Answer:
They are inverses since both composition equal x.
Step-by-step explanation:
Given the functions, f(x) = 3x + 1 and g(x) = (x-1) / 3, to check if they are inverses functions, we are to find the inverse of one of the function and check if it will give us the other function.
Let's look for the inverse of f(x).
Given f(x) = 3x+1
Let y = f(x) so that y = 3x+1
Replace y with x
x = 3y+1
Make y the subject of the formula of the resulting equation;
3y = x-1
y = (x-1)/3
The new function of x will be the inverse of f(x)
Hence f^-1(x) = (x-1)/3 = g(x)
Another way to check is to find their composition. Let's find f(g(x) and g(f(x)
F(g(x)) = f((x-1)/3)
Replace x with (x-1)/3 in f(x)
F(g(x)) = 3[(x-1)/3]+1
F(g(x)) = x-1+1
F(g(x)) = x
Similarly for g(f(x));
g(f(x)) = g(3x+1)
Replace x in g(x) with 3x+1
g(3x+1) = (3x+1-1)/3
g(3x+1) = 3x/3
g(3x+1) = x.
Since g(f(x)) = f(g(x)) = x, hence f(x) and g(x) are Inverses functions
3x+4=17x-10 what is x
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
[tex]3x+4=17x-10[/tex]
Subtract 4 from both sides:
[tex]3x+4-4=17x-10-4[/tex]
[tex]3x=17x-14[/tex]
Subtract 17x from both sides:
[tex]3x-17x=17x-14-17x[/tex]
[tex]-14x=-14[/tex]
Divide both sides by -14:
[tex]\frac{-14x}{-14}=\frac{-14}{-14}[/tex]
[tex]x=1[/tex]
Answer:
1
Step-by-step explanation:
Step 1:
3x + 4 = 17x - 10
Step 2:
4 = 14x + 10
Step 3:
14 = 14x
Answer:
x = 1
Hope This Helps :)
Que es un paralelogramo
9) Gabriel took three math tests last semester. He scored a 91 on the first test, a
72 on the second test, and he couldn't remember what he scored on the third
test. When he saw his progress report, he saw that the average score for his
three tests was an 80. What did Carlos score on his third test?
PLEASE ANSWER ASAP I GOT UNTIL 6:30 AND I DONT GET IT
The average of anything can be calculated by adding up all the terms and dividing by the number of terms.
In this case,
the number of terms = 3
x = the missing test score.
(91 + 72 + x) / 3 = 80
Let's multiply both sides by 3
91 + 72 + x = 240
Combine like terms.
163 + x = 240
Subtract 163 from both sides
x = 77
Carlos scored a 77 on his third test.
simplify to create an equivalent expression-4(z+3)-4(5-4z)
Answer:
12z−32
Step-by-step explanation:
Distribute:
=(−4)(z)+(−4)(3)+(−4)(5)+(−4)(−4z)
=−4z+−12+−20+16z
Combine Like Terms:
=−4z+−12+−20+16z
=(−4z+16z)+(−12+−20)
=12z+−32
A turtle was swimming 2 feet below the surface of a pond. While looking for food, he went
down 7 more feet
What is the position of the turtle now relative to the surface of the pond?
Answer:
-9 feet
Step-by-step explanation:
The turtle was already at -2 feet below sea level, then the turtle went 7 more feet down. Which means that -2 +7 = -9
Looking into the sky one night, Tori wondered how far into outer space she would get if she drove a car for 3.21 × 103 hours at a rate of 70mph. She calculated and determined that a car travelling at 70 mph covers approximately 1.13 × 105 meters per hour. Tori wrote this expression to determine the distance she would travel into outer space. (3.21 × 103)(1.13 × 105) Estimate the distance travelled. Almost-equals30 × 1015 meters Almost-equals3 × 108 meters Almost-equals30 × 108 meters Almost-equals3 × 1015 meters
Answer:
B. Almost-equals3 × 108 meters
Step-by-step explanation:
I just did the assignment:)
Answer:
B
Step-by-step explanation:
Just took the asignment.
is (t+ 2)^2-4t binomial
Answer:
I thinks so
Step-by-step explanation:
What is the most specific name for quadrilateral PQRS? parallelogram rectangle rhombus square
Answer:rhombus
Step-by-step explanation:
Answer:
rhombus
Step-by-step explanation:
The mean of 6 numbers is 3 the median is 6. List the numbers
Answer:
Step-by-step explanation:
We have 6 numbers, the mean is the average of all 6, so adding all 6 numbers together and dividing by 6 will give you 3. Because of this we know the 6 numbers will have to add up to 18.
The median is the middle number, but we have an even number so the median is found by adding the 2 middle numbers and dividing by 2.
Because the mean is low, we can guess the first 2 numbers will be small, so let's try 1.
1 + 1 + _ + _ + _ + _
The remaining 4 numbers will have to add up to 16, and the next 2 numbers need to add up to 12. There would not be any possible combination where this would work. Now we know our first 2 numbers are too big.
Now we try 0.
0 + 0 + _ + _ + _ + _
Now our remaining 4 numbers neet to be 18, but the middle 2 need to add to 12 (so when we divide by 2 we get 6) so 0 is still too big!
-2 + -2 + _ + _ + _ + _
If we try -2 now the next 4 numbers need to add to 22, but that's still not going to work because 22-12 = 10 and the last 2 numbers have to be the same, or larger than the middle 2.
-3 + -3 + _ + _ + _ + _
With -3 then our total of the remaining 4 numbers needs to be 24 and 24-12 = 12 so this could be an option!
Our numbers could be:
-3, -3, 6, 6, 6, 6
Let's check:
-3 + -3 + 6 + 6 + 6 + 6 = 18 18/6 = 3 and our middle 2 numbers are 6 so our median would be 6.
If the numbers all have to be different we can come up with a different solution by making our first 2 numbers smaller.
-9, -5, 5, 7, 9, 11
Let's check
-9 + -5 + 5 + 7 + 9 + 11
-14 + 32 = 18 mean 18/6 = 3 median 5+7 = 12 and 12/2 = 6
So that could also work! There are actually many options that would be correct!
One of the set of numbers whose mean is 3 and median is 6 is 0, 1, 5, 7, 2 and 3.
What is Mean?Mean of a set of numbers is the average value of the numbers. Mean is calculated by taking the sum of the given numbers divided by the total number of numbers.
Let x₁, x₂, x₃, x₄, x₅ and x₆ be the six numbers.
We have mean = 3
⇒ (x₁ + x₂ + x₃ + x₄ + x₅ + x₆) / 6 = 3
⇒ x₁ + x₂ + x₃ + x₄ + x₅ + x₆ = 18
Median is the midpoint of the set of numbers arranged in ascending or descending orders.
If the number of set of numbers are odd, then median is the midpoint of the set and if the number of the set is even, then median is the average of the middle two elements.
Median = 6
Since there are 6 numbers here median = (x₃ + x₄) / 2
(x₃ + x₄) / 2 = 6
(x₃ + x₄) = 12
So x₁ + x₂ + x₅ + x₆ = 18 - 12 = 6
Lets just say x₁ = 0, x₂ = 1, x₅ = 2 and x₆ = 3, the sum of which equals 6.
Now, let x₃ = 5 and x₄ = 7, such that x₃ + x₄ = 12
So one of the set which satisfies the given conditions is x₁, x₂, x₃, x₄, x₅ and x₆ = 0, 1, 5, 7, 2 and 3 respectively.
Hence, one of the list of 6 numbers whose mean equals 3 and median equals 6 is 0, 1, 5, 7, 2 and 3.
To learn more about Mean, click:
https://brainly.com/question/26509052
#SPJ2
The maximum speed that an X43A plane can reach is 7,500 miles per hour. At this speed, how many feet
can the X43A travel in 1 second? (1 mile = 5,280 feet)
Answer:
11000 feet/secondsStep-by-step explanation:
This problem requires that we convert from miles per hour to feet per seconds
Given that the speed of the X43A plane is 7500 mph
and that 1 mile = 5,280 feet)
[tex]=\frac{7500miles}{h} *\frac{5280 feet}{mile} \frac{1hour}{3600 seconds} \\\\=\frac{7500*5280}{3600} \\\\=\frac{396*10^5}{3600} \\\\=11000 feet/seconds\\\\=11*10^3feet/seconds\\\\[/tex]
Therefore the speed of the X43A plane in feet per second is 11000
The age of Noelle’s dad is 6 less than 3 times Noelle’s age. The sum of their ages is 74. Find their ages
1. Identify the domain of the relation.
{ (2.5). (3. 8), (4, 11). (5. 14)}
Answer:
The domain is 2,3,4,5
Step-by-step explanation:
Domain is the x values of the input values
You have to put the domain numbers in least to greatest format. And separate the number is commas, not braces
The domain is 2,3,4,5
Hope this helps!
The age of Noelle’s dad is 6 less than 3 times Noelle’s age. The sum of their ages is 74. Find their ages
Answer:
Noelle: 20 Dad: 54
Step-by-step explanation:
The age of Noelle's Dad is 6 less than 3 times Noelle's age looks like this:
d=3n-6
While the sum of their two ages is 74, looks like this:
n+d=74
The system is:
{d=3n−6
{n+d=74
Now, substitute the first equation into the second equation and solve for n.
n+(3n−6)=74
4n-6=74
Add 6 to both sides
4n=80
Divide both sides by 4
n=20 (<---- Noelle's Age!)
Now plug n into the second equation
d=3(20)-6
d=60-6
d=54 (<---- Noelle's Dad's Age!)
2. Calculate your total variable costs for the summer at each price. a. 35 lawns per weekx 12 weeks x $24.25 variable cost = b. 20 lawns per weekx 12 weeks x $24.25 variable cost = c. 5 lawns per weekx 12 weeks x $24.25 variable cost =
Answer:
Total variable costs for the summer at each price:
a. = $10,185
b. = $5,820
c. = $1,455
Step-by-step explanation:
a. 35 lawns per week x 12 weeks x $24.25 variable cost
= 35 * 12 * $24.25
= $10,185
b. 20 lawns per week x 12 weeks x $24.25 variable cost
= 20 * 12 * $24.25
= $5,820
c. 5 lawns per week x 12 weeks x $24.25 variable cost
= 5 * 12 * $24.25
= $1,455
d. The variable cost, as can be seen from above, changes based on the volume of activity or production. The number of lawns influenced the cost, since the other indexes are the same in each case.
Round to the nearest ten thousand: 324,799 pls help I dont know how 2 right it
Answer:
It is 300000...........
Answer:
300,000+20,000+4,000+700+90+9
Step-by-step explanation:
Your welcome!!
Ace's brother is 9 years older than three times his age. the sum of their ages is 57 .how old is Chris?
show me your equation and answer
Answer:
3x+9=57; Chris is 16 years old
Step-by-step explanation:
3x+9=57
Move the Constant to the right
3x=57-9
Calculate
3×=48
Divide both sides
x= 16
Rachel works 5 days a week and works 7.5 hours on each of the days she works. How many hours does
Rachel work in 3 weeks
Answer: 112.5 hours
Step-by-step explanation:
The fifth grade team ordered 5,000 markers for a project. Only 1/10 of the markers have been delivered. How many markers does the team have?
Answer:
500 markers
Step-by-step explanation:
Multiply 5000 by 1/10
[tex]5000*\frac{1}{10} \\\\= \frac{5000}{10}\\[/tex]
Simplify (dividing the numerator and denominator by 10)
[tex]\frac{5000}{10} \\= \frac{500}{1}\\= 500[/tex]
I hope this helped! If it did, a brainliest would be much :)
Does the ordered pair (−1,−3) satisfy the following system of equations? {2x+5y=−17−4x+3y=−5
Answer:
yes
Step-by-step explanation:
Try it and see:
2(-1) +5(-3) = -2-15 = -17 . . . . . works in the first equation
-4(-1) +3(-3) = 4 -9 = -5 . . . . . . works in the second equation
Yes, the ordered pair (-1, -3) satisfies the equations.
__
Or, you can check the solution using a graphing calculator.
1/2 of the total dog population in your town is 130 dogs. How many dogs are there in your town?
Answer:
260
Step-by-step explanation:
hope it helps
What is the degree of the polynomial −6x3y2+5x4−7z?
Answer:
4
Step-by-step explanation:
The degree of a polynomial is a coefficient with the highest power. In the polynomial given, the highest degree (power) is 4.
Best of Luck!
10 – 9 x 24 ÷ 8 x 6 Solve With Pemdas
Answer:
The answer is − 152
Step-by-step explanation:
That was found using PEMDAS.
Answer:
-152
Step-by-step explanation:
use pemdas method
What conclusions can you draw from the distances that you recorded in question 7
Answer:
If corresponding vertices on an image and a preimage are connected with line segments, the line segments are divided equally by the line of reflection. That is, the perpendicular distance from the line of reflection to either of the corresponding vertices is the same. Line is a perpendicular bisector of the connecting line segments.
Step-by-step explanation:
What does it mean for a function to have a root?
Answer:
Step-by-step explanation:
A function has a root when it crosses the x-axis, i.e. . A function can have more than one root, when there are multiple values for that satisfy this condition. The goal is to find all roots of the function (all values). In general we take the function definition and set to zero and solve the equation for .
Answer:
A function has a root when it crosses the x-axis, i.e. . A function can have more than one root, when there are multiple values for that satisfy this condition. The goal is to find all roots of the function (all values). In general we take the function definition and set to zero and solve the equation for .
Transformations of Functions - Algebra 2
i don’t understand this :(
Answer:
c
Step-by-step explanation:
i haven't done this in over a year so my explanation wont be good but i know the answer is right
What is the value of x in the equation 3/2(4x – 1) – 3x = 5/4 – (x + 2)?
i have attached a file you can see it from there.
Let U = {English, French, History, Math, Physics, Chemistry, Psychology, Drama}, A = {Math, History, Chemistry, English}, B = {Psychology, Drama, French, Chemistry, English}, and C = {Physics, History, French}. Find the following. n(B) + n(C)
Answer:
b. psychology drama French chemistry English
Which of the following statements are true and which are false? Give reasons for your answers.(i) Only one line can pass through a single point.(ii) There are an infinite number of lines which pass through two distinct points.(iii) A line can be produced indefinitely on both sides.(iv) If two circles are equal, then their radii are equal.(v) if AB=PQ and PQ=XY, then AB=XY.
Complete Question
Which of the following statements are true and which are false? Give reasons for your answers.
(i) Only one line can pass through a single point.
(ii) There are an infinite number of lines which pass through two distinct points.
(iii) A line can be produced indefinitely on both sides.
(iv) If two circles are equal, then their radii are equal.
(v) if AB=PQ and PQ=XY, then AB=XY.
A (i),(ii) - True
(iii),(iv),(v)-False
B(i),(ii),(iii) -True
(iv),(v)-False
C (i),(ii) -False
(iii),(iv),(v)-True
D (i),(ii),(iii) -False
(iv),(v)-True
Answer:
The correct option is C
Step-by-step explanation:
i is false because several lines can pass through a single point
ii is false because only one line can pass through two distinct points
iii is true because you can extend a line from both points (start and end points )
iv is true because when two equal circle are placed together and radius is trace we will discover that they are equal
v is true because from Euclid's First Axiom , if a= c and c = d the a = d
dot is taller than dab but shorter than dee, and dave is taller than don prove: E is the last letter of the name of the tallest person
Step-by-step explanation:
It starts off by saying Dot is taller than Dab.
Then it says he is shorter the dee.
Then it states that another name dave is taller then don.
We dont necessarily know if dee or dave is the tallest but both of there last names end with E so it proves the question at hand.
Exams are approaching and Helen is allocating time to studying for exams. She feels that with the appropriate amount of studying, she has an 80% chance of getting an A in Marketing. She also feels that she has a 60% chance of getting an A in Spanish with the appropriate amount of studying. Given the demands on her time, she feels that she has only a 45% chance of getting an A in both classes. What is the probability that Helen does not get an A in either class?
Answer: 0.05
Step-by-step explanation:
Let M = Event of getting an A in Marketing class.
S = Event of getting an A in Spanish class,
i.e. P(M) = 0.80 , P(S) = 0.60 and P(M∩S)=0.45
Required probability = P(neither M nor S)
= P(M'∩S')
= P(M∪S)' [∵P(A'∩B')=P(A∪B)']
=1- P(M∪S) [∵P(A')=1-P(A)]
= 1- (P(M)+P(S)- P(M∩S)) [∵P(A∪B)=P(A)+P(B)-P(A∩B)]
= 1- (0.80+0.60-0.45)
= 1- 0.95
= 0.05
hence, the probability that Helen does not get an A in either class= 0.05