Your answer is D. 16x² - 56xy + 49y².
A perfect square trinomial is the result of a squared binomial, like (a + b)². Using this example, the perfect square trinomial would be a² + 2ab + b², as that is what you get when you expand the brackets.
Therefore, to determine which of these is a perfect square trinomial, we have to see if it can be factorised into the form (a + b)².
I did this by first square rooting the 16x² and 49y² to get 4x and 7y as our two terms in the brackets. We automatically know the answer isn't A or B as you cannot have a negative square number.
Now that we know the brackets are (4x + 7y)², we can expand to find out what the middle term is, so:
(4x + 7y)(4x + 7y)
= 16x² + (7y × 4x) + (7y × 4x) + 49y²
= 16x² + 28xy + 28xy + 49y²
= 16x² + 56xy + 49y².
So we know that the middle number is 56xy. Now we assumed that it was (4x + 7y)², but the same 16x² and 49y² can also be formed by (4x - 7y)², and expanding this bracket turns the +56xy into -56xy, forming option D, 16x² - 56xy + 49y².
I hope this helps!
To take a percent, move the decimal point of the percent two places to the left. 7% = 0.07
Then multiply:
12.60 • 0.07 = 0.88
12.60 + 0.88 = 13.48
The total cost is: $13.48
We are given: On january 1, 2000 initial population = 67,255.
Number of people increase each year = 2935 people.
Therefore, 67,255 would be fix value and 2935 is the rate at which population increase.
Let us assume there would be t number of years after year 2000 and population P after t years is taken by function P(t).
So, we can setup an equation as
Total population after t years = Number of t years * rate of increase of population + fix given population.
In terms of function it can be written as
P(t) = t * 2935 + 67255.
Therefore, final function would be
P(t) = 2935t +67255.
So, the correct option is d.P(t) = 67255 + 2935t.
