Answer:
C.
and ![y=x^2-6x+9](https://tex.z-dn.net/?f=y%3Dx%5E2-6x%2B9)
Step-by-step explanation:
before answering the problem let us remind the formula for square of sum and differences
![(a+b)^2=a^2+2 \times a \times b + b^2](https://tex.z-dn.net/?f=%28a%2Bb%29%5E2%3Da%5E2%2B2%20%5Ctimes%20a%20%5Ctimes%20b%20%2B%20b%5E2)
![(a-b)^2=a^2-2 \times a \times b + b^2](https://tex.z-dn.net/?f=%28a-b%29%5E2%3Da%5E2-2%20%5Ctimes%20a%20%5Ctimes%20b%20%2B%20b%5E2)
We are going to use the above two formulas to solve each part and come to an answer
A. ![y = (x + 3)^2](https://tex.z-dn.net/?f=y%20%3D%20%28x%20%2B%203%29%5E2)
![(x + 3)^2=x^2+2 \times x \times 3 + 3^2](https://tex.z-dn.net/?f=%28x%20%2B%203%29%5E2%3Dx%5E2%2B2%20%5Ctimes%20x%20%5Ctimes%203%20%2B%203%5E2)
![(x + 3)^2=x^2+6x+9](https://tex.z-dn.net/?f=%28x%20%2B%203%29%5E2%3Dx%5E2%2B6x%2B9)
Hence this option is not correct pair
B. ![y = (x-5)^2](https://tex.z-dn.net/?f=y%20%3D%20%28x-5%29%5E2)
![(x - 5)^2=x^2-2 \times x \times 5 + 5^2](https://tex.z-dn.net/?f=%28x%20-%205%29%5E2%3Dx%5E2-2%20%5Ctimes%20x%20%5Ctimes%205%20%2B%205%5E2)
![(x -5)^2=x^2-10x+25](https://tex.z-dn.net/?f=%28x%20-5%29%5E2%3Dx%5E2-10x%2B25)
Hence this option is also not correct pair
C. ![y = (x -3)^2](https://tex.z-dn.net/?f=y%20%3D%20%28x%20-3%29%5E2)
![(x - 3)^2=x^2-2 \times x \times 3 + 3^2](https://tex.z-dn.net/?f=%28x%20-%203%29%5E2%3Dx%5E2-2%20%5Ctimes%20x%20%5Ctimes%203%20%2B%203%5E2)
![(x -3)^2=x^2-6x+9](https://tex.z-dn.net/?f=%28x%20-3%29%5E2%3Dx%5E2-6x%2B9)
Hence this option is correct as it have equivalent pair
D. ![y = (x + 5)^2](https://tex.z-dn.net/?f=y%20%3D%20%28x%20%2B%205%29%5E2)
![(x + 5)^2=x^2+2 \times x \times 5 + 5^2](https://tex.z-dn.net/?f=%28x%20%2B%205%29%5E2%3Dx%5E2%2B2%20%5Ctimes%20x%20%5Ctimes%205%20%2B%205%5E2)
![(x + 5)^2=x^2+10x+25](https://tex.z-dn.net/?f=%28x%20%2B%205%29%5E2%3Dx%5E2%2B10x%2B25)
Hence this option is also not correct pair
Answer:
Prime factorization: 80 = 2 x 2 x 2 x 2 x 5 which can also be written 80 = 2⁴ x 5. Prime factors are 2*2*2*2*5. 2 and 5 are the prime factors of 80 .
Step-by-step explanation:
I hope i helped you <3
The year of the empire fell = 1610.
We are given x as a variable that represents the year after the given year 1610.
We need to setup an inequality for this situation.
Please note: The year after the year number 1610 will have a number that greater than 1610.
Let us make a statement for inequality to be written.
"The year after the 1610 is greater than 1610".
The year after the 1610 is x and gerater than symbol is >.
So, we can setup an inequality as:
x > 1610 : Read as x is greater than 1610.
Answer: $600
Step-by-step explanation:
The marked price is the price of the trouser without a sales tax.
The sales tax is 10% which means it increased the marked price by 10% to get to $660.
Assume that price is x:
660 = (1 + 10%) * x
x = 660/(1 + 10%)
x = $600