the first term is 2 and the 20th term is 1048576 .
<u>Step-by-step explanation:</u>
Here we have , If the sum of the first 12 terms of a geometric series is 8190 and the common ratio is 2. We need to Find the first term and the 20th term. Let's find out:
We know that Sum of a GP is :
⇒
So ,Sum of first 12 terms is :
⇒ 
⇒ 
⇒ 
⇒ 
Now , nth term of a GP is
⇒ 
So , 20th term is :
⇒ 
⇒ 
⇒ 
Therefore , the first term is 2 and the 20th term is 1048576 .
Answer:
The squared form is not a correct form of the quadratic function.
Step-by-step explanation:
Given some forms of quadratic equation. we have to choose the form which is not correct of the quadratic equation.
As the general form and the standard form of quadratic equation is
where a,b and c are constant.
Also, the vertex form is
where (a,b) is vertex.
Only the three forms of quadratic equation exist. No other form like squared form exist.
Hence, the squared form is not a correct form of the quadratic function.
43/5 this is an improper fraction so we will convert it to a mixed number...
(40+3)/5
8+3/5
So he can make 8 complete groups and will have 3 left over.
Answer: Choice A
g(x) = sqrt(2x)
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Explanation:
"sqrt(x)" is shorthand for "square root of x"
f(x) = 3x^2 is given
g( f(x) ) = x*sqrt(6) is also given
One way to find the answer is through trial and error. This would only apply of course if we're given a list of multiple choice answers.
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Let's start with choice A
g(x) = sqrt(2x)
g( f(x) ) = sqrt(2 * f(x) ) .... replace every x with f(x)
g( f(x) ) = sqrt(2 * 3x^2 ) .... plug in f(x) = 3x^2
g( f(x) ) = sqrt(6x^2 )
g( f(x) ) = sqrt(x^2 * 6)
g( f(x) ) = sqrt(x^2)*sqrt(6)
g( f(x) ) = x*sqrt(6)
We found the answer on the first try. So we don't need to check the others.
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But let's try choice B to see one where it doesn't work out
g(x) = sqrt(x + 3)
g( f(x) ) = sqrt( f(x) + 3)
g( f(x) ) = sqrt(3x^2 + 3)
and we can't go any further other than maybe to factor 3x^2+3 into 3(x^2+1), but that doesn't help things much to be able to break up the root into anything useful. We can graph y = x*sqrt(6) and y = sqrt(3x^2 + 3) to see they are two different curves, so there's no way they are equivalent expressions.
9, 27, 45, 54, 81,
These are the multiples of 9.
9 *1
9 *3
9 *5
9 *6
9 *9