Answer:
You aren't dumb
Plot a point at -6. on the y-axis. (y to the sky. It is vertical)
Now count down 2 units and right one.
Plot a point there.
Draw a line through the points with a ruler
☼DONE☼
Answer:
see attached
Step-by-step explanation:
y = -2x + 6
x intercept: 0 = -2x + 6
2x = 6
x = 6/2
x = 3
(3, 0)
y intercept = (0, 6)
In a certain chemical, the ratio of zinc to copper is 3 to 19. A jar of the chemical contains 874 grams of copper. How many grams of zinc does it contain?
Answer:
138
Step-by-step explanation:
\(\frac{3}{19}\) = \(\frac{x}{874}\) cross multiply
19 x = 3(874)
19x = 2622 Divide both sides by 19
x = 138
simplify 5 to the second power and 5 to the ninth power
We can simplify 5 to the second power and 5 to the ninth power as follows:
5² = 25
5⁹ = 1, 953, 125
How to simplify the expressionTo simplify the expression, we will first raise 5 to the power of 2 by multiplying it in two places. This gives us:
5² = 5 * 5
= 25
Also, for the second expression, we can simplify by raising 5 to the power of 9 to get
5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 = 1, 953, 125
So, the best way to simplify the expressions will be by multiplying 5 by as many times as its power specifies.
Learn more about the simplification of powers here:
https://brainly.com/question/5376862
#SPJ1
a small apartment has a 11ft by 11ft bedroom, a 4ft by 6ft bathroom, and a single multi-use 15ft by 16ft living room/kitchen. what is the total square footage (area) of the apartment?
The total square footage (area) of the apartment is 385 square feet.
The total square footage, also known as the area, of an apartment is a measure of how much space the apartment has.
First, let's find the area of the 11ft by 11ft bedroom. To do this, we multiply the length and the width of the room. In mathematical terms, the area of a rectangle is equal to the length times the width. So, for the bedroom, the area is
=> 11ft * 11ft = 121 square feet.
Next, let's find the area of the 4ft by 6ft bathroom. The formula for the area of a rectangle is still the same, so the area of the bathroom is
=> 4ft * 6ft = 24 square feet.
Finally, we'll find the area of the multi-use living room/kitchen, which is 15ft by 16ft. The area of this room is
=> 15ft * 16ft = 240 square feet.
Now that we have the area of each room, we can add them together to find the total area of the apartment. So, the total area is
=> 121 square feet + 24 square feet + 240 square feet = 385 square feet.
To know more about area here.
https://brainly.com/question/14994710
#SPJ4
For the linear regression y = ẞ1 + ẞ2x + e, assuming that the sum of squared errors (SSE) takes the following form:
SSE = 382 +681 +382 + 18ẞ1ẞ2
Derive the partial derivatives of SSE with respect to B1 and B2 and solve the optimal values of these parameters.
a. B₁ = B1
b. B₂ =
The optimal values of these parameters are:
a. β₁ = 0
b. β₂ = 0
The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:
SSE = 382 + 681 + 382 + 18β1β2
Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.
Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0
Now, we need to find the partial derivative of SSE with respect to β1.
∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0
Therefore, we obtain the optimal value of β2 as 0.
Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0
Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.
Thus, the optimal values of β1 and β2 are 0 and 0, respectively.
Therefore, the answers are: a. β₁ = 0 b. β₂ = 0
Learn more about regression analysis at
https://brainly.com/question/31691955
#SPJ11
(a) In unit -vector notation, what is the sum vec (a)+vec (b) if vec (a)=(4.0m)hat (i)+(3.0m)hat (j) and vec (b)=(-13.0m)hat (i)+(7.0m)hat (j) ? What are the (b) magnitude and (c) direction of
"
The magnitude of the vector
\($\vec{c}$ is $\sqrt{181}$ m\)
and its direction is approximately.
\($-48.59^{\circ}$.\)
Given:
\($\vec{a}
= 4.0 \hat{i} + 3.0 \hat{j}$, and $\vec{b}
= -13.0 \hat{i} + 7.0 \hat{j}$\)
The sum of the two vectors,
\($\vec{a}+\vec{b}$\)
can be calculated by adding the x-components and y-components of the two vectors separately.
$\vec{a}+\vec{b} = (4.0 \hat{i} + 3.0 \hat{j}) + (-13.0 \hat{i} + 7.0 \hat{j})$$= (4.0 - 13.0) \hat{i} + (3.0 + 7.0) \hat{j}$$= -9.0 \hat{i} + 10.0 \hat{j}$
Therefore, the sum of the vectors
\($\vec{a}$ and $\vec{b}$ is $-9.0 \hat{i} + 10.0 \hat{j}$\)
in unit vector notation. Magnitude of vector
\($\vec{c}$\)
can be calculated by the Pythagorean theorem and its direction can be calculated as:
\($|\vec{c}| = \sqrt{(-9.0)^2 + (10.0)^2}
= \sqrt{181} \approx 13.45$$\theta
= \tan^{-1} \frac{y}{x}
= \tan^{-1} \frac{10.0}{-9.0} \approx -48.59^{\circ}$\)
The magnitude of the vector
\($\vec{c}$ is $\sqrt{181}$ m\)
and its direction is approximately.
\($-48.59^{\circ}$.\)
To know more about two visit:
https://brainly.com/question/14852288
#SPJ11
Victoria searched her house for quarters. She started with 17 quarters and found 6 more quarters. She then goes to the arcade. If a game costs 2 quarters to play, how many games can she play and how many quarters are left over? Victoria can play times and there will be quarters left over.
Answer:
11 games
Step-by-step explanation:
17+6=23
23/2=11.5
Victoria can play 11 games. You'd usually round up, but in this case you can't play half a game so she'll play 11 games and have one quarter leftover.
Answer:
Victoria can play 11 games and have 1 quarter left over.
Step-by-step explanation:
17 given quarters +6 found quarters = 23 total quarters.
Since 23 is an odd number and we want to divide by 2, we have to go down to the last even number: 22. (This gives us the left over quarter)
22 quarters/2quarters per game = 11 games
Karen measures the width of a garden plot and records that it is 55.25 meters. Its actual width is 52.25 meters. What is the percent error in the measurement, to the nearest tenth of a percent?
The percent error in the measurement is approximately 5.7% whose garden's width is 55.25.
What is percent error?Percent error is a measure of the accuracy of a measurement, comparing the measured value to the actual value. It is calculated as the absolute difference between the measured value and the actual value, divided by the actual value, and then multiplied by 100 to express the result as a percentage.
According to question:To find the percent error, we need to compare the measured value to the actual value, and express the difference as a percentage of the actual value.
Measured value = 55.25 meters
Actual value = 52.25 meters
Step 1: Find the difference between the measured value and the actual value:
Difference = Measured value - Actual value
Difference = 55.25 - 52.25
Difference = 3
Step 2: Calculate the absolute value of the difference:
|Difference| = |Measured value - Actual value|
|Difference| = |55.25 - 52.25|
|Difference| = 3
Step 3: Calculate the percent error:
Percent error = |Difference| / Actual value x 100%
Percent error = 3 / 52.25 x 100%
Percent error = 5.74%
Therefore, the percent error in the measurement is approximately 5.7%.
To know more about percent error visit:
https://brainly.com/question/29107960
#SPJ1
please help me thankyou lol
Answer:
Yes, they are congruent
Step-by-step explanation:
They are congruent because they both have same length sides
Find the perimeter or circumference and area of each figure. Round to the nearest hundredth.
The perimeter or circumference is 42 ft and area is 68 ft.
From the figure:
The figure represents a rectangle so opposite sides are equal.
Length l = 17 ft
width w = 4 ft
we know that:
Perimeter of rectangle = 2(l+w)
= 2(17+4)
= 2*21
= 42 ft
Area of rectangle = l*w
= 17*4
= 68 ft.
Learn more about the rectangle here:
https://brainly.com/question/15019502
#SPJ1
in the adjoining figure, ABC is a right-angled triangle, where
B = 90°, AB = 3 cm and AC
3V2 cm, find the size of ®.
Answer:
the value of theta i 45°
The functions f(x)=−34x+214 and g(x)=(12)x+1 are shown in the graph. What are the solutions to −34x+214=(12)x+1? Select each correct answer.
The graphs cross at x=-1 and x=1. Those are the solutions to to the equation
How to explain the graphWe know that, If two functions are equal then there solution is the intersection point of the curves.
When we determine the graph the intersection points are (0,2) and (1,1.25).
The values of x of the intersection points are the solutions of the system
Using a graphing tool, there are two intersection points and therefore the solutions are x = -1 and x [ 1.
Learn more about graph on
https://brainly.com/question/8658188
#SPJ1
The total area of Russian is about 20,000,000
Answer: 19,990,000 times
Step-by-step explanation: Land area of Russia = 20000000
Land area of Puerto Rico = 10000
20000000 - 10000 = 19,990,000
2.9 x 10^5 + 8.7 x 10^5
Answer:
So this is scientific notation what you do is
2.9x10^5 so you put however many zeros the is powered to 10. See there is a 5 It has to be behind or in front of the decimal you might be saying how do you know if its behind or in front well negative is in front and positive is behind .
290,000 there was a number already behind the decimal so there you go 5 number behind the decimal.
Same for the second one
290,000 870,000 is your answers so now you add hem together
1,160,000 is your final answer
Step-by-step explanation:
A twelve-sided die with sides labeled 1 through 12 will be rolled once. Each number is equally likely to be rolled.
What is the probability of rolling a number greater than 10?
Write your answer as a fraction in the simplest form.
Answer:
Here;
Step-by-step explanation:
The numbers greater than 10 are 11 and 12 on the dice meaning we've got 2 options out of 12.
So, 2/12 gives 1/6 in its simplest form
necesito ayuda con esto
Answer:
nacho taco Guadalupe Juan ching chong
Step-by-step explanation:
Noob
If you borrow $400 for 5 years at an annual interest rate of 3%, what is the total amount of money you will pay back?
Answer: $460
Step-by-step explanation:
To calculate the total amount of money you will pay back after borrowing $400 for 5 years at an annual interest rate of 3%, you can use the following formula:
Total amount = principal + interest
Principal = the amount you borrowed = $400
Interest = the amount of interest paid over the 5 years period.
To calculate the interest, we can use the formula:
Interest = Principal x Rate x Time
Rate = the annual interest rate expressed as a decimal = 0.03
Time = the time period in years = 5
So, the interest for the 5-year period is:
Interest = $400 x 0.03 x 5 = $60
Therefore, the total amount of money you will pay back is:
Total amount = $400 + $60 = $460
You will pay back $460 over five years if you borrow $400 at an annual interest rate of 3%.
Answer: To calculate the total amount of money to be paid back for borrowing $400 for 5 years at an annual interest rate of 3%, we need to use the formula for simple interest:
Simple interest = Principal x Rate x Time
where:
Principal = $400 (the amount borrowed)
Rate = 3% per year
Time = 5 years
Plugging these values into the formula, we get:
Simple interest = $400 x 0.03 x 5
= $60
Therefore, the total amount of money to be paid back is the sum of the principal and the simple interest:
Total amount = Principal + Simple interest
= $400 + $60
= $460
So, you will need to pay back a total of $460 after 5 years of borrowing $400 at an annual interest rate of 3%.
Step-by-step explanation:
Find the critical points of the autonomous differential equation dy = y2 – y?, dr sketch a phase portrait, and sketch a solution with initial condition y(0) = 4. a
The critical points occur when y = 0 or y = 1.
How to find the critical points of the autonomous differential equation?To find the critical points of the autonomous differential equation dy/dt = \(y^2 - y\), we set dy/dt equal to zero:
\(y^2 - y = 0\)
Factoring out y:
y(y - 1) = 0
So, the critical points occur when y = 0 or y = 1.
Next, let's sketch the phase portrait for the given autonomous differential equation. To do this, we plot the critical points and analyze the behavior of the equation in different regions.
The critical points are y = 0 and y = 1.
For y < 0 (below the critical points):
dy/dt = \(y^2 - y\)is positive since\(y^2\) is positive and -y is negative.The solution y(t) will be increasing.For 0 < y < 1 (between the critical points):
- dy/dt = \(y^2 - y\)is negative since both \(y^2\) and -y are positive.
- The solution y(t) will be decreasing.
For y > 1 (above the critical points):
dy/dt = \(y^2 - y\) is positive since both\(y^2\) and -y are positive.The solution y(t) will be increasing.Based on this analysis, the phase portrait can be represented as follows:
--[--> y > 1 --[--> y < 0 --[--> 0 < y < 1 --[-->
Arrows indicate the direction of increasing y.
Finally, let's sketch a solution to the autonomous differential equation with the initial condition y(0) = 4.
Starting at y(0) = 4, we can follow the phase portrait and see that y will decrease towards the stable critical point y = 1.
Sketching the solution curve:
y
| /\
| / \
| / \
| / \
| / \
| / \
| / \
| / \
| / \
|/________ \___________ t
0 1
The solution curve starts at y(0) = 4 and approaches the stable critical point y = 1 as t increases.
Learn more about critical points
brainly.com/question/32077588
#SPJ11
Find the derivative of the function using the definition of derivative. f(x) = 5x
The derivative is f'(x) = 5.
The limit definition of the derivative tells us that the derivative of a function is f is
f' (x) = \(\lim_{h \to \0} 0\) \(\frac{f(x+h)-f(x)}{h}\)
For this, f(x) = 5x and f(x + h) = 5(x + h)
So:
f'(x) = \(\lim_{h \to \}0\) \(\frac{5(x+h)-5x}{h}\)
= \(\lim_{h \to \}0\) \(\frac{5x+5h-5x}{h}\)
= \(\lim_{h \to \}0\) \(\frac{5h}{h}\)
= \(\lim_{h \to \}0\) 5
= 5
So, when f(x) = 5x , we see that its derivative is f'(x) = 5.
Learn more about Derivative at:
https://brainly.com/question/28104078
#SPJ4
4 problems with Volume with the awnser being 3,10,11 and 24
We want to design a math problem, where we calculate a volume and the answer is 24.
So, we will try first to imagine a figure with an easy shape, so we can calculate its volume. Take for example a box
This box has dimensions length l, width w and height h. A box with this dimensions would have a volume of
\(l\cdot w\cdot h\)Lets say that we want the volume to be 24. So we have the equation
\(l\cdot w\cdot h=24\)Now, we want to choose numbers to each variable. Lets say what l=4, w=3. So we would have
\(4\cdot3\cdot h=24=12\cdot h\)Then, by dividing both sides by 12 we get
\(h=\frac{24}{12}=2\)So we know that a box with a length of 4, width of 3 and a height of 2 has a volume of 24. So the problem could be
what is the volume of a box of length 4, width 3 and height 2?
plzzzzzzzzzzzzzzzzzzzz halppppppppppppppppp
Answer:
Exact Form:
7/2
Decimal Form:
3.5
Mixed Number Form:
3 (1/2)
I hope this helps! :)
Convert the units.
24 in. = _____ ft
24 inches equals 2 feet
Answer:
2 ft
Step-by-step explanation:
1ft = 12 inches
24/12 = 2
I need help!!! please help me!!!
Answer:
um ok the laiyflylfug;ou;
Step-by-step explanation:
One of your users calls you with a complaint that he can't reach the site www.. You try and access the site and discover you can't connect either but you can ping the site with its IP address. What is the most probable culprit
The site and discover can't connect either but can ping the site with its IP address is given by,
The most probable culprit in this scenario is a Domain Name System issue.
DNS is responsible for translating human-readable domain names into IP addresses that computers can understand.
When you enter a domain name into a web browser, it relies on DNS to resolve the domain name to the corresponding IP address.
If you are unable to access the site using its domain name .
But can ping the site successfully using its IP address, it suggests that the DNS resolution is failing.
The IP address connectivity indicates that the site itself is reachable and accessible, but the domain name is not being resolved correctly.
There are a few potential reasons for this DNS issue.
DNS server problems,
The DNS server you are using might be experiencing issues or downtime.
This can occur if the DNS server is misconfigured, overloaded, or undergoing maintenance.
DNS cache issue,
Your local DNS cache or the DNS cache of your internet service provider may have incorrect or outdated information.
Clearing the DNS cache on your computer or using alternative DNS servers can help resolve this issue.
DNS misconfiguration,
There might be a misconfiguration in the DNS settings for the domain itself.
This could include incorrect DNS records or problems with the domain's authoritative DNS servers.
Network connectivity issue,
There could be a network connectivity problem between your computer and the DNS server, preventing the resolution of domain names.
To troubleshoot and resolve the issue, you can try the following steps.
Clear your DNS cache,
Flush the DNS cache on your computer to ensure that any incorrect or outdated DNS information is cleared.
Change DNS servers,
Temporarily switch to alternative DNS servers, such as DNS or OpenDNS, to see if the issue persists.
Contact your ISP,
If the issue persists, contact your internet service provider and inform them about the problem.
They may be able to provide assistance or identify any broader DNS issues.
Check domain configuration,
If you are responsible for managing the domain, review the DNS settings and ensure they are correctly configured.
By investigating and addressing the DNS issue,
Able to resolve the problem and regain access to the site using its domain name.
Learn more about site here
brainly.com/question/31725792
#SPJ4
You sells It in Dest for will 9 $13000 bond $13 161 currently. mature in 6 6 years. thut Yield to maturity is Q What is the coupon rate? a) 11,987. b 16,28%. c) 18,61%. d) 14,32%
The coupon rate of the bond is 9.04% as calculated in the main answer.
Given:Selling price of bond= $13000Maturity value= $13161Time to maturity= 6 yearsThe yield to maturity of the bond is not given.Coupon rate refers to the rate of interest that is paid on the face value of the bond.
The formula to calculate the coupon rate is as follows: Coupon rate = (Annual coupon payment / Face value of the bond) x 100%The main answer to the given problem is as follows:We can find the annual coupon payment by using the formula as shown below:
Annual coupon payment = Yield to maturity x Face value of the bondSubstituting the given values, we getAnnual coupon payment = Yield to maturity x $13161Let the yield to maturity be ‘y’.Annual coupon payment = y x $13161We are given that the selling price of the bond is $13000
. Therefore, using the formula for yield to maturity, we can find the yield to maturity as shown below: 13000 = Annual coupon payment / (1+y/2)⁶ + $13161 / (1+y/2)¹²Simplifying the above expression,
we get a quadratic equation as shown below:2y² + 35y – 629 = 0On solving the above equation, we get y = 0.090398 or y = -17.540398We can ignore the negative value of ‘y’.
Therefore, the yield to maturity of the bond is 9.04%. Substituting this value in the formula for annual coupon payment,
we get Annual coupon payment = 9.04% x $13161. Annual coupon payment = $1189.72Using the formula to calculate the coupon rate, we get:
Coupon rate = (Annual coupon payment / Face value of the bond) x 100%Coupon rate = ($1189.72 / $13161) x 100%Coupon rate = 9.04%Therefore, the coupon rate of the bond is 9.04%.Option A - 11.987
The coupon rate of the bond is 9.04% as calculated in the main answer.
Therefore, the correct option among the given options is (A) 11.987. The solution to the given problem is explained in detail.
To know more about quadratic equation visit:
brainly.com/question/29269455
#SPJ11
PLEASE SOMEONE HELP MEEEE I AM LITERALLY FRYING NY BRAIN. NO LINKS OR I WILL REPORT YOU... PLEASE AND THANKS
Answer:
1. True
2. False
3. True
4. False
Step-by-step explanation:
If you fit a slope and intercept at the same time, then their errors will be correlated. True or False?
The given statement "if you try to match a slope and an intercept at the same time, their mistakes will be related" is TRUE.
What is the intercept?A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis.
This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y.
These points satisfy x = 0 because of this.
The errors of a slope and an intercept will be connected if you fit them simultaneously.
By changing Y to 0 in the equation and figuring out X, you can always determine the X-intercept.
Similarly, by putting X to 0 in the equation and solving for Y, you can always determine the Y-intercept.
Therefore, the given statement "if you try to match a slope and an intercept at the same time, their mistakes will be related" is TRUE.
Know more about the intercept here:
https://brainly.com/question/25722412
#SPJ4
solve sinx = 2x-3 using false position method
The root of the equation sinx = 2x-3 is 0.8401 (approx).
Given equation is sinx = 2x-3
We need to solve this equation using false position method.
False position method is also known as the regula falsi method.
It is an iterative method used to solve nonlinear equations.
The method is based on the intermediate value theorem.
False position method is a modified version of the bisection method.
The following steps are followed to solve the given equation using the false position method:
1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.
Here, f(x) = sinx - 2x + 3.
2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))
3. Evaluate the function at point c and find the sign of f(c).
4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.
5. Repeat the steps 2 to 4 until we obtain the required accuracy.
Let's solve the given equation using the false position method.
We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.
So, the root lies between 0 and 1.
The calculation is shown in the attached image below.
Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).
Learn more about equation
brainly.com/question/29657983
#SPJ11
What is the area, in square centimeters, of an 8.5 inch by 11 inch sheet of paper?A) 94 cm2 B) 240 cm2 C) 420 cm2 D) 6.0 × 102 cm2 E) 1.2 × 104 cm2
The square of the centimeter of the area is calculated by the square of the centimeter. The area of the rectangle is calculated by the formula width x length. So the rectangles area is 94cm
Squares have only one side that is squared to find the area of the shape. But in rectangle there will be two sides given that width and length of the shape. So to find the area the width and the length of the rectangle is given so the numerical must be multiplied. In the given question the width of the rectangle is 8.5 and the length of the rectangle is 11.
o the area of the rectangle can be found by the formula= w x l
=8.5 x 11
=93.5
approximately can be taken as 94 cm.
A rectangle can is a four sided shape that includes the length, width and height and that opposites sides are equal in the rectangle. The adjacent sides of the rectangle is perpendicular and the angle is right angle that is it is measured as 90 degree. A rectangle can be a parallelogram but parallelogram can not be equal to the rectangle.
To know more about the area of rectangle follow the link below:
https://brainly.com/question/8663941
#SPJ4
The question has an area because the square because the square has only one side and the area of the square can be found by squaring one side of square. So the actual question should be What is the area, in rectangle centimeters, of an 8.5 inch by 11 inch sheet of paper?
The New Horizons space probe passed the moon 8 hours and 35 minutes after launch. Write this number as a fraction and reduce. Choose the correct answer. Use 60 as your denominator, not 100, because there are 60 minutes in one hour. A. 9 3/7 hours B. 8 hours C. 8 1/2 hours D. 8 7/12 hours
Answer:
D
Step-by-step explanation:
8 hours and 35 minutes can be rewritten as the mixed fraction 8 35/60.
You can reduce this fraction by dividing the numerator and denominator by 5.
35/5 = 7
60/5 = 12
So, 35/60 = 7/12
Now add 8 to your reduced fraction.
8 + 7/12 = 8 7/12
Hope this helped!
Question 5 of 10
Which pair of functions are inverses of each other?
O A. f(x) = 2 + 15 and g(x) = 12x - 15
O B. f(x) = √3x and g(x) = () ³
O c. f(x) = 3 - 10 and g(x) = +10
3
D. f(x) = 11x-4 and g(x) = +4
The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11
To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.
Let's test each option:
Option A:
f(x) = x/2 + 15
g(x) = 12x - 15
f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x
g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x
Option B:
f(x) = ∛3x
g(x) = (x/3)^3 = x^3/27
f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x
g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x
Option C:
f(x) = 3/x - 10
g(x) = (x + 10)/3
f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x
g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x
Option D:
f(x) = 11x - 4
g(x) = (x + 4)/11
f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x
g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x
Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:
D. f(x) = 11x - 4 and g(x) = (x + 4)/11
for such more question on inverses
https://brainly.com/question/15066392
#SPJ8