Answer:
Step-by-step explanation:
Hello, please consider the following.
So this is divisible by 3.
Now, to prove that this is divisible by 9 = 3*3 we need to prove that
is divisible by 3. We will prove it by induction.
Step 1 - for n = 1
4+17=21= 3*7 this is true
Step 2 - we assume this is true for k so 
is divisible by 3
and we check what happens for k+1
is divisible by 3 and
is divisible by 3, by induction hypothesis
So, the sum is divisible by 3.
Step 3 - Conclusion
We just prove that is divisible by 3 for all positive integers n.
Thanks
Answer:
AX : XB as AB : AC
AX = 5
XB = 4
AC = 6
AB = x
Step-by-step explanation:
5 : 4 as to x : 6
ratios can also be written as fractions...
5/4 = x/6 ..now we have a proportion...so we cross multiply
(4)(x) = (5)(6)
4x = 30
x = 30/4
x = 15/2 <==== AB = 15/2
Answer: 15.7 minutes
Step-by-step explanation:
Let x be the time in the beginning (in minutes).
Given: The track team is trying to reduce their time for a relay race.
First they reduce their time by 2.1 minutes.
Then they are able to reduce that time by 10
If their final time is 3.96 minutes, then
x-t1-t2= 3.6
x= 3.6+ t1+ t2
x= 3.6+ 2.1+ 10
x= 15.7
Hence, their beginning time was 15.7 minutes.
Answer:
The equivalent expression is;
Step-by-step explanation:
The given expression is:
Recall that:
In our case, 
and 
.
We use this property of exponent to obtain;
2x + 3x + 5x = 60
10x = 60
a = 6
Shortest side = 2x = 12 inches
