Point C is on the midpoint of a section of highway, represented by AB. If AB = 32 miles, AC = 4x miles, and CB = 12 + x miles, explain three different ways
that
you
could
solve for x.

To solve this question, we need to understand the concept of midpoint.

Doing this, we get that x is equals to 4 miles., and we find it using each of these three ways:

Segment:

C is the midpoint of the segment AB, which means that:

The distance of the initial point A to the midpoint C is the same as the distance of the midpoint C to the final point B.

The distance of the midpoint to one of the endpoints is half the total distance, that is:

Solution:

We have to solve for x, considering one of the three relations.

Considering:

The solution for x is x = 4 miles.

A similar question is found at

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:

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step-by-step explanation: