Answer:
(2a +b)·(13a^2 -5ab +b^2)
Step-by-step explanation:
The factorization of the difference of cubes is a standard form:
(p -q)^3 = (p -q)(p^2 +pq +q^2)
Here, you have ...
so the factorization is ...
(3a -(a -b))·((3a)^2 +(3a)(a -b) +(a -b)^2) . . . . substitute for p and q
= (2a +b)·(9a^2 +3a^2 -3ab +a^2 -2ab +b^2) . . . . simplify a bit
= (2a +b)·(13a^2 -5ab +b^2) . . . . . . collect terms
9514 1404 393
Answer:
a) yes; 12/15/17 ~ 20/25/x; SAS
b) x = 28 1/3
Step-by-step explanation:
The left-side segments are in the ratio ...
top : bottom = 12 : 8 = 3 : 2
The right side segments are in the ratio ...
top : bottom = 15 : 10 = 3 : 2
These are the same ratio, and the angle at the peak is the same in both triangles, so the triangles are similar by the SAS postulate.
Normally, a similarity statement would identify the triangles by the labels on their vertices. Here, there are no such labels, so we choose to write the statement in terms of the side lengths, shortest to longest:
12/15/17 ~ 20/25/x
__
The sides of similar triangles are proportional, so the ratio of longest to shortest sides will be the same in the two triangles. In the smaller triangle, the longest side is 17/12 times the length of the shortest side. The value of x will be 17/12 times the length of the shortest side in the larger triangle:
x = 17/12 · 20 = 340/12
x = 28 1/3
Answer:
4
Order of Operations is what you have to use
I'm assuming you meant to write a^4 = 625.
If that is the case, then note how 625 = 25^2, and how a^4 is the same as (a^2)^2
So we go from this
a^4 = 625
to this
(a^2)^2 = 25^2
Apply the square root to both sides and you'll end up with: a^2 = 25
From here, apply the square root again to end up with the final answer: a = 5 or a = -5
As a check:
a^4 = (-5)^4 = (-5)*(-5)*(-5)*(-5) = 25*25 = 625
a^4 = (5)^4 = (5)*(5)*(5)*(5) = 25*25 = 625
Both values of 'a' work out
F(14) would be, 14=1/2x-2
