Answers
========================================================
Explanation:
Start with the f(x) function. Then plug in g(x) like so
[tex]f(x) = 4x+3\\\\f(g(x)) = 4(g(x))+3\\\\f(g(x)) = 4\left(\frac{1}{4}x-\frac{3}{4}\right)+3\\\\f(g(x)) = 4\left(\frac{1}{4}x\right)+4\left(-\frac{3}{4}\right)+3\\\\f(g(x)) = x-3+3\\\\f(g(x)) = x\\\\[/tex]
----------------------------
Now we'll start with the g(x) function and then plug in f(x)
[tex]g(x) = \frac{1}{4}x-\frac{3}{4}\\\\g(f(x)) = \frac{1}{4}(f(x))-\frac{3}{4}\\\\g(f(x)) = \frac{1}{4}(4x+3)-\frac{3}{4}\\\\g(f(x)) = \frac{1}{4}(4x)+\frac{1}{4}(3)-\frac{3}{4}\\\\g(f(x)) = x+\frac{3}{4}-\frac{3}{4}\\\\g(f(x)) = x\\\\[/tex]
----------------------------
We've shown that the two equations are true
f(g(x)) = xg(f(x)) = xTherefore, f and g are inverses of each other.
Related Questions
1. Kim's age is three times that of her sister. When you add Kim's age to her sister's age, you get 48. How old is each sister? (a) Write an equation that represents the situation. Explain any variable used. (1 point) (b) Solve the equation from Part (a). Show your work. (4 points)
Answers
Answer:
3k=48
Step-by-step explanation:
k=kim's age
3k=48
/3
k=16
Mrs. marks has to pay if she drives 300 miles. 25 + 0.30*m=
Answers
Answer:25.3
Step-by-step explanation:
Because your adding 25 to 0 and leaving the decimal point and taking away 0 from 30
Find the mean of the data
Answers
Explanation:
Refer to the table below. I've added a third row where I multiplied each x value with its corresponding frequency value f. We can refer to this row as the xf row.
Once we know the xf values, we add them up to get 245.
We'll then divide that result over the sum of the frequency values (add everything in the second row). The sum of the frequency values is 39.
So the mean is approximately: 245/39 = 6.282051 which rounds to 6.282
Notice that this mean value is fairly close to the x value which has the highest frequency.
What term best describes the graph of y=-15
Answers
Step-by-step explanation:
x,y = 0,-15
for another you have to draw Cartesian plane
Answer:
The answer is:- Zero slope
Step-by-step explanation:
Hope it helps you ✌️
nearest tenth of .6752
Answers
.7 is the nearest tenth to the number .6752 because of the 1-4 rounds down and 5-9 round up.
Answer:
Step-by-step explanation:
6750
find the mean of 100
Answers
Answer:
100.
Step-by-step explanation:
100 + 0 = 100
100 ÷ 1 = 100
What is the value of y?
Answers
Answer:
80° because 50° 60° 70° and 80°
(–5) + [(–3) + (–2)] = [(–5) + (–2)] + (–3) answer it fast as you can
Answers
SOMEONE PLEASE HELP Me . My child doesn’t understand this MaTh and THeY really need help. Take this seriously bc we really really need help y’all.
Answers
Answer:
158.4
Step-by-step explanation:
NO LINKS!!
Which type of comic does not have vertices or foci?
Answers
Answer:
b) Circle
Step-by-step explanation:
All of the conic sections have vertices and foci. These features are not usually talked about for a circle, so perhaps "circle" is the expected answer.
__
A circle is a special case of ellipse with eccentricity 0. Its foci are coincident at its center, and its vertices are the ends of any pair of perpendicular diameters.
change 93 to base 4
Answers
Help: Whats 8-2x=10?
Answers
Answer:
x=-1
Step-by-step explanation:
8-2x=10
(8-2x)-8=10-8
-2x=2
-2x/-2=2/-2
x=-1
Find
∂f
∂x
,
∂f
∂y
, and
∂f
∂z
.
f(x, y, z) = 32xyz
Answers
Answer:
what are the measurements for 1 and 2?
Step-by-step explanation:
George Washington
Admission to the zoo costs $15 per person. Which graph correctly represents the total cost for a group to visit the zoo? Total Cost of Admission to the Zoo On a coordinate plane, the x-axis is labeled visitors and the y-axis is labeled Dollars. Points are at (1, 15), (2, 30), (3, 45), (4, 60), (5, 75), (6, 90), and (7, 105). Total Cost of Admission to the Zoo On a coordinate plane, the x-axis is labeled visitors and the y-axis is labeled Dollars. Points are at (1, 15), (2, 15), (3, 15), (4, 15), (5, 15), (6, 15), and (7, 15). Total Cost of Admission to the Zoo On a coordinate plane, the x-axis is labeled visitors and the y-axis is labeled Dollars. Points are at (1, 15), (2, 16), (3, 17), (4, 18), (5, 19), (6, 20), and (7, 21). Total Cost of Admission to the Zoo On a coordinate plane, the x-axis is labeled visitors and the y-axis is labeled Dollars. Points are at (1, 15), (1, 30), (1, 45), (1, 60), (1, 75), (1, 90), (1, 105).
Answers
Admission to the zoo costs $15 per person.
The graph y = 15x correctly represents the total cost for a group to visit the zoo.
Given;
Admission to the zoo costs per person = $15
Let:
The total number of people visiting the zoo = x
The total cost for a group to visit the zoo = y
So, y ∝ x
y = 15x
Therefore, the graph y = 15x correctly represents the total cost for a group to visit the zoo.
Answer:
A
Step-by-step explanation:
Given [tex]cot(\alpha )=-\sqrt{3}[/tex] and [tex]\pi/2 \ \textless \ \alpha \ \textless \ \pi[/tex], find the exact values of the five remaining trigonometric functions:
1. [tex]sin(\alpha )[/tex]
2. [tex]cos(\alpha )[/tex]
3. [tex]tan(\alpha )[/tex]
4. [tex]csc(\alpha )[/tex]
5. [tex]sec(\alpha )[/tex]
Answers
Immediately, by definition of cotangent, we find
tan(α) = 1/cot(α) = 1/(-√3)
⇒ tan(α) = -√3
Given that π/2 < α < π, we know that cos(α) < 0 and sin(α) > 0. In turn, sec(α) < 0 and csc(α) > 0.
Recall the Pythagorean identity,
cos²(α) + sin²(α) = 1
Multiplying both sides by 1/sin²(α) recovers another form of the identity,
cot²(α) + 1 = csc²(α)
Solving for csc(α) above yields
csc(α) = + √(cot²(α) + 1) = √((-√3)² + 1) = √4
⇒ csc(α) = 2
⇒ sin(α) = 1/2
Solve for cos(α) using the first form of the Pythagorean identity:
cos(α) = - √(1 - sin²(α)) = - √(1 - (1/2)²) = - √(3/4)
⇒ cos(α) = -√3/2
⇒ sec(α) = -2/√3
You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $2.25 and each soda costs $1.50. At the end of the night, you made a total of $225.75. You sold a total of 126 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. What equations did you use to solve this? How many hot dogs were sold and how many sodas were sold?
A.
x + y = 126 and 2.25x + 1.50y = 225.75 ; 49 hot dogs and 77 sodas.
B.
x + y = 126 and 2.25x + 1.50y = 225.75 ; 77 hot dogs and 49 sodas.
C.
2.25x + 1.50y = 126 and x + y = 225.75 : -283.5 hot dogs and 509.25 sodas.
D.
There is not enough information
Answers
The equations and the number of hotdogs and sodas sold are: x+ y = 126 and 2.25x + 1.50y = 225.75 ; 49 hot dogs and 77 sodas.
Two equations can be derived from this question:
2.25x + 1.50y = 225.75 equation 1
x + y = 126 equation 2
Where:
x = number of hotdogs sold
y = number of soda sold
In order to determine the value of y, multiply equation 2 by 2.25
2.25x + 2.25y = 283.50 equation 3
Subtract equation 1 from 3
57.75 = 0.75y
y = 77
Substitute for y in equation 2
x + 77 = 126
x = 49
To learn more about simultaneous equations, please check: brainly.com/question/23589883
Answer:
The correct answer is A) x + y = 126 and 2.25x + 1.50y = 225.75 ; 49 hot dogs and 77 sodas
Step-by-step explanation:
hope this helps
Mara is playing a game. There are two marbles in a bag. Ifshe chooses the purple marble, she will win $10. If she chooses the orange marble, she will win $200. What is the expected value of Mara's winnings from the game?
Answers
Answer:
Step-by-step explanation:
Mara has a 50% chance of getting the purple marble and 50% of getting an orange marble, since there's 2 marble; 1 purple and one orange; 1/2 = 50%
So she has a 50% chance of receiving $10 and a 50% chance of receiving the $200.
2. A faucet for a 30-gallon bathtub fills at a rate of 3 gallons per minute.
If the drain lets water out at 1.5 gallons per minute, how long would it
take for the tub to overflow if both the faucet and drain were open at the
same time?
Answers
Answer:
20
Step-by-step explanation:
Knowing that it is a 30-gallon bathtub.
And it fills at a rate of 3 gallons per minute.
But also drains 1.5 gallons per minute.
So this is for the first minute.
3 - 1.5 = 1.5
So there will be 1.5 gallons of water in the tub after the first minute.
Now do,
30 ÷ 1.5 = 20
It will take 20 full minutes for the bathtub to fill up.
The length of a man's shadow is directly proportional with his height.
At the same time of day, a man who is 1.8 meters tall casts a 25.2
meter shadow and his son casts a 21 meter shadow. What is the
height of the man's son, in meters? If necessary, round to the nearest
tenth.
Answers
Answer:
The man's son height is 1.5m
Step-by-step explanation:
[tex]\frac{x}{21} =\frac{1.8}{25.2}[/tex]
[tex]\frac{21x1.8}{25.2}[/tex]
21x1.8= 37.8
37.8 ÷ 25.2= 1.5
Hope this helps
sorry if i got it wrong
Match the verbal phrase on the left with the corresponding equation on the right. Write the letter of the answer on the space provided1.c increased by 5 is 5 2.4 more than a number is 12 3. The product of 4 and n is 12 4. The difference of 27 and k is 15 5.8 less than 3 times x is 10 6. 3 times x increased by 8 is 20 7. a number minus 8 is 3 8. three times a number is 9 9. twice a number plus 1 is 11 10.6 less than a number is 5a. 27-k=15 b. n + 4 = 12 d. 3x+8 = 20 e. k-8=3 f. 3x-8=10 g. 2x + 1 = 11 h. c + 5 = 15 i. 4n = 12 c. c-6=15 j. 3n = 9
Answers
Answer:
See belowStep-by-step explanation:
1. c increased by 5 is 5 ⇒ h. c + 5 = 5 2. 4 more than a number is 12 ⇒ b. n + 4 = 12 3. The product of 4 and n is 12 ⇒ i. 4n = 12 4. The difference of 27 and k is 15 ⇒ a. 27 - k = 155. 8 less than 3 times x is 10 ⇒ f. 3x - 8 = 10 6. 3 times x increased by 8 is 20 ⇒ d. 3x + 8 = 20 7. A number minus 8 is 3 ⇒ e. k - 8 = 3 8. Three times a number is 9 ⇒ j. 3n = 99. Twice a number plus 1 is 11 ⇒ g. 2x + 1 = 11 10. 6 less than a number is 5 ⇒ c. c - 6 = 155) Solve 5 - 2x < 7.
A) x < -1
B) x>-1
0x<-12
D) X > -12
Answers
Answer:
i think B. x>-1 is answer
Step-by-step explanation:
good luck
Help help help help math
Answers
Answer:
<6 = 158°
Step-by-step explanation:
we know a = 6
22 + a = 180
a = 180 - 22
a = 158
PLEASE HELP ME!! I NEED HELP WITH THIS
Answers
Answer: It is answer C.
Step-by-step explanation: Because of the location and angle of the line, it intersects at 9 on the y axis and 1 on the x, therefore giving you 9 over 1
If the radius of the planet Mars is measured to be 3350 km, with a measurement error of plus or minus 100 km. What is the percent error when calculating the volume of the planet? Round your answer to 2 decimal places. Your answer
Answers
Mars is measured to be 3350 km, with a measurement error of plus or minus 100 km.
The percent error when calculating the volume of the planet is 8.95% if the radius of the planet Mars is measured to be 3350 km.
What is the error?The difference between the measured and analysis of the financial statements might well be defined as an error. For instance, if the two operators use the same complete and precise tool.
We have:
If the radius of the planet Mars is measured to be 3350 km, with a measurement error of plus or minus 100 km.
The radius r = (3350 ± 100) km
As we know, volume can be defined as a three-dimensional space enclosed by an object or thing.
V = (4/3)πr²
The percent error:
= [(experimental value - accepted value)/experimental value]×100
The percent error in volume = 3(100/3350)×100
The percent error in volume = 8.95%
Thus, the percent error when calculating the volume of the planet is 8.95% if the radius of the planet Mars is measured to be 3350 km.
Learn more about the error here:
https://brainly.com/question/22248350
#SPJ2
PLZ HELP MATH QUESTION! LOOK AT THE PICTURE BELOW!I I WILL GIVE BRAINILEST TO CORRECT FAST ANSWER!
Answers
Answer:
x<2
Step-by-step explanation:
You're answer is wrong because the circle on the number line is not closed. If it was closed, it would be x ≤ 2 , but because it is open, it would be just be x<2
Find the area of the triangle
Answers
Answer:
5/2 units²
Step-by-step explanation:
Area of triangle = 1/2 x base x altitude => 1/2 x 5 x 1=> 5/2Conclusion:
Therefore, the area of the triangle is 5/2 units².
Hoped this helped.
[tex]GeniusUser[/tex]
what does a discrete quantitative variable mean?
Answers
Answer:
A discrete quantitative variable is one that can only take specific numeric values (rather than any value in an interval)
Step-by-step explanation:
A discrete quantitative variable is one that can only take specific numeric values (rather than any value in an interval), but those numeric values have a clear quantitative interpretation. Examples of discrete quantitative variables are number of needle punctures, number of pregnancies and number of hospitalizations.
Need help a lot stuck
Answers
Answer:
yes, sounds linear.
this is an mx + b scenario.
here's the model:
y = )3/1)x + 50
or
y = 3x + 50
where the 1 in the slope denominator is a square foot.
11,16,21,...
Find the 43rd term.
Find the 43rd term.
Answers
Answer:
You add 5 each time so we just need to multiple 5 by 40 since we alredy have the first three terms.
40*5=200
21+200=221
Hope This Helps!!!
Directions on a box of 5 cups of wallpaper paste are to mix the contents with 4 qt of water. To mix a smaller batch using 1 cup of paste, how much water (in ounces) should be added? note that 1qt=32oz
Answers
Step-by-step explanation:
For standard embossed we recommend 8 pints/4.5L for 4-5 rolls. For heavy embossed we recommend 7 pints/4L for 3-4 rolls.
hope that help you