At hour one, there is 1 organism. At hour two, there is five more organism. At hour three. there will be 6 x 5 = 30 more organisms, etc
This is a geometric sequence with a = 1 (i.e. number of organisms at hour one), r = 5 (number of reprications per hour).
The total number of organisms at hour seven is the sum of the first seven terms of the sequence given by a(r^n - 1)/(r - 1) = 1(5^7 - 1)/(5 - 1) = (78125 - 1)/4 = 78124/4 = 19,531
Set it up as a ratio:
mans shadow over mans height (4/6 ) equals flag pole shadow over flag pole height (15/x)
set them to equal each other:
4/6 = 15/x
cross multiply: 4*x =4x, 15*6 = 90
so you have 4x = 90
now divide both sides by 5 to solve for x, which is the height of the flag pole:
x = 90 / 4 = 22.5 feet tall
Answer:
Step-by-step explanation:
So we have the trinomial:
First, factor out a 2:
Now, factor within the parentheses.
To do so, we want to find two numbers. When multiplied, these two numbers must equal (a)(c) and when added, they must equal b
(a)(c) is 2(-5) or -10 and b is -3. So, we want two numbers that when multiplied together gives -10 and when added gives -3.
-5 and 2 works. Therefore:
Replace -3x with 2x and -5x:
Factor out a 2x for the first two terms. And factor out a negative 5 for the remaining two:
Grouping:
And we're done!
The general rule for 90° counterclockwise rotation about the origin is given by:
(x,y)→(-y,x)
thus given that S has coordinates of (5,4), then rotation through 90° will map the the figure on S'(-4,5). Hence the answer is:
C](-4,5)
Answer:
the answer is B.
Step-by-step explanation:
It makes the problem solve smoother.
