Answers
The composite function's value, (gof)(5), is equivalent to 6.
What are composite functions?A mathematical procedure called composite combines two functions, f and g, to produce a third function, h(x), where g(x) is the sum of f(x) and h(x).
Given the aforementioned functions,
f(x) = x^2-6x+2 and;
g(x) = -2x
The composite function is known as the gof (5)
(gof) = g(f(x)) where;
f(x) = g(x2-6x+2) and;
f(x) = -2(x2-6x+2).
Substitute the given functions into the composite;
g(f(5)) = -2(5^2-6(5)+2)
g(f(5)) = -2(-3) = 6
The comparable composite value is provided by this.
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Related Questions
Write the equation of the function shown below. Identify domain and range.
Answers
The function can be split in 2 straight lines: the first one from x = 2 to the left, and the other one from the same point to the right.
Now, a straight line equation is of the form
[tex]ax+m[/tex]Where a is the slope and m is the y-intercept.
"Left" line:
- m (y-intercept):
To find it we need to see where the line cross (intercepts) the y-axis. From the figure we can see that m = -2.
- a (slope):
To calculate the slope, we can use the following equation:
[tex]a=\frac{\Delta y}{\Delta x}[/tex]Where, chossing 2 points in the line, we have:
[tex]\begin{gathered} \Delta y=how\text{ much do we move up or down between the 2 points} \\ \Delta x=\text{ how much do we move to the right betw}en\text{ the 2 points} \end{gathered}[/tex]Look that for x we have to move to the right. Let's see a drawing:
In our case, we can take the points (0, -2) and (2, 4), so, we have:
[tex]a=\frac{\Delta y}{\Delta x}=\frac{4-(-2)}{2-0}=\frac{6}{2}=3[/tex]So, we have the equation for the "left" line:
[tex]3x-2[/tex]-"Right" line:
- m (y-intercept):
In this case we can not see where the line cross (intercepts) the y-axis. Let's leave this for latter.
- a (slope):
As we did before, we can pick to points on the line, like (3, 1) and (2, 4).
[tex]a=\frac{\Delta y}{\Delta x}=\frac{1-4}{3-2}=\frac{-3}{1}=-3[/tex]- m (y-intercept) continues:
We now know that the equation for this line is:
[tex]-3x+m[/tex]To find m, we can pick one single point and solve for that variable. For example, taking the point (2,4), we have:
[tex]\begin{gathered} y=ax+m \\ y=-3x+m \\ 4=-3\cdot(2)+m \\ 4=-6+m \\ 4+6=m \\ 10=m \end{gathered}[/tex]And so, for the right line, we have:
[tex]-3x+10[/tex]Finally, the equation of the function can be written as:
[tex]f(x)=\begin{cases}3x-2\text{ if x }\leq\text{ 2} \\ -3x+10\text{ if x }\ge\text{ 2}\end{cases}[/tex]Now, the domain of the function is the set of points (or numbers) for which the function has values. The set of departure. In this case, all the numbers can be "trasnformed" or mapped with this function, so the domain is all the numbers, the set of real numbers, R:
[tex]\begin{gathered} -\inftyLastly, the range of the function is the complete set of all possible resulting values after aplying the function. We can see that the function can takes, as maximum, a value of 4, then the range is:[tex]\begin{gathered} (\infty;\text{ 4}\rbrack \\ or \\ y\leq4 \end{gathered}[/tex]Max's bedroom is rectangular shaped and has a total area
of 140 square feet. If the short wall is at 10 feet long,
what is the length of the longer wall?
Answers
Answer:
14 ft
Step-by-step explanation:
Area is length times width. So, you need to find something times 10 that equals 140. Or, you could just do 140 divided by 10. 140/10=14.
8. Solve:
The cd player costs $45 and is sells for $69. Find the mark up rate.
Answers
Answer:
53.3333333+ %In 3 decimal places (if you prefer):
53.333 %Step-by-step explanation:
mark up rate = gross profit/ cost (expressed as a percentage)
gross profit = sale price - cost
mark up rate = (69-45)/45 *100
=24/45 * 100
= 53.333%Answer:
53.33%
Step-by-step explanation:
Hello!
First, let's find out how much the cost went up:
69 - 4524The cost went up by 24 dollars. To find the markup, we have to see what percentage of 45 is 24.
24/45 * 1000.5333... * 10053.33 %The markup is 53.33 percent.
help me pleaseeeeeeeeeeeeeeeeeeeeeeeee !!!
Answers
Answer:
f(x) = 5/6x +21
Step-by-step explanation:
You want the equation of the line with slope 5/6 through point (-18, 6) written using function notation.
Point-slope formGiven a slope and a point, it can be useful to write the equation of the line in point-slope form:
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
The line of interest has slope m = 5/6 through point (h, k) = (-18, 6), so its equation can be written as ...
y -6 = 5/6(x -(-18))
y = 5/6x +15 +6 . . . . . eliminate parentheses, add 6
y = 5/6x +21
Function notationFunction notation gives a name to the relation, and identifies the independent variable. We want to call this f(x), meaning the name of the relation is "f", and the independent variable is "x". Essentially, "f(x)" replaces "y" in the above equation:
f(x) = 5/6x +21
1. Brian's math test scorés: 86, 90, 93, 85, 79, 92, 20, 84Mean:Median:
Answers
Answer:
[tex]\begin{gathered} \text{ Mean=78.625} \\ \text{Median}=84 \end{gathered}[/tex]Step-by-step explanation:
The mean is the sum of all the values in a set of data, divided by the number of values on the list.
Hence, the mean of Brian's math test scores:
[tex]\begin{gathered} \text{ Mean= }\frac{86+90+93+85+79+92+20+84}{8} \\ \text{ Mean=}\frac{629}{8} \\ \text{ Mean=78.625} \end{gathered}[/tex]The median is the middle number in a sorted, ascending or descending, list of numbers:
Arrange the data set from smallest to largest, if the number of data set is even, the median is the average of the two middle data points in the list.
[tex]20,79,84,82,86,90,92,93[/tex]Hence, the median is the average of 82 and 86:
[tex]\begin{gathered} \text{Median}=\frac{82+86}{2} \\ \text{Median}=84 \end{gathered}[/tex]going to send u a pic of the q
Answers
we have the phrase
fifteen occupant or less
[tex]\begin{gathered} n\leq15 \\ n\ge0 \end{gathered}[/tex]Remember that the occupants can not be negative numbers
so
n=0,1,2,3,.....,15we have
seventy stadiums or more
the algebraic expression is
[tex]n\ge70[/tex]so
n=70,71,72,73,...
option Abecause the number of stadiums must be a whole number be aequation [tex] - 3 - 4x \leqslant 21.[/tex]solve..........
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In the las t image you can see that when you multiply both sides of the inequality for ( - 1 ) the symbol less than or equal changes to greater than or equal
What is the correct answer there are more selective choices I’ll show you later
Answers
distribute 2(3x - 1) =
Answers
Given:
2(3x - 1)
Let's distrubute 2 to the terms in the parenthesis.
To distribute, use distributive property to distribute 2 to (3x - 1).
Thus, we have:
2(3x - 1)
= 2(3x) + 2(-1)
= 6x + -2
= 6x - 2
ANSWER:
6x - 2
Factor out the GCF in the polynomial 18x-12
Answers
Select all correct solutions for the equation.
15(2x - 10) + 4x = -2(15x + 4)
A. x = 2.21875
B. x = 14264x = 14264
C. x = 35.5
D. x = 7132x = 7132
E. x = 39.5
F. x = 792x = 792
G. x = 714
Answers
Answer:
Step-by-step explanation:
We can rewrite:
15(2x-10) + 4x = -2(15x+4)
gives
30x - 150 + 4x = -30x -8
Adding 30x on both sides and adding 150 on both sides gives us:
30x + 4x - 150 + 30x + 150 = -30x - 8 + 150 + 30x
which gives us: 64x = 142
We can now divide both sides by 64, which gives us:
x = 142 / 64 = 2.21875
So the only right answer is A
You can fill in all the other options into the starting equation if you want too see this is indeed true
60 is 24% of what number?
Answers
Explanation
Question
60 is 24% of what number?
Let the number be n.
is represent = in mathematics
of represent x
60 is 20% of what number?
60 = 20% x n
[tex]undefined[/tex]The number of bacteria present after t hours is given by the function B = 100e^0.563t. How many bacteria will there be after 4 hours? Round to the nearest whole number and label your answer.
Answers
Answer;
[tex]B\text{ = 951}[/tex]Explanation;
Here, we want to get the number of bacteria that will be present after 4 hours
What we have to do here is to substitute 4 for t in the equation of the model given
Mathematically, we have this as;
[tex]\begin{gathered} B=100e^{0.563t} \\ B=100e^{(0.563\times4)} \\ B\text{ =950.67 = 951} \end{gathered}[/tex]Which represents the equation 6x+3y= 12 whO y=-2x+4O y = 2x+4Oy=-2x-4O y=2x-4
Answers
Given the equation:
6x + 3y = 12
We need to solve for y. Dividing by 3:
2x + y = 4
Subtracting 2x:
y = -2x + 4
First choice
a. What is the dependent variable?b. What is the independent variable?c. What is the slope (rate of change) of the line?d. What does this number mean for the circus?e. What is the y-intercept (initial condition) of the line? Why?
Answers
Part (a)
The dependent variable should be y for a function y=f(x).
Therefore, in this case dependent variable is profit
Part (b)
The independent variable is number of tickets sold.
Part (c)
Consider two coordinates in the graph (40,60) and (20,30).
Then, the slope will be,
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ =\frac{60-30}{40-20} \\ =1.5 \end{gathered}[/tex]Therefore, the avlue of slope is 1.5.
Part (d)
The slope is the rate of change profif with repect to the number of tickets sold for a circus.
Part (e)
From the graph, it can be noted that the y intersept is 0. Because intitial point is (0,0).
In a two digit number, the tens digit s twice the ones digit. the diffrence of the ones digit and half the tens digit is 0. An equation created to find the digit in the ones place will have:No solutionOne soulutionMany solutions
Answers
let
the two digit = xy
x= tens digit
y = ones digit
2x = y
[tex]\begin{gathered} y-\frac{1}{2}(2x)=0 \\ y-x=0 \end{gathered}[/tex]2x - x =0
x = 0
Between which steps does Morgan use the subtraction property of equality to justify her work?
Answers
Morgan uses the subtraction property of equality in step 5.
What is the subtraction property of equality?The subtraction property of equality describes the balancing of an equation by subtracting the same value on both sides of the equality.
There is also the addition property of equality which states adding the same number to both sides of the equality also balances an equation.
Given Morgan's work Step 1 - 6(x+5) = 25.
Step 2 - 6(x) + 6(5) = 25 . (Distributive property).
Step 3 - 6x + 30 = 25.
Step 4 - 6x + 30 - 30 = 25 - 30 (Subtraction property of equality)
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Whats 5 and 6/4 ×8 and 9/6
Answers
Given that 5 6/4 x 8 9/6
Firstly, we need to convert the mixed fraction into improper fractions
[tex]undefined[/tex]The sum of three numbers is 107. the second number is 7 less than the first. The third number is 2 times the second. What are the numbers?
Answers
x = 32
First number is 32.
Second number is 25.
Third number is 50.
32 + 25 + 50 = 107
Math checks out
Write the correct equation for the following statement.
You decide to rent a limo for prom. The rate is $175 plus $5 per mile
traveled. Write an equation to calculate your total cost (c) at the end of
the evening for a given number of miles (m).
If you travel 45 miles what will be your total bill at the end
of the evening?
Answers
The most appropriate choice for equation and linear equation will be given by-
c = 175 + 5m is the equation for calculation of total cost (c) at the end of
the evening for a given number of miles (m).
For travelling 45 miles, total cost at the end of the evening is $400
What is equation and linear equation?
A statement that shows the equality between two mathematical expressions by connecting the two mathematical expression with an equal to (=) sign is called equation.
A one degree equation is known as linear equation.
Here,
Let the number of miles be m
Fixed cost for renting a limo for prom = $175
For travelling one mile by limo, amount charged = $5
For travelling m miles by limo, amount charged = $5m
Total cost for renting a limo for pron = $(175 + 5m)
By the problem,
c = 175 + 5m
This is the equation for calculation of total cost (c) at the end of
the evening for a given number of miles (m).
Now,
Putting m = 45 in the above equation,
[tex]c = 175 + 5 \times 45\\c = 175 + 225[/tex]
[tex]c =[/tex] $[tex]400[/tex]
For travelling 45 miles, total cost at the end of the evening is $400
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For every five 'g's in the drama club, there are 4 'b's in the club. Suppose there are 24 'b's participating in drama club. How many 'g's are there?
Answers
There is 30 ‘g’s in the club by using proportions.
What is proportion?
Mathematically compare two numbers by comparing them proportionally. In terms of proportion, two sets of given numbers are said to rise or decrease in the same ratio if they are directly proportionate to one another.
Two ratios are said to be in proportion when they are the same. For instance, a train needs to cover 250 kilometers in 5 hours if it is moving at a speed of 50 kilometers per hour. 250 km/5 hours at 50 km/h, for instance.
Given, for 5 ‘g’ there are 4 ‘b’
There are 24 ‘b’ in drama club,
g = 24/4×5
g=30
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"How can an understanding of thenumber properties help you to solveequations that represent real-worldsituations?"
Answers
Undersatanding number properties helps you to solve equation because we can transfom ans simplify any equation in a way we just have to add or rest numbers. for example when you go shopping and there is a sale or a promotion, knowing this properties would help you to get the best price.
Help! Help! 9261 divided by 57
Answers
162.4736842 is 9261 divided by 57
david borrowed $4 from his mother each of the last tree months how much money does he owe his mother?
Answers
Answer:
12$
Step-by-step explanation:
He borrowed 4$ for three months.
4 x 3 = 12.
Answer = 12.
Hope this helps!
(Brainliest would mean a lot to me, thanks!)
Use the following graph of quadratic function f(x)=x2+2x−3 to answer the question. The graph of the function f(x) as described in the problem passing through (-3, 0), (-1, -4) & (1, 0). Which of the following domain restrictions allow an inverse function?There is more than one correct answer. Select all correct answers.
Answers
Looking at the graph of f(x), we can see that some values of y have two corresponding values of x.
Since the inverse function changes y with x and vice versa, there will be values of x that will have more than one corresponding value of y, this way it will not be a function.
In order to ensure that f(x) has an inverse function, we need a domain restriction that makes every value of y have only one corresponding value of x.
The domain restrictions that cause every value of y to have only one corresponding value of x are:
x >= -1
x <= -1
0 <= x <= 3
Therefore the correct options are the first, third and fourth options.
6. Taylor lost 5 chips to Minnie while playing a card game. Taylor then lost 20 chips toSally in the second round. Taylor won 10 chips from Paul in the 3rd round. Howmany chips did Taylor make or lose during these 3 rounds?
Answers
Step 1
[tex]\begin{gathered} \text{Given; } \\ \text{Taylor lost 5 chips to Minnie in round 1} \\ \text{Taylor lost 20 chips to Sally in round 2} \\ \text{Taylor won 10 chips from Paul in the 3rd round.} \end{gathered}[/tex]Step 2
Find how many chips Taylor made or lost during these 3 rounds.
[tex]\begin{gathered} \text{Taylor made 10 chips} \\ \text{Taylor lost (20+5) chips} \end{gathered}[/tex][tex]\begin{gathered} \text{Total chips made or lost= 10+(-25)} \\ \text{Total chips made or lost}=10-25=-15 \\ \text{The negative sign means he lost chips} \end{gathered}[/tex]
Since the total number of chips made or lost = -15, then Taylor lost 15 chips during the 3 rounds. If it where to be positive, then it woud have ment Taylor won some chips.
Therefore, Taylor lost 15 chips in the 3 rounds
6. Three formulas for calculating present value are shown below.Formula #1Formula #2Formula #311PV =FV(1 + i)PVOA = CG--)PVAD = CG--T) +0Ci(1 + i)nti(1+i)nt-1Part 1: Using complete sentences, explain how each of these formulas is used.Part 2: Create an example scenario for at least one of the formulas.(3
Answers
SOLUTION:
Case: Present Value
Present Value is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has interest-earning potential.
Part 1
[tex]PV=\frac{FV}{(1+i)^{nt}}[/tex]Sentence:
The Present Value is the Future Value divided by 1 is added to the rate of returns(i), raised to the number of periods(nt).
Part 2:
Present Value of Ordinary Annuity
[tex]PVOA=C[\frac{1}{i}-\frac{1}{i(1+i)^{nt}}][/tex]C is the annuity payment deposited or received at the end of each period.
i= discount or interest rate per period
n= number of periods.
The factor with interest rate and the number of periods is multiplied by annuity payments
Part 3:
Present value of Annuity due
[tex]PVAD=C[\frac{1}{i}-\frac{1}{i(1+i)^{nt-1}}]+C[/tex]C is the annuity payment deposited or received at the end of each period.
i= discount or interest rate per period
n= number of periods.
The factor with interest rate and the number of periods less 1 is multiplied by annuity payments and then added again to the annuity payments
Example of Part 1 (Present Value)
What is $56000 in 5 years time worth now, at an interest rate of 10%?
Based on a poll,67 % of Internet users are more careful about personal information when using a public Wi-Fi hotspot. What is the probability that among 4 randomly selected Internet users, at least one is more careful about personal information when using a public Wi-Fi hotspot? How is the result affected by the additional information that the survey subjects volunteered to respond?
Answers
The probability that among 4 randomly selected Internet users, at least one is more careful is 0.988.
Because of the bias toward convenience when retrieving the sample, the outcome might be higher. because respondents to the survey were chosen voluntarily, not at random.
What is probability?Calculating the likelihood of an event occurring, which is represented as a number between 1 and 0, is the subject of the mathematical branch known as probability. A coin toss, for instance, has a probability of 1 because, assuming the coin lands flat, there are only two possible outcomes: "heads" or "tails."
This means that any event with this probability is guaranteed to occur. For instance, a coin toss has an equal chance of coming up "heads" or "tails," so an event with a probability of.5 can be regarded as having equal odds of happening or not happening.
According to the poll, 67% of Internet users are more careful about personal information when using a public Wi-Fi hotspot.
Which means the probability of more careful is 0.67
And probability of not careful is: 1-0.67 = 0.33
We have selected four random Internet users and we need to find the probability that at least one is more careful about personal information.
P(At least one careful) = 1 - P(None of them careful)
P(At least one careful) = 1 - (0.33×0.33×0.33×0.33)
P(At least one careful) = 1 - 0.012
P(At least one careful) = 0.988
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Please help!!!!!!! I am stuck and don't understand
Given that f(x)=x^2-x and g(x)=3x+9, Find
(A) (f+g)(-2)=
(B) (f-g)(-2)=
(C) (fg)(-2)=
(D) (f/g)(-2)=
Answers
The value of the following composite function is as follows:
(f + g)(-2) = 5(f - g)(-2) = - 5(fg)(-2) = 18(f/g)(-2) = 2How to solve composite function?The composite functions can be solved as follows:
Therefore, the given function are:
f(x) = x² - x
g(x) = 3x + 9
Hence,
a.
(f + g)(-2) = f(-2) + g(-2)
f(-2) + g(-2) = (2)² - 2 + 3(-2) + 9
f(-2) + g(-2) = 4 - 2 - 6 + 9
f(-2) + g(-2) = 5
Therefore, the function (f + g)(-2) = 5
b.
(f - g)(-2) = f(-2) - g(-2)
f(-2) - g(-2) = (2)² - 2 - (3(-2) + 9)
f(-2) - g(-2) = 4 - 2 - 3
f(-2) - g(-2) = -5
Therefore, the function (f - g)(-2) = - 5
c.
(fg)(-2)= f(-2) × g(-2)
f(-2) × g(-2) = (-2)² - (-2) × 3(-2) + 9
f(-2) × g(-2) = 4 + 2 × 3
f(-2) × g(-2) = 6 × 3
f(-2) × g(-2) = 18
Therefore, the function (fg)(-2) = 18
d.
(f/g)(-2) = f(-2) / g(-2)
f(-2) / g(-2) = -2² - -2 / 3(-2) + 9
f(-2) / g(-2) = 6 / 3
f(-2) / g(-2) = 2
Therefore, the function (f/g)(-2) = 2
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what is 7754-(9x34)+667
Answers
Answer:
the answer is 8115
Step-by-step explanation:
you do 9 times 34 which is 306. then u do 7754 minus 306 which is 7448. then u add 667 to that which is 8115.