Point w is on line segment v x. given vw = 4x - 7, v x = 5x + 1, and
wx = 3x, determine the numerical length of vw:

Step-by-step explanation:

we have that

Point W is between point V and point X

Points W,V and X are collinear

so

-----> equation A (by addition segment postulate)

we know

substitute the given values in the equation A and solve for x

Combine like terms in the right sides

Group terms that contain the same variable

Find the length of VW

substitute the value of x

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

the volume is the product of the area of the base, 3x(3x+4), and the height, 3x-1

step-by-step explanation: