Ms. Hawkinson is planning to take more pictures of her students. She bought 8 rolls of film and 2 camera batteries for $23.00. The next day, she went back and bought 6 more rolls of film and 2 batteries for $18.00. How much did each roll of film and battery cost?

1 Roll = $2.50

1 Battery = $1.50

Step-by-step explanation:

From the question we know that,

8 Rolls + 2 Batteries = $23, and

6 Rolls + 2 Batteries = $18

We can subtract the two equations to obtain a third equation,

(8 Rolls + 2 Batteries) - (6 Rolls + 2 Batteries) = $23 - $18

(8 - 6) Rolls + (2 - 2) Batteries = $23 - $18

2 Rolls = $5

Divide RHS and LHS by 2, to obtain the cost of a roll,

2 Rolls / 2 = $5 / 2

1 Roll = $2.50

If one roll costs $2.50 then 6 rolls cost $15,

6 x $2.50 = $15

We plug in this value into the second equation,

$15 + 2 Batteries = $18

Subtract both sides by $15,

$15 + 2 Batteries - $15 = $18 - $15

2 Batteries = $3

Divide RHS and LHS by 2 to obtain the final answer,

2 Batteries / 2 = $3 / 2

1 Battery = $1.50

the bottom of the spinner is not flat.

step-by-step explanation:

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: