Question

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.​

Answer 1

P, Q, V, and K are collinear, the distance VP=214

Given :

P, Q, V, and K are collinear with V between K and P, and Q between V and K

Make a diagram using the above given information

$VP = 14x + 4, \\PK = x + 630, \\VQ = 17x + 6, \\and KQ = 11x + 5$

The diagram is attached below

From the diagram we can see that ,

$PK=VP+VQ+KQ\\Replace \; the \; expressions\\x+630=14x+4+17x+6+11x+5$

Solve the equation for x

$x+630=14x+4+17x+6+11x+5\\x+630=14x+17x+11x+4+6+5\\combine \; like \; terms\\x+630=42x+15\\x=42x+15-630\\x=42x-615\\x-42x=-615\\-41x=-615\\divide\; by \; -41\\x=15$

so , the value of x is 15

We know that VP=14x+4

Replace 15 for x  to solve for VP

$VP=14x+4\\VP=14(15)+4\\VP=214$

Learn more : brainly.com/question/17542197