Answer: 7.5
Step-by-step explanation:
The following three functions look very similar, but define very different functions. Think about how they are defined and write each as a composition of functions given the information below. (None of the functions in your compositions should be the same as the given function.) 1. sin^4 (x) = f(g(x)) where f(x) = , and g(x) = . 2. sin(sin(x)) = f(g(x)) where f(x) = , and g(x) = . 3. sin x^4 = f(g(x)) where f (x) = , and g(x) = .
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following functions :
sin^4 (x) = f(g(x)) where f(x) = and g(x) =
Sin⁴(x) = sin(x)⁴
g(x) = sin(x),
f(x) = f(g(x)) = f(sin(x)⁴) = x⁴
2.) sin(sin(x)) = f(g(x)) where f(x) = , and g(x) =
g(x) = sin(x) ; sinx = x
g(x) = sin(x)
f(x) = f(g(x)) = sin(x) ; sin(x) = x
f(x) = f(g(x)) = f(sin(x))
f(x) = sin(x)
3. sin x^4 = f(g(x)) where f (x) = , and g(x) = .
Here,
g(x) = x⁴
f(x) = f(g(x)) = sin(g(x)) = sin x
f(x) = sinx
The functions are illustrations of composite functions, where multiple functions are combined in one.
(1) sin^4 (x) = f(g(x))
Rewrite the above function as:
[tex]f(g(x)) = \sin^4(x)[/tex]
So, we have:
[tex]f(g(x)) = (\sin(x))^4[/tex]
From the above equation, we have:
[tex]g(x) = \sin(x)[/tex]
So, we have:
[tex]f(g(x)) = (g(x))^4[/tex]
Substitute x for g(x)
[tex]f(x) = x^4[/tex]
Hence, the functions are: [tex]f(x) = x^4[/tex] and [tex]g(x) = \sin(x)[/tex]
2.) sin(sin(x)) = f(g(x))
Rewrite the above function as:
[tex]f(g(x)) = \sin(\sin(x))[/tex]
From the above equation, we have:
[tex]g(x) = \sin(x)[/tex]
So, we have:
[tex]f(g(x)) = \sin(g(x))[/tex]
Substitute x for g(x)
[tex]f(x) = \sin(x)[/tex]
Hence, the functions are: [tex]f(x) = \sin(x)[/tex] and [tex]g(x) = \sin(x)[/tex]
3. sin x^4 = f(g(x))
Rewrite the above function as:
[tex]f(g(x)) = \sin(x^4)[/tex]
From the above equation, we have:
[tex]g(x) = x^4[/tex]
So, we have:
[tex]f(g(x)) = \sin(g(x))[/tex]
Substitute x for g(x)
[tex]f(x) = \sin(x)[/tex]
Hence, the functions are: [tex]f(x) = \sin(x)[/tex] and [tex]g(x) = x^4[/tex]
Read more about composite functions at:
https://brainly.com/question/10687170
1. If 4 = ( p – 2 ) then the solution of p = ------
2.In the expression x/4 = 2/3 what is the value of the x
Answer:
x = 8/3
Alternative form
x = 2 2/3, x = 2.6
Step-by-step explanation:
First, simplify the equation using cross-multiplication
3x = 8
then divide both sides of the equation by 3 and there's your answer
x = 8/3
A basketball court is shaped like a rectangle 20 meters long and 10 meter
wide? What is the area of the court?
Answer:
200 squared meters.
Step-by-step explanation:
Since we know the court is a rectangle, we can use the formula for the area of a rectangle:
[tex]A=lw[/tex]
Where l is the length and w is the width.
We are given that the length is 20 meters and the width is 10 meters. Substitute:
[tex]A=20(10)[/tex]
Multiply:
[tex]A=200\text{ meters}^2[/tex]
So, the area of the court is 200 squared meters.
pls help ASAP
Which number is missing from the prime factorization of 348?2 x ____ x 3 x 29
A. 2
B. 3
C. 5
D. 7
Answer: The answer is A. 2.
Answer: your answer is A
Which term has a coefficient of 1?
Answer:
Variables with no number have a coefficient of 1.
Step-by-step explanation: x is really 1x.
Rita bakes pies at The Corner Bakery. The number of pies she can bake, x, is limited by the ingredients
they have in stock. This situation is represented by the compound inequality 2x - 3 < 7 and 5 - x < 8.
Solve the compound inequality and select all the viable solutions.
-2 pies
2 pies
1 pie
O pies
-1 pies
-3 pies
5 pies
6 pies
4 pies
3 pies
Answer:
The solution for the inequality is -3< x <5
The viable solutions are;
-2 pies, -1 pies, 0 pies, 1 pie, 2 pies, 3 pies, and 4 pies
Step-by-step explanation:
The given inequalities are;
2·x - 3 < 7 and 5 - x < 8
Therefore, we have;
2·x - 3 < 7
2·x < 7 + 3
2·x < 10
x < 5
From the other inequality, we have;
5 - x < 8
-x < 8 - 5 = 3
-x < 3
-x/(-1) > 3/(-1)
x > -3
Therefore, the solution for the inequality is given as follows;
-3< x <5
The possible values are;
-2 pies, -1 pies, 0 pies, 1 pie, 2 pies, 3 pies, and 4 pies.
convert 2000m to centimeters
Answer:
200,000cm
Step-by-step explanation:
1m = 100cm
2000m = ?
2000 × 100 = 200,000cm
2,00,000cm
Step-by-step explanation:
1m= 100cm
2000m=?
2000m= 2000× 100 cm
= 2,00,000cm
Helpppppppppppppppp plz plz plz plz plz
Answer:
-19
Step-by-step explanation:
We know:
Samuel walks forward 19 steps. So number is+19
We need to find:
How would he represent the opposite of this number
Answer :
Number = 19
To represent the opposite of this number Samuel should first take 19 steps back to reach his original position that is zero and then needs to move 19 steps backward to get -19.
A ream of a certain brand of paper weighs about 3.225 pounds. A ream contains 500 sheets of paper. How much does a sheet of paper weigh?
Answer:
about 0.00645 pounds
Step-by-step explanation:
3.225 / 500 = 0.00645
Answer:
A single paper should weigh about 0.00645
Step-by-step explanation:
All you really need to do is divide 3.225 by 500.
determine the quotient of 1 2/3 ÷ 4/5
Answer:
The desired quotient is 25/12.
Step-by-step explanation:
Rewrite 1 2/3 as an improper fraction: 5/3.
Then divide this 5/3 by 4/5:
5
------ ÷ 4/5
3
It's easier (but completely correct) to invert the divisor (4/5) and then multiply 5/3 by (5/4):
5 5 25
----- * ----- = ------
3 4 12
if 7x - 11 = 17, then x = 4
I really need help I don’t understand anything and my teacher isn’t a big help either
Layla uses 1.75 cups of sugar per batch of cookies. How many cups of sugar would she require to bake 9 batches of cookies?
Answer:
15.75 cups
Step-by-step explanation:
If she uses 1.75 cups each batch to find how much she uses for 9 batches you just multiply 1.75 by 9 which gives you 15.75 cups
38 + − 21 = ???????????????????????????
Answer:
17
Step-by-step explanation:
Answer:
38 - 21 = 17.Step-by-step explanation:
because - + = - ....Hope it helps you..
Thanks
.
The endpoints of GH are G(3,3) and H(-7,7).
Find the coordinates of the midpoint M.
Step-by-step explanation:
Hey there!!
You can simply use midpoint formulae to find midpoint of the coordinates.
Here, Given that;
G(3,3) and H(-7,7).
Using midpoint formulae,
[tex]midpoint \: of \: gh = (\frac{x1 + x2}{2} ,\frac{y1 + y2}{2} [/tex])
[tex]midpoint \: of \: gh = (\frac{3 - 7}{2} ,\frac{3 + 7}{2} [/tex])
After simplifying it we get,
= (-2,5).
Therefore, midpoint of GH is M(-2,5).
Hope it helps....
What is 1.4 repeating as a percent.
Answer:
140%
Step-by-step explanation:
Move the decimal over to the right two places!
:D
Answer: 140 percent I hope this answers your question!
Pls help solve the equation
Answer:
34 boxes
Step-by-step explanation:
Please see attached picture for full solution.
200 ones into standard form
Please help me solve this Question Explanation will be appreciated.
Answer:
for the first question, the answer is B
6 × 6 (faces of a dice) = 36, there are 6 way to add 1-6 to 7 (1+6, 2+5, 3+4), so the answer is 6/36 or simplified into 1/6
for the second question, the answer is B
3/4 = 15/20, 3/5 = 12/20 (least common multiple is 20)
15/20 - 12/20 = 3/20
Write the inverse of f(x) = 3x - 1
f -1(x) =
log 3 x + 1
log 3 ( x - 1)
log 3 x - 1
Answer:
log 3 x +1 = f^-1(x)=[tex]\frac{10^x^-^1}{3}[/tex]
log 3 (x-1) = f^-1(x)=[tex]\frac{x}{log(3)} +1[/tex]
log 3 x - 1 = f^-1=[tex]\frac{10^x^+^1}{3}[/tex]
The inverse of the function f(x) = 3x - 1 is f⁻¹(x) = (x + 1)/3.
What is an inverse function?First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.
We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.
Given, f(x) = 3x - 1.
Or y = 3x - 1.
3x = y + 1.
x = (y + 1 )/3.
f⁻¹(x) = (x + 1)/3.
learn more about the inverse of functions here :
https://brainly.com/question/2541698
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simplify the equation (2x³) (x⁴)² / 8x¹¹
Answer:
Hey there!
(2x³) (x⁴)² / 8x¹¹
2x^3(x^8)/8x^11
2x^11/8x^11
1/4
Let me know if this helps :)
I WILL MAKE BRAINLEST!!!!!!
Order the numbers from least to greatest. 1=least and 4=greatest LaTeX: \sqrt{\frac{9}{4}}9 4 LaTeX: \sqrt{5}5 LaTeX: 2.52.5 LaTeX: \frac{5}{3}5 3
Answer:
[tex] \sqrt{\frac{9}{4}} [/tex] < [tex] \frac{5}{3} [/tex] < [tex] \sqrt{5} [/tex] < 2.5
Step-by-step explanation:
Given the following numbers, [tex] \sqrt{\frac{9}{4}}, \sqrt{5}, 2.5, and, \frac{5}{3} [/tex], let's express each as whole or decimal numbers, to find out the least to the greatest.
[tex] \sqrt{\frac{9}{4}} = \frac{\sqrt{9}}{\sqrt{4}} [/tex]
[tex] \frac{3}{2} = 1.5 [/tex]
[tex] \sqrt{5} [/tex] ≈ 2.2
2.5 (already in decimal form)
[tex] \frac{5}{3} [/tex] ≈ 1.7
From the least to the greatest, we have:
[tex] \sqrt{\frac{9}{4}} [/tex] < [tex] \frac{5}{3} [/tex] < [tex] \sqrt{5} [/tex] < 2.5
Solve 10-13 find each measurement
Answer:
10)17.5
11)18
12)70
13)110
Problem 10
Answer: RS = 17.5This is because the opposite sides of any parallelogram are congruent (PQ = RS and QR = PS)
======================================
Problem 11
Answer: QT = 18Diagonal QS is cut in half (bisected) by the other diagonal PR. The smaller pieces QT and ST are the same length.
======================================
Problem 12
Answer: angle PQR = 70 degreesThe angle QRS is given to be 110 degrees. Angle PQR adds to this to get 180, so we effectively solve x+110 = 180 to get x = 70. Any pair of adjacent angles of any parallelogram are supplementary.
======================================
Problem 13
Answer: 110 degreesOpposite angles of a parallelogram are congruent. Angle SPQ is opposite of angle QRS = 110.
evaluate the expression for the given value of the variable 9 | 9 -8x | = 2x + 3
Steps to solve:
9|9 - 8x| = 2x + 3
~Divide 9 to both sides
|9 - 8x| = 2/9x + 1/3
~Solve absolute value (part one)
|9 - 8x| = 2/9x + 1/3
-74/9x + 9 = 1/3 (Subtracted 2/9x to both sides)
-74/9x = -26/3 (Subtracted 9 to both sides)
x = 39/37 (Multiplied 37/39 to both sides)
~Solve absolute value (part two)
|9 - 8x| = -(2/9x + 1/3)
|9 - 8x| = -2/9x - 1/3 (Distributed negative sign to left side)
-70/9x + 9 = 11/3 (Added 2/9x to both sides)
-70/9x = -28/3 (Subtracted 9 to both sides)
x = 6/5 (Multiplied 9/-70 to both sides)
Therefore, the solutions are x = 39/37 and x = 6/5
Best of Luck!
You found hardwood flooring priced by the square foot. To find the price per square yard, you should do which of the following.
a.) Divide the price per square foot by 9
b.) Multiply the price per square foot by 3
c.) Multiply the price per square foot by 9
d.) Divide the price per square foot by 3
Answer:
D. Divide the price per square foot by 3
Step-by-step explanation:
1 foot = 0.333333 yard
price per square yard of the hardwood = price per square foot / 3
For instance, If the price per square foot is $900, then the price per square yard is
price per square yard of the hardwood = price per square foot / 3
= 900 / 3
= 300
price per square yard of the hardwood = $300
4+(x+5)+4+(x+5)+4=48
do you know the awnser to 4(-8x+5)-(-33x-26)=
Answer:
x+46
Step-by-step explanation:
-32x+20+33x+26=
x+20+26=
x+46
Answer:
x +46
Step-by-step explanation:
4(-8x+5)-(-33x-26)=
Distribute
-32x+20 +33x +26
Combine like terms
x +46
-2(k - 5) + 2k = 5k + 5
Convert 1.9647 to a percent.
Answer:
196.47%
Step-by-step explanation:
1 is 100
So the rest just add in
A designer found the area of a wall to be 5.0 square yards. What is the area of the wall in square meters?hhhshxhxhd
Step-by-step explanation:
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Which number is rational?Which number(s) below belong to the solution set of the inequality? Check all that apply. x + 6 < 38 A. 31 B. 26 C. 88 D. 44 E. 32 F. 70
Answer:
A. 31 and B. 26
Step-by-step explanation:
In order for x+6<38 to be true, we need to find the maximum number x can be. So we move 6 to other side which gives us x<32
Of the options A. 31 and B. 26 are the only ones that are less that 32. E. 32 does not count because x must be less than 32, not equal to it.
Hope this helped!