One way is to find the prime factorization for the denominators which are 3 and 4. The prime factorization of 3 would be 1 x 3 and 4 would be 2 x 2. Since we only use prime numbers to find the prime factorization we would have 2 x 2 x 3 = 12 which give us the the least common denominator for 2/3 and 3/4. Final answer is 12.
school is asking us to find the probability of dogs breeding I’m sorry I don’t understand
Answer:
1. 7
2. 8
Step-by-step explanation:
Answer:
$94.50
Step-by-step explanation:
2 times 9 is 18 leaves a remainder of 1
then that leaves 15 an 2 times 7 gives you 14
so that will be $94.50 for a single meal
First off, we factor out the expression:

In the bracket, separate 8 out of the expression.
![\displaystyle \large{y = 2[ ( {x}^{2} - 6x + 8)] }\\ \displaystyle \large{y = 2[ ( {x}^{2} - 6x) + 8]}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7By%20%3D%202%5B%20%28%20%7Bx%7D%5E%7B2%7D%20-%206x%20%2B%208%29%5D%20%7D%5C%5C%20%20%5Cdisplaystyle%20%5Clarge%7By%20%3D%202%5B%20%28%20%7Bx%7D%5E%7B2%7D%20-%206x%29%20%2B%208%5D%7D)
In x^2-6x, find the third term that can make up or convert it to a perfect square form. The third term is 9 because:

So we add +9 in x^2-6x.
![\displaystyle \large{y = 2[ ( {x}^{2} - 6x + 9) + 8]}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7By%20%3D%202%5B%20%28%20%7Bx%7D%5E%7B2%7D%20-%206x%20%2B%209%29%20%20%2B%208%5D%7D)
Convert the expression in the small bracket to perfect square.
![\displaystyle \large{y = 2[ {(x - 3)}^{2} + 8]}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7By%20%3D%202%5B%20%20%7B%28x%20-%203%29%7D%5E%7B2%7D%20%20%20%2B%208%5D%7D)
Since we add +9 in the small bracket, we have to subtract 8 with 9 as well.
![\displaystyle \large{y = 2[ {(x - 3)}^{2} + 8 - 9]} \\ \displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7By%20%3D%202%5B%20%20%7B%28x%20-%203%29%7D%5E%7B2%7D%20%20%20%2B%208%20-%209%5D%7D%20%5C%5C%20%20%5Cdisplaystyle%20%5Clarge%7By%20%3D%202%5B%20%20%7B%28x%20-%203%29%7D%5E%7B2%7D%20%20%20-%201%5D%7D)
Then we distribute 2 in.
![\displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]} \\](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7By%20%3D%202%5B%20%20%7B%28x%20-%203%29%7D%5E%7B2%7D%20%20%20-%201%5D%7D%20%5C%5C%20)
![\displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]} \\ \displaystyle \large{y = [2 \times {(x - 3)}^{2} ]+[ 2 \times ( - 1)] } \\ \displaystyle \large{y = 2 {(x - 3)}^{2} - 2 }](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7By%20%3D%202%5B%20%20%7B%28x%20-%203%29%7D%5E%7B2%7D%20%20%20-%201%5D%7D%20%5C%5C%20%5Cdisplaystyle%20%5Clarge%7By%20%3D%20%5B2%20%5Ctimes%20%20%7B%28x%20-%203%29%7D%5E%7B2%7D%20%5D%2B%5B%202%20%5Ctimes%20%28%20-%201%29%5D%20%7D%20%5C%5C%20%5Cdisplaystyle%20%5Clarge%7By%20%3D%202%20%7B%28x%20-%203%29%7D%5E%7B2%7D%20%20-%202%20%7D)
Remember that negative multiply positive = negative.
Hence the vertex form is y = 2(x-3)^2-2 or first choice.