The diagram of the right-angled triangle is shown below
Using the Pythagoras theorem
6² = a²+a²
36 = 2a²
18 = a²
a = √18 = 3√2
Using the Pythagoras theorem
6² = a²+a²
36 = 2a²
18 = a²
a = √18 = 3√2
Write an equation in slope intercept form for the graph of the line.
1 answer:
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Answer:
-3
3/2
Step-by-step explanation:
Y intercep is the point where the line intercepts the y axis. That is 3 in this graph.
slope. Choose two points. For the sake of explainin, I am choosing
(-3,1)
and (0,3). That’s the y intercept!!
The slope is the rate of increase. We have to measure it like we do with stairs. The rise divided by the run
the rise is 2. See the picture. The run is 3(change in x) the x increases by 3 between 2 integer points while the y changes by 3(change in y —>3 minus 1)
Rise= 3
run =2
Slope=rise/run=3/2
Problem 1)
The notation you wrote down is a bit odd. There seems to be a typo. Please double check.
Assuming you meant to write
then the answer is choice D) 2, 6, 18, 54, 162, ...
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Why is this? Because each term is found by multiplying the previous term by 3
first term = 2
second term = (first term)*3 = 2*3 = 6
third term = (second term)*3 = 6*3 = 18
fourth term = (third term)*3 = 18*3 = 54
fifth term = (fourth term)*3 = 54*3 = 162
this pattern continues forever
Extra information: The closed form equation is where 2 is the first term, 3 is the common ratio, and n is a positive integer.
some more info: notice picking any term in sequence {2,6,18,54,162,...} and dividing it over its previous term leads to 3
6/2 = 3
18/6 = 3
54/18 = 3
162/54 = 3
None of the other sequences listed have this property of the adjacent terms dividing to a constant ratio. So none of the other sequences are geometric.
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Problem 2)
The first term is (ie, the first term is 2)
The recursive definition is basically telling us "to get the next term, raise the prior term as an exponent with 3 as the base"
The general template looking like this: nth term = 3^(term just before the nth term)
The first term is 2, so the next term must be 3^2 = 9
The third term would be 3^9 = 19683 and so on.
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<h3>Final Answer: choice B) 9</h3>