An acute triangle has two sides measuring 8 cm and 10 cm. what is the best repres
for the third side, s?
o 2 o 6«s< 12.8
os< 2ors > 18
os< 6ors > 12.8

2 < s < 18

Step-by-step explanation:

If we know 2 sides of a triangle to be A & B and let the third side be C, the triangle inequality theorem tells us:

A - B < C < A + B

This means that the third side can take values between the sum and difference of the lengths of the other 2 sides.

So simply, we have

10 - 8 = 2

and

10 + 8 = 18

Hence, the third side can have lengths between 2 and 18

Let third side be s, so we can write:

2 < s < 18

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: