1. given points , −5) and , −1), find the coordinates of point that sit 3/8 of the way along ab ,close to a than to b.

 The required co-ordinates of point C are (9, -3.5).

Step-by-step explanation:   We are given the points A(3, -5) and B(19, -1).

We are to find the co-ordinates of point C that sit 3/8 of the way along AB, where the point P is close to A than to B.

According to the given information, we have

So, point C divides the line segment AB in the ratio 3 : 5.

We know that

if a point Q divides a line segment joining the points S(a,b) and T(c,d), in the ratio m : n, then the co-ordinates of Q are

Therefore, the co-ordinates of point C are

Thus, the required co-ordinates of point C are (9, -3.5).

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:

46.2+112.3

step-by-step explanation: