Lines j and k are intersected by line m. At the intersection of lines j and m, the uppercase left angle is 93 degrees. At the in
tersection of lines k and m, the bottom right angle is 93 degrees. Given the information in the diagram, which theorem best justifies why lines j and k must be parallel? a) alternate interior angles theorem b) alternate exterior angles theorem c) converse alternate interior angles theorem d) converse alternate exterior angles theorem
2 answers:
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.
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Answer:
Sophie will get <u>$56</u> in exchange.
Step-by-step explanation:
Given:
TravelEz sells dollars at a rate of ($1.40)/(1 euro).
And dollars they buy at a rate of ($1.80)/(1 euro).
Sophie exchanged $540 to get 300 euros, at the beginning of trip.
And, she is left with 40 euros at the end of trip.
So exchanges the euros back to dollars.
Now, to find the dollars Sophie will get in exchange.
Let the dollars Sophie will get in exchange be
The rate at which TravelEz sells dollars =
Number of euros Sophie is left with =
Now, to get the dollars she will get we set proportion:
<em>As, </em><em> is equivalent </em>
<em>.</em>
<em>So, </em><em> is equivalent to </em>
<em>.</em>
Thus,
By cross multiplying we get:
Therefore, Sophie will get $56 in exchange.
Answer:
The larger cross section is 24 meters away from the apex.
Step-by-step explanation:
The cross section of a right hexagonal pyramid is a hexagon; therefore, let us first get some things clear about a hexagon.
The length of the side of the hexagon is equal to the radius of the circle that inscribes it.
The area is
Where is the radius of the inscribing circle (or the length of side of the hexagon).
Now we are given the areas of the two cross sections of the right hexagonal pyramid:
From these areas we find the radius of the hexagons:
Now when we look at the right hexagonal pyramid from the sides ( as shown in the figure attached ), we see that
form similar triangles with length
Therefore we have:
We put in the numerical values of ,
and solve for
:
