Answers
Answer:
g and f are inverse functions because g(f(x)) = f(g(x)) = x
Step-by-step explanation:
Let's start by finding f(g(x)) and g(f(x)). As we discussed in another question, to find a composite function, apply the outer function to whatever the inner function evaluates to. We can start with f(g(x)):
[tex]f(g(x))=f(\frac{x+6}{7})=7(\frac{x+6}{7} )-6=x+6-6=x[/tex]
Now, let's find g(f(x)):
[tex]g(f(x))=g(7x-6)=\frac{(7x-6)+6}{7} =\frac{7x}{7}=x[/tex]
There is a property that says that if f(g(x)) = g(f(x)) = x, the two functions are inverse. This suggests that g and f are inverse functions. We can verify this by taking one function, switching y and x, and then solving for y. If we complete this process and find that we get the OTHER function, it means the two functions are inverse. Let's try that:
[tex]f(x)=y=7x-6[/tex]
Swap x and y:
[tex]x=7y-6[/tex]
Solve for y:
[tex]x+6=7y\\y=\frac{x+6}{7}[/tex]
Notice that we got g, which means f and g are inverse.
Related Questions
Tan(x) *cos(x)*cos(x)= ( the answer should have sin only ) ASAP
Answers
This doesn't make any sense because you didn't give a value to cos like you did to sin.
Let me guess the actual question is tan(x)*cos(x) write this in term of sin.
Now from trigonometry identities, we know that tan(x)=sin(x)/cos(x)
So the expression can be written as sin(x)/cos(x)*cos(x)
which results in sin(x) as the answer, if I guessed the question wrong, sorry and please tell me in the comments what the correct question is, because this question doesn't seem complete :)
Micah invests $5,280 in an account that earns 4.2% interest, compounded monthly.
Part A
Write a function for the amount that will be in the account after t years.
Part B
What is the value of the account after 8 years?
Answers
a) The function is given as follows: [tex]A(t) = 5280\left(1 + \frac{0.042}{12}\right)^{12t}[/tex]
b) The value of the account after 8 years is given as follows: $7,384.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameter values for this problem are given as follows:
P = 5280, r = 0.042, n = 12.
Hence the equation is given as follows:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(t) = 5280\left(1 + \frac{0.042}{12}\right)^{12t}[/tex]
The value of the account after 8 years is obtained as follows:
[tex]A(8) = 5280\left(1 + \frac{0.042}{12}\right)^{12 \times 8}[/tex]
A(8) = $7,384.
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What is the domain of the function y = 2e graphed below?
Answers
Answer:
All Real Numbers
General Formulas and Concepts:
Algebra I
Interval NotationDomain is the set of x-values that can be inputted into function f(x)Step-by-step explanation:
According to the graph and function y = 2eˣ, we see that our x-values span from negative infinity to positive infinity. We also see that we can plug in any number x into our function:
(-∞, ∞)
or
All Real Numbers
Answer: D) all real numbers
Step-by-step explanation:
HELP ASAP! EXPONENTIAL FUNCTIONS
Answers
A 45 ounce box of cereal costs $3.99. Find the unit price. Round your unit
price to the nearest cent if needed.
Answers
Answer:
0.1125 ounces per cent
A newspaper invited readers to call a telephone number and record their comments. The next day they reported that readers overwhelmingly prefer two-way traffic flow to one-way streets. This is an example of: A. A convenience sample B. A self-selected sample C. A systematic sample D. A random sample does anyone know the answer
Answers
Answer: Self selected sample
Step-by-step explanation:
They people chose themselves
This is an example of: B. A self-selected sample , Option B is the answer.
What is a self-selected sample ?A self selected sampling technique is one in which the researcher puts out a call or publicises so that individuals and organisations can take part in the survey on their own will which saves the time for searching for the appropriate people .
It is given that
A newspaper invited readers to call a telephone number and record their comments.
This is an example of: B. A self-selected sample
Therefore Option B is the answer.
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Distance between (-1,-2) and (8,0)
Answers
Answer:
9.219544
Step-by-step explanation:
(8 - -1)^2 + (0 - -2)^2 = 85, sqrt 85 = 9.219544
Answer:
Step-by-step explanation:
Distance formula : d=√((x_2-x_1)²+(y_2-y_1)²)
d=√((8-(-1))²+(0-(-2))²)
d=√((9)²+(2)²)
d=√(81+4)
d=√(85)
d = 9.21954445729
The Big Wheel at a theme park has a diameter of 5m. How far would you travel in one complete revolution of the wheel?
Answers
Answer:
15.71m
Step-by-step explanation:
One revolution is equal to the circumference of the wheel
Circumference = πD
22/7 X 5 = 15.71m
Im willing to give 20 points maybe even more
A teacher purchased 20 calculators and 10 measuring tapes for her class and paid $495. Later, she realized that she didn't order enough supplies. She placed another order of 8 of the same calculators and 1 more of the same measure tape and paid $178.50.
The system represents the situation
`20c+10m=495`
`8c+1m=178.50`
Find the cost of one calculator and the cost of one measure tape using one of our methods of solving systems.
Answers
Answer:
Equations are
20c + 10m = 495..............(1)
8c + 1m = 178.5.................(2)
Now , equation (2) * 10 = 80c + 10m = 1785...........(3)
So, Eq. (3) - Eq(1) =
80c + 10m - 20c - 10m = 1785 - 495
60c = 1290
c= 21.5
********************************************************
Now place the value of c in Eq (2)
So , m =6.5
Mark my answer as brainlist answer
Step-by-step explanation:
Find the area of the circle 18in
Answers
1017.88in^2
You need to use pi
Answer:
1017.88inches^2
Step-by-step explanation:
Area of a circle=pi * radius^2
324*pi=1017.88
At the market you can buy 6 bags of apples for $25. At the orchard you can get 8 bags of apples for $35. Which is the better deal?
Answers
Answer:
6 bags for $25
Step-by-step explanation:
25/6 = 4.16666666667 = $4.17 per bag
35/8 = 4.375 = $4.37 per bag
The better deal for the bags of apples is at the market
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
To determine which is the better deal, we can compare the prices per bag of apples at the market and the orchard.
At the market:
Price of 6 bags of apples = $25
Price per bag of apples = $25 / 6 ≈ $4.17 (rounded to two decimal places)
At the orchard:
Price of 8 bags of apples = $35
Price per bag of apples = $35 / 8 ≈ $4.38 (rounded to two decimal places)
Comparing the two prices per bag of apples, we can see that the price per bag at the market is $4.17, while the price per bag at the orchard is $4.38.
Hence , the better deal is at the market where you can buy 6 bags of apples for $25, resulting in a lower price per bag compared to the orchard.
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this question is hard help..........
Answers
Answer:
sorry i dont know
Step-by-step explanation:
Answer:
.OOF Sorry im not good in math
Algebraic Expression
x + y + 2
Constants | Variable/s/term/s Degree of term
Answers
Constants : 1 (the only constant term is 2)
Variables : 2 (x and y)
Terms : 3 ( x, y and 2)
Degree of term : 1
What is an equation of the line that passes through the points (4,-4) and (-4,-4)
Answers
Answer:
Step-by-step explanation:
Use the formula x-x1/x1-x2 = y-y1/y1-y2
Dont be shy- drop the answer :)
Answers
Answer:
-11x = -55
x = 5
Step-by-step explanation:
Hope that helps!
The equation below shows the total volume (V), in cubic units, of 4 identical boxes with each side equal to s units: V = 453 If s = 2.5 units, what is the value of V?
Answers
Answer:
in cubic units, of 4 identical boxes with each side equal to s units: V = 4s3 If s = 2.5 units, what is the value of V? (5 points) 25 cubic units 30 cubic units 62.50 cubic units 156.25 cubic units
Step-by-step explanation:
Vincent had 97 rocks in his collection. He found 48 more at the beach. How many did he have in all ?
Answers
Answer:
145
Step-by-step explanation:
97+48
7+8=15
9+4+1=14
145
Which pair of fractions is not equivalent fractions?
A.1/9,2/18
B.7/8,5,6
C.3/16,9/48
D.6/15,4/10
Answers
Answer:
b is correct
Step-by-step explanation:
as 7/8 can't be further simplified and it is not making equivalent with 5/6
hope it helps you
please mark me as brainlist
Solve the inequality:
-15 + 5x > 25
Answers
Answer:
x > 8
Step-by-step explanation:
-15 + 5x > 25
Add 15 on both sides
5x > 40
x > 8
Answer:
here
Step-by-step explanation:
inequality form ---- x>8
interval form ----- (8,infinite)
Mrs. Beppu's property has four sides. An aerial view of her property is shown below. What term best describes the shape of her property?
Answers
Answer:
rectangle
Step-by-step explanation:
From the picture attached below of the aerial view of Mrs. Beppu's house we can see that it is a rectangle. That is because it has 4 sides with only the parallels being the same size. Meaning that both the width and the length of the house are not the same. This removes the possibility of it being a square. Since all the angles seem to be right angles it also removes the possibility of it being a trapezoid. The best choice would be that it is a rectangle.
1. Which of the following equations would NOT contain the point (4,12)?
A. y=-1/2x+14
B. y=1/2x+8
C.y=-2x+20
D.y=3/4x+9
Answers
Answer:
the answer is b hope this helps :)
Si 2X -7 = 3, luego 3X + 1 =
(1) 4
(2)5
(3)7
(4)12
(5)16
Answers
Answer:
2x-7=3
2x=3+7
{2x=10}÷2
x=5
꧁꧁꧂꧂
3x+1=
{3x=1}÷3
x=1/3
Write your question here (Keep it simple and clear to get the best answer) simplify (3x-4y)(5x+2y)-(x+y)
Answers
Answer:
15x^2−14xy−8y^2−x−y
Step-by-step explanation:
Combine like units.
Answer:
hope it helped
have a good day
You are designing a simulation for which day of the week people are born. You assign numbers
to each day of the week from, Sunday = 0 through Saturday = 6. You decide to use a sample
size of 20.
Use the random number table to conduct your first trial, working from left to right.
39017 66124 37046 59285 15208 47185 76426 23648
51239 88346 59268 71307 37420 69307 98648 45960
Which chart matches the results from your first trial?
Answers
Answer:
The chart should have the pattern 3332333
Step-by-step explanation:
59:
Evaluate the function requested. Write your answer as a fraction in lowest terms.
B
39
15
36
Find tan A
a
5
tan A =
13
C.
5
tan A -
12
b.
13
d.
12
tan A =
tan A -
5
Answers
Answer:
Step-by-step explanation:
Two containers of gasoline hold a total of 100 gallons. The big container can hold 20 gallons less than twice the small container. How many gallons does each container hold?
Answers
Answer:
The big container holds 60 gallons
The small container holds 40 gallons
Step-by-step explanation:
If the small container held 40 gallons of gasoline then double that would be 80 gallons and 20 gallons less than that would be 60 gallons.
I NEED HELP ASAP WILL GIVE BRAINLYEST
Answers
Answer:
-8
Step-by-step explanation:
First simplify the expression to -(2^5)^3/5. Then you get -2^3, which is simplified again to -8.
Find the original price.
The discount on a toy robot is 40%. The toy robot is on sale for $54?
Answers
Answer:
$75.60
Step-by-step explanation:
Well, I don't exactly know why, but I know that you need to 54 multiply by 1.40 to get the answer.
Answer:
$75.60
Step-by-step explanation:
54 increase 40% =
54 × (1 + 40%) = 54 × (1 + 0.4) = 75.6
Please I need help with these questions its Algebra
Answers
1. 14/3
2. 9
4. 5
5. 15
(Sixth one is confusing sorry! But I hope you do well on it since I can't help you :|)
10 + 2.5x > 35 please help meeee
Answers
[tex]x > 10[/tex]
Step-by-step explanation:
1) Subtract 10 from both sides.
[tex]2.5x > 35 - 10[/tex]
2) Simplify 35 - 10 to 25.
[tex]2.5x > 25[/tex]
3) Divide both sides by 2.5.
[tex]x > \frac{25}{2.5} [/tex]
4) Simplify 25/2.5 to 10.
[tex]x > 10[/tex]
Therefor the answer is, x > 10.