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!
We assume you want to find the inverse transform of s/(s^2 +3s -4). This can be written in partial fraction form as
(4/5)/(s+4) + (1/5)/(s-1)
which can be found in a table of transforms to be the transform of
(4/5)e^(-4t) + (1/5)e^t
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There are a number of ways to determine the partial fractions. They all start with factoring the denominator.
s^2 +3x -4 = (s+4)(s-1)
After that, you can postulate the final form and determine the values of the coefficients that make it so. For example:
A/(s+4) + B/(s-1) = ((A+B)s + (4B-A))/(s^2 +3x -4)
This gives rise to two equations:
(A+B) = 1
(4B-A) = 0
Answer:
coefficient of x: 2
coefficient of y: 3
coefficient of z: -7
Step-by-step explanation:
To solve this problem, first we need to sum the polynomials A and B, then we need to check the coefficients of x, y and z.
The sum of the polynomials is:
A + B = 5z + 4x^2 - 6y + 2 + 2x + 9y - 12z - 2
A + B = 4x^2 + 2x + 3y - 7z
So, the coefficients are:
coefficient of x^2: 4
coefficient of x: 2
coefficient of y: 3
coefficient of z: -7
Answer:
Step-by-step explanation:
The two angles are inside a right angle. The small box signifies a right angle/ 90° angle.
Therefore, the sum of the angle measures must equal 90. We can set up an equation.
Combine the like terms on the right side. The 2 constants: 56 and 16 can be added.
Since we are solving for x, we must isolate the variable. 72 and x are being added. The inverse of addition is subtraction, so subtract 72 from both sides.
x is equal to 18 and choice A is correct.
