If the ratio of cats to dogs in the veterinarian clinic is 2 to 3, which ratio does NOT show a possible number of cats to dogs in the clinic?
24 cats, 36 dogs

36 cats, 54 dogs

30 cats, 45 dogs

34 cats, 21 dogs

34 cats, 21 dogs

Step-by-step explanation:

cats: dogs

2   : 3

Multiply by 12 to get 24 cats

2*12 = 24   3*12 = 36   so the first is correct

Multiply by 18 to get 36 cats

2*18 = 36 cats  3*18 = 54 dogs  so the second is correct

Multiply by 15 to get 30 cats

2*15 = 30   3*15 = 45   so the third is correct

Multiply by 17 to get 34 cats

2*17 = 34   3*17 = 51   so the fourth is incorrect

34 cats, 21 dogs

Step-by-step explanation:

34 cats, 21 dogs

34 : 21 is not equivalent to 2 : 3

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:

2(2x + 3) = -4 + 2(2x + 5)

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 6

4x - 6 + 6 = 4x - 6 + 6

4x = 4x

x = x

unlimited solutions.