angle EKJ is the same as EKF and that FHJ is the same as FHE.
Once again, since angles EKF and FHJ are congruent, and angle EKD is supplementary to the angle EKJ when angle FHG is supplementary to angle FHJ, then we have that angles EKD and angle FHG are congruent.
Using again the SAS criteria, we determine that triangles EKD and FHG are congruent.
From this reasoning, we have proved the following facts:
Triangle DEK is congruent to triangl GFH
Angle EKF is congruent to angle FHE
Segment EK is the same as segment FH
Answer: 2 19/24 hours was spent in practising.
Step-by-step explanation:
During the first hour, they practiced for 5/8 of an hour. During the second hour, they practiced for 2/3 of an hour. This means that the total time for which they practiced in the first 2 hours would be
5/8 + 2/3 = 31/24 hours
During the last two hours, they first practiced for 3/5 of an hour, took a 1/2 hour break and then practiced the rest of the time. This means that the rest of the time for which they practiced is
2 - (3/5 + 1/2) = 2 - 11/10 = 9/10
Therefore, the time they spent practicing in total would be
31/24 + 3/5 + 9/10 = 67/24 =
2 19/24 hours
