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P, Q, V, and K are collinear with V between K and P, and Q between V and K. If VP = 14x + 4, PK = x + 630, VQ = 17x + 6, and KQ = 11x + 5, solve for VP.

Sagot :

sqdancefan

9514 1404 393

Answer:

  VP = 214

Step-by-step explanation:

The order of points on the line is KQVP. The whole is the sum of the parts, so we have ...

  KQ +QV +VP = KP

  (11x +5) +(17x +6) +(14x +4) = x +630

  42x +15 = x +630 . . . . . . . . . . . . . . . . . collect terms

  41x = 615 . . . . . . . . . . . subtract x+15

  x = 15 . . . . . . . . . . divide by 41

Then the measure of VP is ...

  VP = 14x +4 = 14·15 +4 = 210 +4

  VP = 214

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