Answer:
Given: In triangle ABC and triangle DBE where DE is parallel to AC.
In ΔABC and ΔDBE
[Given]
As we know, a line that cuts across two or more parallel lines. In the given figure, the line AB is a transversal.
Line segment AB is transversal that intersects two parallel lines. [Conclusion from statement 1.]
Corresponding angles theorem: two parallel lines are cut by a transversal, then the corresponding angles are congruent.
then;
and
Reflexive property of equality states that if angles in geometric figures can be congruent to themselves.
by Reflexive property of equality:
By AAA (Angle Angle Angle) similarity postulates states that all three pairs of corresponding angles are the same then, the triangles are similar
therefore, by AAA similarity postulates theorem
Similar triangles are triangles with equal corresponding angles and proportionate side.
then, we have;
[By definition of similar triangles]
therefore, the missing statement and the reasons are
Statement Reason
3. Corresponding angles theorem
and
5. AAA similarity postulates
6. BD over BA Definition of similar triangle
Step-by-step explanation:
given,
Answer:
The inverse is 1/2x -3/2
Step-by-step explanation:
y =2x+3
Exchange x and y
x = 2y+3
Solve for y, subtracting 3 from each side
x-3 = 2y+3-3
x-3 =2y
Divide each side by 2
(x-3)/2 = 2y/2
1/2x - 3/2 =y
The inverse is 1/2x -3/2
Answer:
C
Step-by-step explanation:
2x + 1 = 85 (Alternate Interior Angles Theorem)
2x = 84
<em>x = 42</em>
(3y + 5) + (2x + 1) = 180 (Linear Pair Theorem)
3y + 5 + (85) = 180
3y + 5 = 95
3y = 90
<em>y = 30</em>
This is tricky. Fasten your seat belt. It's going to be a boompy ride.
If it's a 12-hour clock (doesn't show AM or PM), then it has to gain
12 hours in order to appear correct again.
How many times must it gain 3 minutes in order to add up to 12 hours ?
(12 hours) x (60 minutes/hour) / (3 minutes) = 240 times
It has to gain 3 minutes 240 times, in order for the hands to be in the correct positions again. Each of those times takes 1 hour. So the job will be complete in 240 hours = <em>10 days .</em>
Check:
In <u>10</u> days, there are <u>240</u> hours.
The clock gains <u>3</u> minutes every hour ==> <u>720</u> minutes in 240 hours.
In 720 minutes, there are 720/60 = <u>12 hours</u> yay !
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If you are on a military base and your clocks have 24-hour faces,
then at the same rate of gaining, one of them would take 20 days
to appear to be correct again.
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Note:
It doesn't have to be an analog clock. Cheap digital clocks can
gain or lose time too (if they run on a battery and don't reference
their rate to the 60 Hz power that they're plugged into).
