A line, which goes through the point of intersection of the diagonals of a trapezoid, divides one of the bases into two segments
. The ratio of the length of these segments is m:n. What is the ratio of the length of the segments of the other base?
1 answer:
Answer:
from the same end, the ratio is n : m
Step-by-step explanation:
(Letter refer to the attached figure.)
The diagonals (AC, BD) of a trapezoid (ABCD) divide the figure into triangles. Those triangles having parallel bases are similar (ABP, CDP). A line through the common point of those triangles (P, the intersection point of the diagonals) will further divide those similar triangles into similar triangles.
The ratio of the base segments will be the same (AX:XB = XY:YD). Since one triangle is "upside down" with respect to the other one, if the segment lengths are considered from the same side of the trapezoid, they are in the ratio m:n (=AX:XB) on one base and n:m (=DY:YC) on the other base.
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Answer:
Step-by-step explanation:
We are given that a card is drawn from a hat.
Probability that a red card is drawn, P(red) =
Probability that a blue card is drawn, P(blue) =
Probability that a black card is drawn, P(black) =
Probability that a pink card is drawn, P(pink) =
All these events are mutually exclusive i.e. they do not have anything in common.
For any two events A and B which are mutually exclusive, with probability P(A) and P(B), the probability that any one of the two events occur:
Here event A can be thought of as drawing a blue card and
event B can be thought of as drawing a black card
So, P(blue or black) = P(blue) + P(black)
So, the probability that a blue or black card is drawn from the hat:
Based on the exchange rate, at the end of the trade, Lewis will have 31 puppets and 2 puzzles left over while Geppeto will have 158 puzzles and 4 puppets left over.
<h3>What is the exchange rate of puzzles for puppets?</h3>The exchange rate of puzzles for puppets is 3 to 1.
Geppeto has 20 puppets to exchange for puzzles.
Lewis has 50 puzzles to exchange for puppets.
Number of times Lewis can exchange puzzles for puppets = 50/3 = 16 times.
Lewis will get 16 puppets in exchange for 48 puzzles.
Therefore;
Lewis will have 16 + 25 puppets = 31 puppets and 2 puzzles left over
Geppeto will have 48 + 100 puzzles = 158 puzzles and 4 puppets left over.
in conclusion, the exchange rate determines the how many puzzles and puppets will each one have after they complete their trade.
Learn more about exchange rate at: brainly.com/question/2202418
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