Answer:
yn +y -xn
Step-by-step explanation:
Mean= sum of numbers ÷number of numbers
x= sum of n numbers ÷n
<em>Multiply</em><em> </em><em>both</em><em> </em><em>sides</em><em> </em><em>by</em><em> </em><em>n</em><em>:</em>
xn= sum of n numbers
sum of n numbers= xn -----(1)
Let the number added be a.
After a has been added,
y= (sum of n numbers +a) ÷(n+1)
<em>Multiply</em><em> </em><em>both</em><em> </em><em>sides</em><em> </em><em>by</em><em> </em><em>(</em><em>n</em><em> </em><em>+</em><em>1</em><em>)</em><em>:</em>
y(n +1)= sum of n numbers +a
sum of n numbers= y(n +1) -a -----(2)
Substitute (1) into (2):
xn= y(n +1) -a
<em>Expand</em><em>:</em>
xn= yn +y -a
a= yn +y -xn
<u>Let's check!</u>
Let the numbers be 1, 2, 3 and 4.
mean, x= 10 ÷4= 2.5
n= 4
Let the new number added, a, be 7.
a= 7
mean, y= 17 ÷5= 3.4
a= yn +y -xn
a= 3.4(4) +3.4 -2.5(4)
a= 7
Thus, the expression is true.
2y + 2x = 6
2y - x = 12
Subtract
3x = -6, x = -2
2(-2) + 2y = 6
-4 + 2y = 6
2y = 10, y = 5
Final solution: x = -2, y = 5
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:
50%
Step-by-step explanation:
2,000 is 2 x more than 1,000. Or, 1,000 is half of 2,000 and half of 100%=50%.
