Answer:
The quick answer I think will help you in the long run is that (f*g)(x) is just another way of saying f(x)*g(x). If that is enough, then ignore the rest of my response. Otherwise, keep reading.
For this problem
Step-by-step explanation:(f*g)(x) = f(x)*g(x)
You are given f(x) = 3x + 2 and g(x) = x^2 + 1. Simply substitute these expressions as follows:
f(x)*g(x) = (3x + 2)*(x^2 + 1)
Notice how I put each expression in parentheses. This practice will help immensely when dealing with more complicated expressions like this. Next, we simplify:
(3x + 2)*(x^2 + 1) = (3x)(x^2) + (3x)(1) + (2)(x^2) + (2)(1) <-- the foil method
= 3x^3 + 3x + 2x^2 + 2 <-- simplify each term
= 3x^3 + 2x^2 + 3x + 2 <-- reorganize and group like terms
hope this helped!
The equation of the circle with the new point will be x² + ( y - 2 )² = 16.
<h3>What is a circle?</h3>
The circle is defined as the locus of the point traces around a fixed point called the centre and is equidistant from the outer trace.
Given that:-
- The circle is translated as 2 units up.
The equation of the circle will be formed as:-
We know that the general form of the circle is given as
( x - h )² + ( y - k )² = r²,
where ( h, k ) is the centre and r is the radius. When the circle is shifted 2 units up it means that now its centre will be ( 0, 2). So the equation will be:-
x² + ( y - 2 )² = 16
Therefore the equation of the circle with the new point will be x² + ( y - 2 )² = 16.
Learn more about Circle here:
brainly.com/question/12908707
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First, we would need to figure out how many shelves are needed to build 1 bookcase. To do that, you would need to divide the number of shelves by the number of bookcases it can make.
65 ÷ 13 = 5
Now we know, it takes 5 shelves to build a single bookcase. The next step would be to find out how many shelves it would take to build 6 more bookcases. To find the answer, you would multiply the number of shelves it takes to build 1 bookcase by the number of bookcases that need to be built.
5 x 6 = 30
So, yes, 32 shelves would be more than enough to build 6 more bookcases.
Additive inverses are numbers that when added to another number equal 0. The additive inverse of 5 is -5 and the additive inverse of 6 is -6. Therefore, the new expression is -5-(-6) or -5+6.