Slopes of perpendicular lines are NEGATIVE RECIPROCAL to each other
namely, if say one has a slope of a/b then the other will have a slope of
what the dickens does that mean?
well, it means that their product is
so... in this case, one has a slope of 3/4 and the other has a slope of d/2
thus
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:
Top left
Step-by-step explanation:
We can plug in the y intercept to find which graph has the correct one.
x = 0 is y intercept
Thus
At this point we known the y intercept is -3 so both graph in the left is considerable.
Notice that the base is the negative, thus the graph would goes down. Therefore the top left would be correct.
Answer: (0.465, 5.535)
Step-by-step explanation:
Formula to calculate the confidence interval (<em>when population standard deviation is unknown</em>) is given by :-
, where = sample mean.
s= sample standard deviation.
n= Sample size.
= critical value
By considering the given information , we have
s=0.75
n= 9
Significance level = [1-0.90=0.1]
By using students' t distribution -table , the critical value for 95% confidence level :
[Note: degree of freedom = n-1]
Now, the 90% confidence interval for the true mean weight of these Southern California avocados will be :
Hence, the required confidence interval =(0.465, 5.535)