Answer:
- f(x) = x^5
- g(x) = 2x -6 . . . . . and see below for other possible definitions
Step-by-step explanation:
You are given an expression for the composition H(x) = f(g(x)) and asked to decompose it into two functions. One way to do that is to look at what is being done to the variable in the function H(x):
- the variable is multiplied by 2
- 6 is subtracted from the product
- the difference is raised to the 5th power.
One of the ways to create the functions g(x) and f(x) is to start at the top of this list and work your way down. Any subset of these transformations can be made into g(x). Then the rest of them are made into f(x).
__
For example, using
g(x) = 2x
Then the rest of the list is f(x):
f(x) = (x-6)^5
so when you put 2x as the argument for f(x), you get ...
H(x) = f(g(x)) = f(2x) = (2x -6)^5 . . . . . the function we want.
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We could also do the first two steps of our list as g(x):
g(x) = 2x -6
f(x) = x^5
so
H(x) = f(g(x)) = f(2x -6) = (2x -6)^5
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If we like, we can factor the expression for H(x):
H(x) = (2(x -3))^5 = 32(x -3)^5
Using the methods above, we could write ...
g(x) = x -3
f(x) = 32x^5
so
H(x) = f(g(x)) = f(x -3) = 32(x -3)^5
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The multiplication and the addition can be made into several parts. We could choose ...
g(x) = (1/4)x -1
f(x) = (8x +2)^5
so
H(x) = f(g(x)) = f(1/4x -1) = (8(1/4x -1) +2)^5 = (2x -6)^5
Answer:
41.8887 cm^2
Step-by-step explanation:
area of a circle
A = pi * r^2
A = pi * (3 + 4)^2
A = pi * 49
A = 153.94
120 / 360 = 1/3
153.94 / 3 = 51.3134
now area of inner circle
A = pi * 3^2
A = pi * 9
A = 28.274
28.274 / 3 = 9.4247
subtract
51.3134 - 9.4247 = 41.8887
Answer:
21
Step-by-step explanation:
Use Pemdas.
Parentesis first so 5+4 = 9 and 8-6=2 so, 9X2=18+3=21
Answer: 1 4/5 / 2/7 = 63/
10
= 6 3/10
= 6.3
Step-by-step explanation:
Conversion a mixed number 1 4/
5
to a improper fraction: 1 4/5 = 1 4/
5
= 1 · 5 + 4/
5
= 5 + 4/
5
= 9/
5
To find a new numerator:
a) Multiply the whole number 1 by the denominator 5. Whole number 1 equally 1 * 5/
5
= 5/
5
b) Add the answer from previous step 5 to the numerator 4. New numerator is 5 + 4 = 9
c) Write a previous answer (new numerator 9) over the denominator 5.
One and four fifths is nine fifths
Divide: 9/
5
: 2/
7
= 9/
5
· 7/
2
= 9 · 7/
5 · 2
= 63/
10
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 2/
7
is 7/
2
) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, the fraction result cannot be further simplified by canceling.
In other words - nine fifths divided by two sevenths = sixty-three tenths.
I believe the angle that is congruent to angle 1 is angle 2
The answer would be A.
