Step-by-step explanation:
Hey there!
While factorising you remember to make it take common in most of the expression.
Here;
=mx+cx+my+cy
Take common 'x' in "mx+cx" and 'y' in my + cy.
= x(m+c) + y(m+c)
Now, "(m+c)" common again.
= (m+c) (x+y)
Therefore the factorized form of the expression in (m+c)(x+y).
<u>Hope it helps</u><u>.</u><u>.</u><u>.</u>
The formula for the volume of a cone is (1/3)*pi)*r^3*h. Here, r = 2 units.
Thus, the volume of this particular cone is:
V = (1/3)(3.14)((2 units)^2*(9 units). Please do the math, and then round off your answer to 2 decimal places.
Answer:
D.
Step-by-step explanation:
let's call A the number of copies sold of newspaper A and B the number of copies sold of newspaper B.
So, we can formulate the following equations from the sentence: a certain store sold copies of 256 Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each as:
A + B = 256 (1)
1A + 1.25 B = Total Revenue (2)
Then, r and p are equal to:
(3)
(4)
Isolating A from (4) and B from (1), we get:
(5)
(6)
Finally, replacing (5) and (6) in (3), we get:
Answer: -18 - -18
Step-by-step explanation: Aka negative eighteen minus negative eighteen
Not all expressions of this form can be simplified; but if one can, we
would like the square root to have the form
sqrt(a) + sqrt(b) or sqrt(a) - sqrt(b)
where a and b are positive rational numbers, and a > b to give the
positive square root.
If we assume that sqrt(2-sqrt(3)) has this form, then this must be
true:
(sqrt(a) +- sqrt(b))^2 = 2 - sqrt(3)
Expanding, we get
a + b +- 2 sqrt(ab) = 2 - sqrt(3)
Equating the rational and irrational parts of this equation,
a + b = 2
+-2 sqrt(ab) = -sqrt(3)
The second equation here tells us that we will have to choose the
negative sign in order to have a solution, since square roots have to
be positive. If we now square this equation, we have
a + b = 2
4ab = 3
Solving these equations by substituting in the second, we get
4a(2 - a) = 3
4a^2 - 8a - 3 = 0
8 +- sqrt(64 + 48)
a = ------------------ = 1/2 or 3/2
8
and
b = 2 - a = 3/2 or 1/2.
One choice here will give the positive root, the other the negative
root. We take a > b, so that a = 3/2 and b = 1/2. Consequently, our
solution is
sqrt(2 - sqrt(3)) = sqrt(3/2) - sqrt(1/2) = (sqrt(6) - sqrt(2))/2
Looking for information on this technique, which I didn't recall being
taught, I found this page, which together with some rather advanced
techniques includes a quote from an old algebra text about the method: