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!
Question 23:
x = 4
DE = 44
Question 24:
x = 25
SE = 28
Step-by-step explanation:
As RS is the perpendicular bisector of DE, it will divide DE in two equal parts DS and SE
<u>Question number 23:</u>
Given
DS = 3x+10
SE = 6x-2
As the two segments are equal:
Subtracting 10 from both sides
subtracting 6x from both sides
Dividing both sides by -3
Now
And
<u>Question No 24:</u>
Given
DS = x+3
DE = 56
We know that:
So
DS = 
As DS is 28, SE will also be 28
Hence,
Question 23:
x = 4
DE = 44
Question 24:
x = 25
SE = 28
Keywords: Bisector, Line segment
Learn more about line segments at:
#LearnwithBrainly
Answer:
1/2
Step-by-step explanation:
The radius is 1/2 of the diameter
Answer:
y = 4x + 3
Step-by-step explanation:
To do this, put the new line into the form y = mx + b where m is the slope and b is the y-intercept.
When two lines are parallel, they have the same slope. Since, the slope of the first line is 4, that means the slope of the second line is also 4.
So far, the equation is y = 4x + b.
Then, since you know (-2, -5) is a solution, x = -2, y = -5 is a solution so you can plug this into the equation.
This would be:
-5 = 4 * -2 + b
-5 = -8 + b
3 = b
This means the equation is y = 4x + 3.
