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!
Answer:
whenever you're multiplying terms that have exponents you multiply the coefficients and add their exponents:
Step-by-step explanation:
I think the answer to your first question should be:
30a²b - 30ab²
Your second answer is good
whenever you're multiplying terms that have exponents you multiply the coefficients and add their exponents:
for example, 6a²b³c x 2abc = 6(2)(a²)(a)(b³)(b)(c)(c)
= 12a³b⁴c²
Plug in n = 1 into the nth term formula
a(n) = 4n-1
a(1) = 4*1-1
a(1) = 3
So the first term is 3
The second term will be 7 because we add on 4 each time, as indicated by the slope of 4. This is also known as the common difference.
So the nth term is found by adding 4 to the (n-1)st term, in other words,
a(n) = a(n-1)+4
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In summary, the answer is
a1=3; an=an-1+4
which is choice B
Answer: 72 grams.
Step-by-step explanation:
Let be "s" the amount of sugar in grams that must be used for 252 grams of coconut to keep the same ratio of coconut to sugar.
Knowing that in the recipe for the coconut cookies, should be 420 grams of coconut and 120 grams of sugar, and you only have 252 grams of coconut, you can set up this proportion to find "s":
Now, you need to solve for "s":
You need to find the hypotenuse of the right triangle.
4² + 9² = c²
16 + 81 = c²
97 = c²
9.85 = c
There are 5,280 ft in a mile.
Multiply 9.85 by 5,280.
9.85 × 5,280 = 52,008
Multiply 52,008 by 110.
52,008 × 110 = <span>5,720,880
The estimated cost for constructing the street would be $</span>5,720,880.
