Kelly and greta are asked to write an equation for the scenario below. “one person was able to plant 4 trees in the same amount of time that 5 people working together were able to plant 20 trees.” the girls agree that x represents the number of people working and y represents the number of trees planted. kelly wrote the equation , and greta wrote the equation . which person is correct, and why? kelly is correct; each person plants more trees than the person before them. kelly is correct; and . greta is correct; each person plants 4 more trees than the person before them. greta is correct; and .

Greta is correct.

Explanation:

Greta is correct sine you can substitute different number of people for each of the values of and y and check that each person will still plant 4 trees.

For example:

4x = 4(1) = 4 trees; and

4 x 5 = 20

but you should follow a certain pattern to increase the value of x, such that every foe every value of x, one person is able to plant 4 trees.

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: