Achoreographer uses a number line to position dancers for a ballet. dancers a and b have coordinates 5 and 23, respectively. find the coordinate for the following dancer based on the given location.

dancer e stands at a point that divides the line segment from dancer a to dancer b in a ratio of 2 to 1.

dancer e is
units from dancer a, so the coordinate for dancer e is
.

Dancer E is 12 units from Dancer A, so the coordinate for Dancer E is 17.

Step-by-step explanation:

Distance from Dancer A to Dancer B.

AB = 23 - 5 = 18 units

Distance from Dancer A to Dancer E.

Dancer E is 12 units from Dancer A, so the coordinate for Dancer E is 5 + 12 = 17.

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:

4+4+2x

or

2x+8

step-by-step explanation: