Answer:
4, 8, 16, 32, 64
Step-by-step explanation:
The nth term of a geometric sequence is
= a₁
Given
a₇ = 256 and a₁₀ = 2048 , then
a₁ 
= 256 → (1)
a₁ 
= 2048 → (2)
Divide (2) by (1)
= 
r³ = 8 ( take the cube root of both sides )
r = ![\sqrt[3]{8}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B8%7D)
= 2
Substitute r = 2 into (1)
a₁ × 
= 256
a₁ × 64 = 256 ( divide both sides by 64 )
a₁ = 4
Then
a₁ = 4
a₂ = 2a₁ = 2 × 4 = 8
a₃ = 2a₂ = 2 × 8 = 16
a₄ = 2a₃ = 2 × 16 = 32
a₅ = 2a₄ = 2 × 32 = 64
May need to change into a mixed fraction
33.3 because 27/50=36/x and x=66.67 and thats how much as decayed after 36 hours but you want what is left so subtract from 100 and get 33.3
Answer:
3.8
Step-by-step explanation:
3 8/10 can be written as 3.xx because all we have to do is 8 divided by 10 which equals .8 so 3+.8=3.8
Answers:
- Total equation: x+y = 80
- Legs equation: 2x+4y = 248
- How many ducks? 36
- How many cows? 44
====================================================
Further explanation:
- x = number of ducks
- y = number of cows
x+y = 80 is the total equation (ie the head count equation) since we assume each animal has 1 head, and there are 80 heads total.
That equation can be solved to y = 80-x after subtracting x from both sides.
The legs equation is 2x+4y = 248 because...
- 2x = number of legs from all the ducks only
- 4y = number of legs from all the cows only
- 2x+4y = total number of legs from both types of animals combined
We're told there are 248 legs overall, so that's how we ended up with 2x+4y = 248
------------
Let's plug y = 80-x into the second equation and solve for x.
2x+4y = 248
2x+4( y ) = 248
2x+4( 80-x ) = 248
2x+320-4x = 248
-2x+320 = 248
-2x = 248-320
-2x = -72
x = -72/(-2)
x = 36
There are 36 ducks
Now use this x value to find y
y = 80-x
y = 80-36
y = 44
There are 44 cows.
------------
Check:
36 ducks + 44 cows = 80 animals total
36*2 + 44*4 = 72 + 176 = 248 legs total
The answers are confirmed.
