Hello,
x^2-y^2=(x+y)(x-y)
x^3-y^3=(x-y)(x²+xy+y²)
Let's use Horner's division
.........|a^3|a^2.|a^1..........|a^0
.........|1....|5....|6..............|8....
a=p...|......|p....|5p+p^2....|6p+5p^2+p^3
----------------------------------------------------------
.........|1....|5+p|6+5p+p^2|8+6p+5p^2+p^3
The remainder is 8+6p+5p^2+p^3 or 8+6q+5q^2+q^3
Thus:
8+6p+5p^2+p^3 = 8+6q+5q^2+q^3
==>p^3-q^3+5p^2-5q^2+6p-6p=0
==>(p-q)(p²+pq+q²)+5(p-q)(p+q)+6(p-q)=0
==>(p-q)[p²+pq+q²+5p+5q+6]=0 or p≠q
==>p²+pq+q²+5p+5q+6=0
And here, Mehek are there sufficients explanations?
Answer:
16 cm
Step-by-step explanation:
Suppose that x is the original width. If that original width is enlarged by a scale factor 5/2 that means that x is multiplied by 5/2 and after that multiplication we obtained new width, 40 cm.
Therefore,
x*(5/2) = 40
We multiply the equation by 2 and obtain:
x*5 = 40*2
5x = 80
Now we divide the equation by 5 and obtain:
x = 80/5
x = 16
We obtained that x, the original width was 16 cm
We just use the sinus rule to calculate this
a / sin alpha = b / sin beta
Alpha is the 90 degree angle from the wall to the floor
beta is the angle from the top of the ladder to the wall,
wich is 90 degrees - 75 degrees (triangle has 180 degrees angles, one is 90 degrees), so beta = 15 degrees
14 foot / sin 90 = b / sin 15
sin 90 = 1
we move the sin15 over to the other side
14 foot x sin 15 = b
b = 3.62 foot
A store manager is redesigning a display shelf. The width of an individual deodorant is 2.576 inches
Width of each deodorant = 2.576 inches
We need to store 25 individual deodorants side by side
Width of 1 deodorant = 2.576 inches
Width of 25 deodorant = 2.576 * 25 inches= 64.4 inches
The shelf must be 64.4 inches wide to store 25 individual deodorants side by side
Answer:
A. X = 0 and x = 6
Step-by-step explanation:
The zeros of the function are where the graph crosses the x axis
It crosses at 0 and 6
x=0 and x = 6
