Answers
======================================================
Explanation:
To find the inverse, we swap x and y, then solve for y.
y = 2x-3
x = 2y-3
x+3 = 2y
2y = x+3
y = (x+3)/2
y = x/2 + 3/2
y = (1/2)x + 3/2
This shows the original function y = 2x-3 leads to the inverse y = (1/2)x+3/2, and vice versa.
--------------
Another approach:
Since we're given a list of multiple choice answers, we can rule out the non-answers.
Plug x = 0 into the first equation of choice A. It leads to y = 2
That output 2 is then plugged into the second equation for choice A. It leads to y = 13/2. We do not get the original input 0, which shows that the equations in choice A do not undo one another. They aren't inverses of each other.
This allows us to rule out choice A. Choices B and C are similar stories.
Notice that plugging x = 0 into the first equation of choice D leads to the output y = -3. Then plug this as the input into y = (1/2)x+3/2 and you should get y = 0 to get us back where we started. This partially helps confirm we have a pair of functions that are inverses of each other. I'll let you try other values.
Answer:
Step-by-step explanation:
Algorithm for deriving the formula of the inverse function
Step 1. In the formula for the original function, replace the notation of the argument and the value:
Step 2. From the resulting formula, express y(x).
Step 3. Take into account the constraints on the area of definition and the area of values of the original and/or inverse functions.
\(\displaystyle\\ y=\frac{1}{2}x+2\\\\ 1.\ x=\frac{1}{2}y+2\\ \Rightarrow\ x-2=\frac{1}{2}y \\2.\ Multiply\ both\ parts\ of\ the\ equation\ by\ 2:\\\\2(x-2)=y\\\\2x-4=y\\Thus,\\y=2x-4\neq 3x+\frac{1}{2} \\Answer:\ no\\\\2.\ y=5(x-2)\\\\1.\ x=5(y-2)\\\\2.\ Divide\ both\ parts\ of\ the\ equation \ by\ 5:\\\\\frac{x}{5} =y-2\\\\\Rightarrow\ \frac{x}{5}+2=y \\Thus,\\\\y=\frac{x}{5}+2 \neq \frac{1}{5}(x+2)\\ Answer:\ no\)
\(y=2x-3\\1.\ x=2y-3\\\\2,\ x+3=2x\\\\Divide\ both\ parts\ of\ the \ equation\ by \ 2:\\\\\frac{1}{2}(x+3)=y\\\\ Thus,\\\\y=\frac{1}{2}x+\frac{3}{2} \equiv\frac{1}{2}x+\frac{3}{2} \\\\Answer:\ yes\)
Related Questions
Find the particular solution of the differential equation that satisfies the initial equations. f"(x) = 3/x²' f(1) = 2, f(1) = 1, x > 0
Answers
The particular solution of the differential equation f"(x) = 3/x², with initial conditions f(1) = 2 and f'(1) = 1, can be obtained by integrating the equation twice.
Integrating the given equation f"(x) = 3/x², we get f'(x) = -3/x + C₁, where C₁ is a constant of integration. Integrating again, we find f(x) = -3ln(x) + C₁x + C₂, where C₂ is another constant of integration.
Using the initial conditions, we substitute x = 1, f(1) = 2, and f'(1) = 1 into the equation above. This yields the following equations:
2 = -3ln(1) + C₁(1) + C₂, which simplifies to C₁ + C₂ = 2,
1 = -3(1) + C₁.
Solving these equations simultaneously, we find C₁ = 4 and C₂ = -2.
Thus, the particular solution satisfying the given initial conditions is f(x) = -3ln(x) + 4x - 2.
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Select the number line that shows that two opposite numbers have a sum of 0.
Answers
Answer:
B
Step-by-step explanation:
because when we calculate it will be
Answer:
B
Step-by-step explanation:
The 2 numbers are the same just on opposite sides of 0. Therefore is you add them together, they will equal 0
can someone plz explain ratio to me
Answers
A ratio shows how much of one thing there is compared to another. Ratios are usually written in the form a:b. If you are making orange squash and you mix one part orange to four parts water, then the ratio of orange to water will be 1:4 (1 to 4). The order in which a ratio is stated is important.
What was the purpose of exploring North America? Briefly explain who Lewis and Clark were and describe their journey.
Who was Zebulon Pike? How was his experience different from that of Lewis and Clark?
Answers
A project to investigate the American West has been the Clark as well as Lewis Expedition, which was supported by the federal government.
What are Lewis and Clark?The main goal of the mission was to study the Missouri and Columbia river in search of tributaries that would traverse from the heart of the nation to the Western Pacific.
This fleet's main goals are to investigate the Missouri River, investigate the newly acquired Lands, and discover a land way to the Pacific Ocean.
The Lewis and Clark Expedition represented the first time that Americans traveled this far out towards the West by sea and rivers.
Pike, who lost his life in the conflict, rose to fame among American soldiers. Lewis and Clark subsequently eclipsed him with his legacy. Presently, he is famed for his unsuccessful attempt to scale Pike's Peak.
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Please help, I’ll give brainliest as soon as I can! I need an answer quick
Answers
Step-by-step explanation: 0-9-8+xyz
Sarah needded 1/3 cup of flour to make 1 apple pie. If she made 5 apple pies how many cups of flour would sarah need?
convert final answer to a mixed number
Answers
Answer:
1 2/3
Step-by-step explanation:
she will need 1 and 2/3rds cups of of flour
Answer:
1 2/3
Step-by-step explanation:
1/3 for 1 pie
1/3 x 5 for 5 pies = 1 2/3
Some steps to construct an angle MNT congruent to angle PQR are listed below.
Step 1: Draw a segment NT.
Step 2: Use a compass to draw an arc from point Q that intersects the side PQ of angle PQR at point A and the side QR at point B.
Step 3:
Step 4: Adjust the width of the compass to AB, and draw an arc from point X such that it intersects the arc drawn from N in a point Y.
Step 5: Join points N and Y using a straightedge.
Which statement describes step 3 correctly?
Use the same width of the compass to draw an arc from point T that intersects the segment NT at a point X.
Use the same width of the compass to draw an arc from point N that intersects the segment NT at a point X.
Use the same width of the compass to draw an arc from point A that intersects the segment NT at a point X.
Use the same width of the compass to draw an arc from point B that intersects the segment NT at a point X.
Answers
From the description of the construction of the congruent angle, we have;
The statement that describes step 3 correctly is; Use the same width of the compass to draw an arc from point N that intersects the segment AN at a point X
The reason for making the above selection is as follows:
The steps to construct an angle congruent to another angle are;
Step 1: Given an angle PQR, draw a working segment NT
Step 2: Place the needle of the compass at point Q and draw an arc (Q, QA), intersecting sides PQ and QR of the angle ∠PQR at points A and B respectively
Step 3: Place the needle of the compass at point N and draw an arc with the compass width QA from above the to intersect the segment NT at a point X
Step 4: Set the compass width to the distance AB with which an arc is drawn from point X so as to intersect the arc (N, QA) above at point Y
Step 5: The points Y and N are joined with a straight line to form the congruent angle
Analysis of the steps:
Given that in step 4, we have that the the arc drawn from point X with compass width AB is meant to intersect the arc drawn from point N, at point Y, we have that in step 3 an arc was drawn from point N with compass width QA from step 2 to intersect NT at a point X
Therefore;
Step 3 is best described by the following statement;
Use the same width of the compass to draw an arc from point N that intersects the segment AN at a point X
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Use the same width of the compass to draw an arc from point N that intersects the segment NT at a point X.
This option gives us the step 3.
This is because we want to have equal angles. Therefore we select an arc equal in length to arc AB which intersects NT at point X.
This can be explained more with the help of a diagram.
Two angles are equal when their dimensions are equal.
Arcs of equal length would give congruent angles.
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Kelly, Beth, Ann, and Tabitha were asked to draw a model to explain the following problem: Britt had 0.7 of a pan of brownies left. She covered 0.3 of them with chocolate icing. What part of the pan of leftover brownies now has icing? Indicate each diagram that shows this multiplication.
Answers
The proportion of the pan of leftover brownies that now has icing is of 0.21 = 21%.
What is a proportion?A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations to find the desired amounts in whichever context of the problem.
In the context of this problem, these amounts are given as follows:
Amount of the pan left: 0.7.Amount of the pan that was covered in icing: 0.3 of the remaining 0.7.Hence the part of the pan of leftover brownies that now has icing is obtained by the multiplication presented as follows:
0.7 x 0.3 = 0.21.
It can be interpreted by the multiplication of 7 and 3 = 21, and then the result moves two decimal places to the left as each factor of the multiplication has one decimal digit.
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A local car dealership is trying to sell all of the cars that are on the lot. Currently, there are 525 cars on the lot, and the general manager estimates that they will consistently sell 50 cars per week. Estimate how many weeks it will take for the number of cars on the lot to be less than 75. Write an inequality that can be used to find the number of full weeks, , it will take for the number of cars to be less than 75. Since is the number of full or complete weeks, = 1 means at the end of week 1. Write and solve the inequality
Answers
Answer:
525/50=10.5 it will take 10.5 weeks to get rid of every car we however only need to have below 75 so 525/50w<75
Step-by-step explanation:
First you need to divide 525 by 50 to show how many weeks it will take to sell all the cars. And then it should be one less week than the answer you just reacieved.
in PQR if m∠p is 14 less than five times x, m∠q is five less than x and m∠r is nine less than twice x find x and the measure of each angle.
x=
m∠p=
m∠q=
m∠r=
Answers
The value of x =26°, m∠p =116°, m∠q=21°, m∠r=43°
What is an angle?
An angle is formed when two lines meets at the same vertex. It is measured by degree. Based on the measurements angles are of three types.
Consider POR as a triangle.
Given that m∠p=5x-14, m∠q=x-5, m∠r=2x-9.
In triangle the sum of the angle is 180°, then
m∠p + m∠q +m∠r =180°
⇒5x-14+x-5+2x-9 = 180°
⇒8x-28=180°
⇒x=26°
then, m∠p=5x-14 = 5(26)-14 = 116°
m∠q=x-5 = 26-5=21°
m∠r=2x-9 = 2(26)-9=43°
Hence, the value of x =26°, m∠p =116°, m∠q=21°, m∠r=43°
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What role do hypotheses play in scientific inquiry, and why are null hypothesis used sometimes?
Answers
A hypothesis is a testable guess about how a commodity works. It may be an idea, proposition, a possible medium of commerce, or a statement about an effect. A null hypothesis is a vaticination that there's no difference between groups or conditions or a statement or idea that can be falsified or proved wrong.
What's meant by a hypothesis in statistics?
In Statistics, a thesis is defined as a formal statement, which explains the relationship between the two or further variables of the specified population. It helps the experimenter to restate the given problem into a clear explanation for the outgrowth of the study.
Characteristics of hypothesis
The important characteristics of the hypothesis are
• The hypothesis should be short and precise
• It should be specific
• A hypothesis must be related to the being body of knowledge
• It should be able to verification
What's the Null hypothesis?
The null hypothesis is a kind of hypothesis that explains the population parameter whose purpose is to test the validity of the given experimental data. This thesis is either rejected or not rejected grounded on the viability of the given population or sample. In other words, the null hypothesis is a hypothesis in which the sample compliances effect by chance. It's said to be a statement in which the surveyors want to examine the data. It's denoted by H₀.
Hence a hypothesis is a testable guess about how a commodity works. It may be an idea, proposition, a possible medium of commerce, or a statement about an effect. A null hypothesis is a vaticination that there's no difference between groups or conditions or a statement or idea that can be falsified or proved wrong
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The tables of ordered pairs represent points on the graphs of Equation 1 and Equation 2. Which system of equations is represented
by these two tables?
A)
4x + y = 24
2x + 2y = 4
B)
x + 4y = -24
x-y--4
C)
x - 4y= 24
x+y=4
D)
4x - y = 24
2x - 2y - 4
Answers
Answer:
Step-by-step explanation c
Let P (3,6) be a point on a figure and let P be the corresponding point on the image. The figure is dilated by a scale factor of 3. What are the coordinates of p
Answers
When the figure is dilated by a scale factor of 3, the original coordinates of P are (1,2).
What is coordinates?A coordinate system in geometry is a system that uses one or more numbers, or coordinates, to determine the position of points or other geometric elements on a manifold such as Euclidean space. The ordinate is the distance of a point from the x-axis scaled with the y-axis. Coordinates are the abscissa and ordinate combined. The study of algebraic equations on graphs is known as coordinate geometry. Plotting points, lines, and curves on an x and y axis is an example of coordinate geometry. Make corrections.
Here,
scale factor=3
dilated point=(3,6)
original coordinates=(3/3,6/3)
=(1,2)
The original coordinates of P are (1,2) when figure is dilated by a scale factor of 3.
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What is the value of the x variable in the solution to the following system of equations?
4x + 2y = 6
x - y = 3
Answers
Answer:
The solution is x=2 and y=-1
Step-by-step explanation:
(step 1)
4x + 2y = 6
x - y = 3 - then multiply by 2
4x +2y = 6
2x -2y = 6 then add
6x x = 12 x = 12/6 = 2
Substitue back in (step 1)
4 x 2 + 2y = 6
8 + 2y = 6
Answer is = 2y = -2 y= -1
Solution: x= 2
y= -1
Let sin(2x) – sin(x) = 0, where 0 ≤ x < 2π. What are the possible solutions for x?
Answers
Answer:
D. {0,π/3,π,5π/3}
Step-by-step explanation:
If g(x) = 3/4 x + 2, find g(-12).
Answers
Answer:
(-7)
Step-by-step explanation:
just plug in the number in the x place to solve
you were asked to find the p-value for the test statistic, given the following information: a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 423 gram setting. it is believed that the machine is underfilling the bags. a 26 bag sample had a mean of 415 grams with a variance of 256 . assume the population is normally distributed. a level of significance of 0.02 will be used. find the p-value of the test statistic.
Answers
Answer:
A.
Step-by-step explanation:
IM GUEssing that thi sis it
Janiszewski and Uy (2008) conducted an experiment in which they had 43 participants read 10 scenarios. All 43 participants each read all 10 scenarios. In this study, the researchers wanted to determine the impact of the scenario type on the anchoring and adjusting of participants. Anchoring and adjustment occurs when people use a starting point (anchor) as a basis to make judgments about a given scenario (adjustment). This is an example of what type of design
Answers
The design used in the study conducted by Janiszewski and Uy in 2008 is a within-subjects design.
Under this type of design, all candidates are exposed to all different levels of the independent variable.The independent variable is the scenario type, and all 43 participants each reads all 10 scenarios.
By using method, the researchers can directly compare participants responses and eliminating those individual differences as a potential confounding factor. It allows more precise assessment of the impact of the scenario type on the candidates anchoring and adjustment process.
Overall, the study conducted by Janiszewski and Uy in 2008 used a within-subjects design to explore the impact of scenario type on participants' anchoring and adjustment behavior.
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a solid metal prism has a rectangular base with sides of 4 inches and a height of 6 inches. a hole in the shape of a cylinder, with a radius of 1 inch, is drilled through the entire length of the rectangular prism.
Answers
The approximate volume of the remaining solid is 77.43 cubic inches
The volume of the rectangular prism is given by
V_rectangular_prism = base_area x height
where the base area is the area of a square with side length 4 inches
base_area = 4 x 4 = 16 square inches
So, the volume of the rectangular prism is
V_rectangular_prism = 16 x 6 = 96 cubic inches
The volume of the cylinder is given by
V_cylinder = π x r^2 x h
where r is the radius of the cylinder (1 inch) and h is the height of the rectangular prism (6 inches). So, the volume of the cylinder is
V_cylinder = π x 1^2 x 6 = 6π cubic inches
To find the volume of the remaining solid, we need to subtract the volume of the cylinder from the volume of the rectangular prism
V_remaining = V_rectangular_prism - V_cylinder
V_remaining = 96 - 6π ≈ 77.43 cubic inches
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The given question is incomplete, the complete question is:
A solid metal prism has a square base with sides of 4 inches, and a height of 6 inches. A hole in the shape of a cylinder, with a radius of 1 inch, is drilled through the entire length of the rectangular prism. What is the approximate volume of the remaining solid, in cubic inches?
What is the slope of the line?
-5/2 -2/5 2/5 5/2
what is -5 + -2
Answers
Answer:
5/2 it is positive and you always do rise over run.
-5+-2=-7
Step-by-step explanation:
how many feet should be cut off to make a plank 5 7/8 feet long
Answers
Answer:
2 5/8
Step-by-step explanation:
5 7/8 + 2 5/8= 8 1/2
Answer:
3 4/8 or 3 1/2
Step-by-step explanation:
Let R be the region in the first quadrant bounded by the graph of y = Vx - 1. the x-axis, and the vertical line * = 10. Which of the following integrals gives the volume of the solid generated by revolving R about the y-axis? (A) = L " (x - 1) dx (B) - L" (100 - (x - 1) dx (C) 10 dy (D) * 100 dy
Answers
L " (x - 1) dx integrals gives the volume of the solid generated by revolving R about the y-axis
Which one is generated by revolving R about the y-axis?The integration or antiderivative processes can be used to determine the curve's area under it. For this, we require the curve's equation (y = f(x)), the curve's axis boundary, and the curve's border limitations.
Let R be the area in the first quadrant enclosed by the hyperbolas xy = 1 and xy = 3, the lines y = x and y = 3x, and the lines xy = 1. The third quadrant is also constrained by those four curves, which we are ignoring. xy dA. = 1 v .
Let R be the region in the first quadrant bounded by the graph of y = Vx - 1. the x-axis, and the vertical line * = 10.
= L " (x - 1) dx integrals gives the volume of the solid generated by revolving R about the y-axis
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Identify the terminal point for a 45° angle in a unit circle.O A. (24)O B. (1.)Oc. (1,1)O D. (2,3)
Answers
(x, y) = ( cos 45, sin 45) =
\(=\text{ (}\frac{\sqrt[]{2}}{2}\text{ , }\frac{\sqrt[]{2}}{2}\text{ )}\)The correct option is A
One morning, Justin drove 2 hours before stopping to eat lunch. After lunch, he increased his speed by 10 mph. If he completed a 220-mile trip in 6 hours of driving time, how fast (in miles per hour) did he drive in the morning
Answers
Answer:
30
Step-by-step explanation:
Let x be his speed at the morning, in miles per hour.
Then his speed after lunch was (x+10) mph.
2x + 3(x+10) = 220.
2x + 3x + 50 = 220
Find the area of this triangle. Round to
the nearest tenth.
17 m
35°
15 m
[? ]m2
![Find the area of this triangle. Round tothe nearest tenth.17 m3515 m[? ]m2](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/pfLdIWgL64dmRaAHmMcCh7dWelp7bJRC.png)
Answers
Answer:
32m²
Step-by-step explanation:
thanks me later ,correct me if I'm wrong
Answer: 73.1
Step-by-step explanation:
yea
The time series regression model contains a variable W and a regression equation of y = 200 + W + 2W2 to forecast future values. If W represents a time period, what is the forecast for time period 2 and the forecast error if the actual value for time period 2 is 100? Select the best answer.
forecast value = 210; forecast error is 110
forecast value = 210; forecast error is -110
forecast value = 210; forecast error is 0
forecast value = 100; forecast error is 0
Answers
The forecast value for time period 2 is 210, and the forecast error is -110 when the actual value is 100. Option B
To calculate the forecast value for time period 2, we substitute W = 2 into the regression equation:
y = 200 + W + 2W^2
= 200 + 2 + 2(2^2)
= 200 + 2 + 2(4)
= 200 + 2 + 8
= 210
Therefore, the forecast value for time period 2 is 210.
To calculate the forecast error, we compare the forecasted value with the actual value for time period 2. Given that the actual value is 100, the forecast error can be calculated as the difference between the actual value and the forecast value:
Forecast error = Actual value - Forecast value
= 100 - 210
= -110
Hence, the forecast error is -110.
Therefore, the correct answer is:
Forecast value = 210; forecast error is -110. So Option B is correct.
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Chris signed-up for an experiment. The experimenter indicated that Chris would be placed into a group with nineteen other students based on a random number Chris received from the experimenter. The experimenter was most likely conducting ________________________-.
Answers
The experimenter was most likely conducting a randomized controlled trial, also known as a randomized experiment.
In this type of experiment, participants are randomly assigned to different groups, such as an experimental group or a control group, to ensure that any observed effects can be attributed to the intervention being tested rather than other factors.
In this case, the experimenter is using a random number to assign Chris to a group with nineteen other students, which suggests that there may be multiple groups involved in the experiment. This type of design is often used in scientific research to test the effectiveness of a new treatment, intervention, or program.
Randomized controlled trials are considered the gold standard in research design because they provide strong evidence for causal relationships between variables. By randomly assigning participants to different groups, researchers can control for confounding variables and ensure that any observed differences between groups are due to the intervention being tested.
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which of the three curves drawn matches the graph of y = 2x 2 + x?
Answers
Answer:
y= 0 1 2 3 4
Step-by-step explanation:
just minus 2 by all of the numbers from x
in Pittsburgh, the sales tax is charged at the rate of 6%. Find the and the total price of a stereo that cost $860
Answers
help me plss!!!!!!!!!
Answers
Answer:
B. SSSStep-by-step explanation:
We are given two congruent sides.
The third side AB is common and therefore congruent to itself.
It gives us 3 congruent sides.
This is a side-side-side or SSS postulate.
Correct choice is B