Answer: g(f(-1))=-22
Step-by-step explanation:
To find g(f(-1)), you want to first want to solve f(-1). Once you solved that, you plig the answer you get into g(x). Then, you will have your final answer.
f(-1)=-(-1)²+4(-1)-9 [exponent]
f(-1)=-1+4(-1)-9 [multiply]
f(-1)=-1-4-9 [subtract from left to right]
f(-1)=-14
We have found that f(-1)=-14. Now, we know in -14 into g(x) and solve.
g(-14)=(-14)-8 [subtract]
g(-14)=-22
Now, we know that g(f(-1))=-22.
sin(<em>θ</em>) + cos(<em>θ</em>) = 1
Divide both sides by √2:
1/√2 sin(<em>θ</em>) + 1/√2 cos(<em>θ</em>) = 1/√2
We do this because sin(<em>x</em>) = cos(<em>x</em>) = 1/√2 for <em>x</em> = <em>π</em>/4, and this lets us condense the left side using either of the following angle sum identities:
sin(<em>x</em> + <em>y</em>) = sin(<em>x</em>) cos(<em>y</em>) + cos(<em>x</em>) sin(<em>y</em>)
cos(<em>x</em> - <em>y</em>) = cos(<em>x</em>) cos(<em>y</em>) - sin(<em>x</em>) sin(<em>y</em>)
Depending on which identity you choose, we get either
1/√2 sin(<em>θ</em>) + 1/√2 cos(<em>θ</em>) = sin(<em>θ</em> + <em>π</em>/4)
or
1/√2 sin(<em>θ</em>) + 1/√2 cos(<em>θ</em>) = cos(<em>θ</em> - <em>π</em>/4)
Let's stick with the first equation, so that
sin(<em>θ</em> + <em>π</em>/4) = 1/√2
<em>θ</em> + <em>π</em>/4 = <em>π</em>/4 + 2<em>nπ</em> <u>or</u> <em>θ</em> + <em>π</em>/4 = 3<em>π</em>/4 + 2<em>nπ</em>
(where <em>n</em> is any integer)
<em>θ</em> = 2<em>nπ</em> <u>or</u> <em>θ</em> = <em>π</em>/2 + 2<em>nπ</em>
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We get only one solution from the second solution set in the interval 0 < <em>θ</em> < 2<em>π</em> when <em>n</em> = 0, which gives <em>θ</em> = <em>π</em>/2.
The first car consumed 25 gallons of fuel while the second car consumed 30 gallons of fuel.
<h3>What is an equation?</h3>
An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the first car consumption and y represent the second car consumption, hence:
x + y = 55 (1)
Also:
15x + 20y = 975 (2)
From both equations:
x = 25, y = 30
The first car consumed 25 gallons of fuel while the second car consumed 30 gallons of fuel.
Find out more on equation at: brainly.com/question/2972832
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Answer:
Step-by-step explanation:
The given functions are 
and 
.
We now composed the two functions to find:
This function is defined if the denominator is not zero.
We write this in interval notation as:
We need to be cautious here as x=0 is not in the domain of g(x).
Therefore the domain of 
is
Answer: (1,4) (2,7) (3,10)
HOpE iT hElpS
plS mArK As bRaiNlieSt -wiggly
Step-by-step explanation:
