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mixer [17]
3 years ago
13

In △ABC, CM is the median to AB and side BC is 12 cm long. There is a point P∈CM and a line AP intersecting BC at point Q. Find

the lengths of segments CQ and BQ, if P divides CM into CP:PM=1:2.

Mathematics
1 answer:
defon3 years ago
6 0

Answer:

  • CQ = 2.4 cm
  • BQ = 9.6 cm

Step-by-step explanation:

This development is ugly, but it works.

Let area ΔABC = 6a. Then area ΔAMC = 3a, and area ΔAPC = a. Similarly, area ΔBMC = 3a, and area ΔBPC = a.

Let area ΔCPQ = x. Then ...

... area ΔACQ = area ΔAPC + area ΔCPQ

... area ΔACQ = a + x

Define k such that BQ : CQ = k : 1. Then ...

... area ΔBPQ + area ΔCPQ = area ΔBPC

... kx + x = a = (k +1)x

The division of BC into parts of ratio k : 1 means ...

... area ΔABQ = k × area ΔACQ

... area ΔABQ + area ΔACQ = area ΔABC

... k × area ΔACQ + area ΔACQ = area ΔABC

... (k +1)(x +a) = 6a . . . . . . . area ΔACQ = x+a

... (k +1)x +(k +1)a = 6a . . . . . distributive property

... a + (k +1)a = 6a

... k +2 = 6 . . . . . . . . . . . . . . . divide by a, simplify

... k = 4

Now, we know BQ : CQ = 4 : 1, so ...

... BQ = 4/5 × 12 cm = 9.6 cm

... CQ = 1/5 × 12 cm = 2.4 cm

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Georgia [21]

Answer:

There are 68 dogs in the pound.

Step-by-step explanation:

Number of pit bull dogs in a pound = P = 23

Number of chihuahuas dogs in a pound = C = 17

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Total number of dogs in a pound = T

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There are 68 dogs in the pound.

5 0
3 years ago
If b is the midpoint of AC, which of the following choices is the value of x?
katrin [286]
If B is the midpoint of AC, that means that the distances from A to B and B to C are the same. The distance from A to B is 8x + 4, and the distance from B to C is 10x - 6, so we can set these two equivalent:

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Solving for x:

4 = 2x - 6 (subtract 8x from both sides)
10 = 2x (add 6 to both sides)
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8 0
3 years ago
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Dmitry [639]

5/4

(15/16)(4/3) The 4/3 is the reciprocal of 3/4

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Step-by-step explanation:

y=mx+b

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Step-by-step explanation:

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