Answer:
between 30 yards and 150 yards
Step-by-step explanation:
we know that
The <u><em>Triangle Inequality Theorem</em></u> states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Let
x ----> the possible lengths of the third hallway in yards
<em>Applying the Triangle Inequality Theorem</em>
1) 90+60 > x
150 > x
Rewrite
x < 150 yd
2) 60+x> 90
x > 90-60
x > 30 yd
The possible lengths of the third hallway in yards is the interval
(30,150)
All real numbers greater than 30 yards and less than 150 yards
therefore
between 30 yards and 150 yards
I don't think this is a question... could you elaborate a bit?
Answer:
b) alternate exterior angles theorem
Step-by-step explanation:
When two lines are cut by a transversal, the alternate exterior angles are congruent. In the first diagram:
- x and y are congruent
- a and b are congruent
Comparing with our given lines, j, k and m.
We can see that the two given angles are in the same position as in the first image. Therefore, lines j and k are parallel by the alternate exterior angles theorem.
9 books cost 32
Step-by-step explanation:
5 books =20
1 book= 5÷20 = 4
9 books = 4×9 = 32
A regular octagon has 8 sides, so it would coincide exactly each time the vertices fall into the same places. In one full 360-degree rotation, any "selected" vertex would fall into all 7 other vertices one after the other, before going back to its original position. Therefore, there would be 8 times during the rotation that the octagon coincides with the preimage.
