Answer:
see below
Step-by-step explanation:
5*72*32 is not a prime factorization to begin with because neither 72, nor 32 are primes. A prime factorization for this product would be:
2*2*2*2*2*2*2*2*3*3*5
and the number with this factorization is 11520.
There is a small chance that what you meant to write was this: 
in which case the number for this prime factorization is 2205.
Answer:
x=12
Step-by-step explanation:
16x-30-(14x-6)=2x-24=0. add 24 on both sides to get 2x=24. divide by 2 on both sides to get x=12
9514 1404 393
Answer:
(b) √65
Step-by-step explanation:
The modulus of a complex number is the root of the sum of the squares of the real and imaginary parts.
|1 -8i| = √(1² +(-8)²) = √(1+64) = √65
Here's a way to do it.
Let 4e +2 = 5n +1 . . . . . . for some integer n
Then e = (5n -1)/4 = n + (n -1)/4
We want (n-1)/4 to be an integer, so let it be integer m.
... m = (n -1)/4
... 4m = n -1
... 4m +1 = n
Substituting this into our expression for e gives
... e = (5(4m+1) -1)/4 = (20m +4)/4 = 5m +1
e = 5m+1 for any integer m
Answer:
first, find the area of the circle cut.
r= 3 feet
π=3.14
area of a circle= πr²= 3.14×3×3= 28.26 sq.feet
Now, find the area of the rectangle and subtract it by the area of the circle.
area of rectangle = l×b
length of the rectangle= 16 feet
breadth/width of the rectangular garden= 14 feet
area= 16×14= 224 sq. feet
now, area of the garden surrounding the koi pond= 224-28.26
=195.74 sq. feet
