Then make up a word problem that you can use decimals in.
Answer: 12.32
Step-by-step explanation:
7.04 divided by 4 = 1.76. 1.76 x 7 = 12.32.
Answer:
t =log(20) / 0.3 = 10*log(20) / log(1,000) - years - when the tree will have 100 branches.
Step-by-step explanation:
100 = 5 * 10^(0.3t), solve for t
Divide both sides by 5:
20 =10^(0.3t)
Take the log of both sides:
0.3t =log(20)
Divide both sides by 0.3:
Multiply the RHS by 10 / 10
t =log(20) / 0.3 = 10*log(20) / log(1,000) - years - when the tree will have 100 branches.
Answer:
a). r = 
b). At least 5 terms should be added.
Step-by-step explanation:
Formula representing sum of infinite geometric sequence is,
Where a = first term of the sequence
r = common ratio
a). If the sum is seven times the value of its first term.
7(1 - r) = 1
7 - 7r = 1
7r = 7 - 1
7r = 6
r =
b). Since sum of n terms of the geometric sequence is given by,
If the sum of n terms of this sequence is more than half the value of the infinite sum.
![\frac{a[1-(\frac{6}{7})^{n}]}{1-\frac{6}{7}}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5B1-%28%5Cfrac%7B6%7D%7B7%7D%29%5E%7Bn%7D%5D%7D%7B1-%5Cfrac%7B6%7D%7B7%7D%7D)
> 
n[log(0.85714)] < log(0.5)
-n(0.06695) < -0.30102
n > 
n > 4.496
n > 4.5
Therefore, at least 5 terms of the sequence should be added.
Answer:
AB = 24
Step-by-step explanation:
BD = 5x – 26
BC = 2x + 1
AC = 43
Using the segment addition postulate, AC = AB + BC.
We know that BD = BC, BD = 5x-26 and BC = 2x+1. We can set up an equation to find the value of x:
5x - 26 = 2x + 1 Subtract 2x from each side
5x - 26 - 2x = 2x + 1 - 2x
3x-26 = 1 Add 26 to each side
3x-26+26 = 1+26
3x=27 Divide both sides by 3
3x/3 = 27/3
x = 9
This means that BC = 2x + 1 = 2(9) + 1 = 18 + 1 = 19.
We know that AC = AB + BC; using our given information as well as the value of BC we just found, we have
43 = AB + 19 Subtract 19 from each side
43 - 19 = AB + 19 - 19
24 = AB
