Answer:
b||c; c||d; b||d
Step-by-step explanation:
Substituting 10 for x, in the angle beside b we have
7(10)-5 = 70-5 = 65
In the angle beside c we have
10(10)+15 = 100+15 = 115
In the angle beside d we have
12(10)-5 = 120-5 = 115
In the angle beside we have
8(10)-25 = 80-25 = 55
The angle beside c has a vertical angle on the other side of c. This angle would be same-side interior angles with the angle beside b; this is because they are inside the block of lines made by b and c and on the same side of a, the transversal. These two angles are supplementary; this is because 65+115 = 180. Since these angles are supplementary, this means that b||c.
The angle beside c and the angle beside d would be alternate interior angles; this is because they are inside the block of lines made by c and d and on opposite sides of the transversal. These two angles are congruent; this means that c||d.
Since b||c and c||d, by the transitive property, b||d.
Answer:
Step-by-step explanation:
The average scores s (on a 100 point scale) for the students can be modeled by
s = 75 - 6 In(t + 1), 0 < t < 12
where t is the time in months.
a) Since the students were given an exam and then retested monthly with equivalent exams, then,
For the original exam, t = 0
Therefore,
s = 75 - 6 In(0 + 1) = 75 - 6 In1
s = 75 - 6 × 0 = 75
b) the average score after 4 months, t = 4
Therefore,
s = 75 - 6 In(4 + 1) = 75 - 6 In5
s = 75 - 9.66 = 65.34
c) s = 60
Therefore,
60 = 75 - 6 In(t + 1)
6 In(t + 1) = 75 - 60 = 15
In(t + 1) = 15/6 = 2.5
t + 1 = e^2.5 = 12.18
t = 12.18 - 1 = 11.18
t = 11 approximately
