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.
[tex]\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[/tex]
[tex]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[/tex]
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Step-by-step explanation:
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The verb "evaluate" is used in mathematics to mean to discover or determine the worth of something. Finding the precise value of an algebraic expression or numerical computation is relevant here as well as financial mathematics.
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
8x=
8(8)=
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Answer:
64
Step-by-step explanation:
To solve this equation, we have to plug 8 into x.
Plug 8 into x and multiply
8(8)
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Take care and have a lovely rest of your day! :)
4) Sara took a ferry to a nearby island that lasted for 5 days. Although she forgot to check the date when she departed, during the trip she heard someone say the date was August 14". When she arrived on the island, a native told Sara it was August 16th. What date did Sara start her trip?
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How is solving an equation with the variable on both sides of the equation the same as and different from solving an
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Answer:
when the variable is on both sides of the equation first collect the same variable in one side end evaluate it,
Step-by-step explanation:
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In Exercises 19-24, solve the equation. Determine
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Step-by-step explanation:
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Hence answer is
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Answer:
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Answers
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Percent formula, show your work
Answers
======================================================
Work Shown:
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-----------
Shortcut:
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y-z=0 -------(2)
x+3y-2z=5 -----(3)
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CD is a line of length 12 cm
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Answer:
E would be 6 spaces or the middle of points C and D.
Step-by-step explanation:
Please see picture.
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Kloee : [tex]3\frac{1}{4} = \frac{13}{4} =3.25[/tex]
High School :1.0
Middle School : 1.5
Football field : 5.7
KB: [tex]-4\frac{1}{8} = \frac{-33}{8} =-4.125[/tex]
Ben : -2.65
All the data points are plotted on the number line and mentioned clearly as an image with the solution.
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Plotted on the number line and mentioned clearly as an image with the solution.
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let f (t) be the population (in thousands of people) of math city, as a function the time t (in years), where t
Answers
The mean is the population of city in 2026.
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per year}
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The complete question is -
Let f(t) be the population (in thousands of people) of Math City, as a function the time t (in years), where t = 0 corresponds to the year 2020. In 2020, the population was 34000, and each year the population increases by 3000 people. (a) Model the population by finding a formula for f(t), using the appropriate choice of a linear, polynomial, power, trigonometric, or exponential function, or a piecewise combination thereof. (b) Evaluate the expression f(6), and write a sentence explaining what this means. (c) Solve the equation f(t) = 64, and write a sentence explaining what this means
Which of the following is true?
1 meter is the same size as 1 kilometer.
1 meter is greater than 1 kilometer.
1 kilometer is less than 1 meter.
1 kilometer is greater than 1 meter.
Answers
Answer: 1 kilometer is greater than 1 meter
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Sorry if not specific!
Are f(x) = 2x+4, g(x) = x-2 inverse of each other?
Answers
Answer:
This problem has been solved! See the answer Show transcribed image text Expert Answer Transcribed image text: Decide whether or not the functions are inverses of each other. f (x) = 2x + 4, g (x) = x – 2 no yes The function fis one-to-one.
Step-by-step explanation:
owes $56 for tickets to the school play. If each ticket cost $4, how many tickets did she buy?4 −pound bags. How many pounds of potting soil does Marianne buy?
Answers
The number of tickets that she buys will be 14 tickets.
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Marianne owes $56 for tickets to the school play. If each ticket cost $4. Then the number of tickets that she buys will be given as,
⇒ 56 / 4
⇒ 14 tickets
The number of tickets that she buys will be 14 tickets.
Your question was incomplete, but the complete question was given below.
Marianne owes $56 for tickets to the school play. If each ticket cost $4, how many tickets did she buy?
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Which equation represents a linear function? Iready- Understand functions, Level H.
Answers
Answer:
y = 4x + 5
Step-by-step explanation:
y = 4x + 5 is the only one that graphs a straight line
2/14 in simplist form
Answers
Answer: 1/7 or 0.142857
Step-by-step explanation:
Answer:
1/7 :)
Step-by-step explanation:
Find the value of sin c
Answers
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{7}\\ b=\stackrel{opposite}{\sqrt{95}}\\ \end{cases} \\\\\\ c=\sqrt{7^2~~ + ~~(\sqrt{95})^2}\implies c=\sqrt{49+95}\implies c=\sqrt{144}\implies c=12 \\\\[-0.35em] ~\dotfill\\\\ sin(C )=\cfrac{\stackrel{opposite}{\sqrt{95}}}{\underset{hypotenuse}{12}}\implies sin(C)\approx \text{\LARGE 0.81}[/tex]
