Answers
7. The composite functions are given as follows:
a. f(g(x)) = [tex]\frac{3x}{-x^2 + 3x - 1}[/tex].
b. g(f(x)) = [tex]\frac{3x(x - 1)}{9x^2 + x - 1}[/tex]
c. (f(g(3)) = -9.
8. The inverse function is given as follows:
[tex]f^{-1}(x) = \frac{4 + x}{3 - x}[/tex]
How to obtain the composite function?The composite functions are obtained using the inner function as the input to the outer function.
In this problem, the functions are defined as follows:
f(x) = x/(x - 1).g(x) = 3x/(x² + 1).The composite of f and g is:
[tex]f(g(x)) = f\left(\frac{3x}{x^2 + 1}\right) = \frac{\frac{3x}{x^2+1}}{\frac{3x}{x^2+1} - 1} = \frac{\frac{3x}{x^2+1}}{\frac{-x^2 + 3x - 1}{x^2 + 1}} = \frac{3x}{-x^2 + 3x - 1}[/tex]
At x = 3, the numeric value of the composite function is given as follows:
f(g(3)) = 9/(-9 + 9 - 1) = -9.
The composite function of g and f is given as follows:
[tex]g(f(x)) = g\left(\frac{x}{x - 1}\right) = \frac{\frac{3x}{x - 1}}{\left(\frac{3x}{x - 1}\right)^2 + 1} = \frac{3x}{x - 1} \times \frac{(x - 1)^2}{9x^2 + x - 1} = \frac{3x(x - 1)}{9x^2 + x - 1}[/tex]
Inverse functionThe function is given as follows:
y = (3x + 4)/(x - 1)
The find the inverse, the variables x and y are exchanged, and then y is isolated, as follows:
x = (3y + 4)(y - 1)
xy - x = 3y + 4
3y - xy = 4 + x
y(3 - x) = 4 + x
y = (4 + x)/(3 - x)
[tex]f^{-1}(x) = \frac{4 + x}{3 - x}[/tex]
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Related Questions
a marine biologist wants to estimate the mean size of the barnacle semibalanus balnoides on a stretch of rocky shoreline. to do so, he randomly selected twenty 10 by 10 square inch plots and measured the size of every barnacle in each selected plot. this is an example of
Answers
Option B is the correct choice
A marine biologist measured the size of each barnacle in twenty 10 by 10 square inch areas that were chosen at random. Cluster sampling is illustrated by this.
For a study that is a population into clusters, such as districts or schools, researchers will divide the population into multiple groups (clusters) and will then randomly select some of these clusters as your sample. Ideally, each cluster should be a miniature reflection of the population as a whole.
In order to determine the average size of the barnacles Semibalanus balconies along a section of rocky shoreline, a marine biologist is conducting this study. To do this, he measured the size of every barnacle in each of the twenty 10 by 10 square inch plots that were randomly chosen. Cluster sampling is illustrated by this. (Option B)
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COMPLETE QUESTION:
A marine biologist wants to estimate the mean size of the barnacle Semibalanus balconies on a stretch of rocky shoreline. To do so, he randomly selected twenty 10 by 10 square inch plots and measured the size of every barnacle in each selected plot. This is an example of
a. convenience sampling.
b. cluster sampling.
c. stratified random sampling.
d. simple random sampling.
e. voluntary sampling.
Peter puts $300.00 into an account to use for school expenses. The account earns 8%
interest, compounded annually. How much will be in the account after 10 years?
Answers
A farmer sold 50 cows. If this was 20% of his herd, how many cows were in his herd?
Answers
Principal Interest Rate Time Simple Interest
$12,000 4.25% 5 years
Answers
The value of Simple interest for the given data comes as $2550.
Given,
The Principal amount is equal to 12,000 dollars.
The Rate of Interest is stated at 4.25%.
The Total time period given for the question is 5 years.
Let the principal amount be considered as (P), the Rate of Interest per annum be (R), the Time period is (T), and Simple Interest is (S.I).
So, according to the given question,
P = $12,000
R = 4.25%
T = 5 years
We know, Simple interest can be calculated by multiplying the Principal amount with the Rate of Interest as well as the Time period.
If we write it mathematically, the formula will be,
S.I = PRT/100
=> S.I = (12,000* 4.25* 5)/100
=> S.I = (2,55,000)/100
=> S.I = $2550.
Hence, the value of Simple Interest will be 2550 dollars.
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[24+9-(5x3)+10]÷2
what is the value of the following the expression
Answers
Answer:
14
Step-by-step explanation:
[tex](33 - (15) + 10) \div 2 \\ 33 - 15 + 10 \div 2 \\ 18 + 10 \div 2 \\ 28 \div 2 \\ = 14[/tex]
Answer:14
Step-by-step explanation:1/2 (24+9- 5 x 3 + 10
Drag the tiles to the correct boxes. Not all tiles will be used.
Determine which steps are used to find the product shown. Put the steps in the order in which they would be performed.
Answers
Determine which steps are used to find the product shown. Put the steps in the order in which they would be performed.
See photo below. Comment for more clarification.
I need help like asap !!!
only numbers and decimal points
Answers
Answer:
a = 6.63 cm
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ (12)² = a² + (10)²
→ 144 = a² + 100
→ a² = 144 - 100
→ a = √44
→ [ a = 6.63 cm ]
Hence, value of a is 6.63 cm.
Use slope-intercept form to write the equation of a line that has a slope of −3 and passes through the point (1, −5).
Use the drop-down menus to select the proper value for each variable that is substituted into the slope-intercept equation.
y =
✔ –5
x =
m =
Answers
The equation of line passes through the point (1, -5) will be;
⇒ y = - 3x - 14
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point on the line are (1, -5).
And, The slope of the line is,
⇒ m = - 3
Now,
Since, The equation of line passes through the point (1, -5).
And, Slope of the line is,
⇒ m = - 3
Thus, The equation of line with slope - 3 is,
⇒ y - 1 = - 3 (x - (-5))
⇒ y - 1 = - 3 (x + 5)
⇒ y - 1 = - 3x - 15
⇒ y = - 3x + 1 - 15
⇒ y = - 3x - 14
Therefore, The equation of line passes through the point (1, - 5) will be;
⇒ y = - 3x - 14
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a change in the unit of measurement of the dependent variable in a model does not lead to a change in:
Answers
Throughput is often a dependent variable with "bits per second" as its unit.
what is unit and measurment?
Standards are provided by units of measurement so that all of our measurements' numbers correspond to the same item. A physical quantity is described using numbers as part of the measurement procedure. We can gauge an object's size, warmth, weight, and a number of other characteristics.The metre, for instance, is a common unit for measuring length. Before 1982, the measurement of a meter was the separation of two markings on a unique metal rod.At that time, describing anything as having a length of two meters meant that it was exactly twice as long as the rod that served as the standard for measuring distance. Scientists now use the speed of light to define the meter.Different units were employed in many nations in the past.learn more about units and measurment click here:
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Heeelllllllllllp Simplify the expression completely.
√144 +18 √12-5√64
Answers
12 + 36*root(3) - 40
-28 + 36*root(3)
Answer: A
x+3y+z=-8
4x-2y-z=-9
5x+3y+2z=-19
please help me with this
Answers
That aint no question
Alfred begins collecting model cars. He buys 3 new model cars every week. Is the number of cars he owns proportional to the number of weeks that have passed since he started his collection?
Answers
The relationship between the number of weeks and cars are proportional since they are dependent on each other.
ProportionRatio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of a:b, then it is a ratio whereas a proportion states that two ratios are equal. Here, a and b are any two integers. Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios. In proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
In this question, Alfred, buy three car each week. As the number of weeks increase, so is the number of his car increasing at definite proportions.
This implies that we can set an equation to represent the number of cars Alfred will have after certain number of weeks.
Let;
x = number of weeksy = number of carsy = 3x
At week 10, Alfred will have
y = 3(10) = 30 cars
After 10 weeks, Alfred will have 30 cars
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You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is 0. How confident can you be that your predicted value will be reasonably close to the actual value?
Responses
I can’t be confident at all; this is about as close to a random guess as you can get.
I can be a little confident; it might be close, or it might be way off.
I can be very confident; it will be close, but it probably won’t be exact.
Answers
The correct option regarding the correlation coefficient is that A. I can’t be confident at all; this is about as close to a random guess as you can get.
What is a correlation coefficient?The correlation coefficient is a statistical measure of the strength of a two-variable linear relationship. Its values can range between -1 and 1. A correlation coefficient of -1 denotes a perfect negative, or inverse, correlation, in which values in one series rise while those in the other fall, and vice versa.
A coefficient of one indicates that there is a perfect positive correlation, or a direct relationship. A correlation coefficient of 0 indicates that no linear relationship exists. In science and finance, correlation coefficients are used to assess the degree of association between two variables, factors, or data sets.
In this case, the fat that the person gets 0 implies that it's probably a random guess. In conclusion, the correct option is A.
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How do you use distributive property to answer (15x6) + (85x6)
Answers
Answer:
600
Step-by-step explanation:
You want to use distributive property to answer (15x6) + (85x6).
Distributive propertyThe distributive property shows you what you can do with a common factor:
(15×6) + (85×6) = (15 +85)×6 . . . . . . apply the distributive property
= 100 × 6 . . . . . . evaluate the sum in parentheses
= 600 . . . . . . perform the multiplication
John is in charge of feeding the pigs and cows on the farm. The cow's food costs twice as much as the pig's food. There are 46 cows and 22 pigs on the farm. John has a $860 budget for food a month. How much can John spend on food for each cow per month?
I tried solving this and got some random answer like $7.5432... per pig. Please Help
Answers
The cost of feed for a cow in a month is $15.08
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls)
Similarly the ratio of the cost of cow's food to pig is 2:1
represent the cost of feed of a cow by x and the cost of feed for a pig to be y
therefore x= 2y
there are 46 cows, therefore the cost of feed for 46 cows is 46x
there are 22 pigs, therefore the cost of pig is 22y
46x+22y= 860
representing 2y for x
46(2y)+22y= 860
114y= 860
y= 860/114
y=$ 7.54
recall x=2y
x= 7.54×2= $15.08
therefore $15.08 is spent on a cow in a month
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can yall please help
Answers
1. The pairs of polygons are similar.
2. The pairs of polygons are not similar.
3. The missing measure is of x = 5.2.
4. The missing measure is of x = 16.
5. The value is AB = 6.
6. The perimeter of the yellow tile is of 240 cm.
7. The value is DF = 0.75.
What are similar polygons?Similar polygons are polygons that share these two following features:
Congruent angles.Proportional side lengths.Hence, for itens 1 and 2, we have that:
1. The pairs of polygons are similar, as the side lengths are proportional.2. The pairs of polygons are not similar, as the side lengths are not proportional, as the ratio of 6 and 9 is different of the ratio of 3 and 4.For item 3, the side lengths are proportional, hence:
x/2.6 = 8/4
x/2.6 = 2
x = 2 x 2.6
x = 5.2.
Same as item 4, hence:
x/10 = 9.6/6
x/10 = 1.6
x = 16.
For item 5, considering the equivalent side lengths, we have that:
AB/8 = 12/16
AB/8 = 3/4
AB = 24/4
AB = 6.
The perimeter of the yellow tile is of 240 cm in item 6, as the ratio between the side lengths is of 3, hence the ratio of the perimeters will also be of 3, then:
3 x 80 cm = 240 cm.
For item 7, we have that:
DF/3.4 = 2.25/9
DF = 3 x 2.25/9
DF = 0.75.
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Bobby bought 3 T-shirts at the mall
and a pair of pants for $16 at the
clothing store. All together he spent $28
for the clothes. How much was each
shirt?
Answers
Answer: $4
Step-by-step explanation: we know he spent 28 dollars in total and 16 of those was on a pair of pants so we can subtract 16 from 28 to get 12
we also know he bought 3 shirts in total and because 12/3=4 each shirt must have cost 4 dollars.
We can check the answer by combining the price of the shirts (12)
with the price of the pants (16) because 12+16=28 we know the cost of each shirt has to be $4.
Answer:
Each shirt was 4 dollars.
Step-by-step explanation:
28 - 16 = 12. 12 divided by 3 = 4.
Pls solve all the question as per the questions given below
Answers
1a) The additional information required using SAS Congruency postulate is; ∠AOB ≅ ∠BOD
1b) The additional information required using ASA Congruency postulate is BC ≅ QR
2a) The symbolic form of the congruent triangles is written as;
ΔABC ≅ ΔADC
2b) The congruence rule used is SAS Congruency postulate.
How to use congruency postulates?1a) We want to prove that the triangles are congruent by SAS Congruency postulate. SAS congruency postulate means Side - Angle - Side. Thus, the additional information is;
∠AOB ≅ ∠BOD
1b) We want to prove that triangle ABC is congruent to triangle PQR by ASA Congruency. We have that;
∠Q = ∠B and ∠R = ∠C. Thus;
The additional information is BC ≅ QR
2a) The symbolic form of the congruent triangles is written as;
ΔABC ≅ ΔADC
2b) The congruence rule used here is SAS Congruency postulate.
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Find the measure of the exterior angle.
Answers
Answer:
since the degree of the adjacent angles is 180°, we find the answer from that
Answer:
128°
Step-by-step explanation:
it is a right triangle, the bottom right one is, from the drawing, 90 °, the sum of the internal angles of all the triangles is 180 °, so making 180 - 90 - 38 we have the missing internal angle of 52 °.
Then we find the outer angle, the inner-outer sum is 180 °, 180 - 52 = 128 ° (your answer)
When you answer, could you just put the letter of the number you have? Thank you.
Answers
In the given triangle KLM with coordinates K(0,2) ,L(2 ,9) ,M(4,2), the sets of points which represent the dilation from the origin is K'(0,8), L'(8, 36) , M'(16, 8) multiply by scale factor 4.
As given in the question,
In the given triangle KLM,
Coordinates of the triangle KLM are given by :
K(0,2) ,L(2 ,9) ,M(4,2)
Dilation from the origin is represented by:
a. K'(0,2) , L'(8,9) , M'(16, 2)
Dilation scale factor does not effect on all the coordinates .
Not a correct option.
b. K'(0,2) , L'(2,36) , M'(16, 2)
Dilation scale factor does not effect on all the coordinates .
Not a correct option.
c. K'(0,8) , L'(8,36) , M'(16, 8)
Multiply by scale factor 4.
Dilation exist.
d. K'(4,6) , L'(6,13) , M'(8, 6)
Scale factor of addition of 4.
Dilation does not exist.
Therefore, in the given triangle KLM with coordinates K(0,2) ,L(2 ,9) ,M(4,2), the sets of points which represent the dilation from the origin is K'(0,8), L'(8, 36) , M'(16, 8) multiply by scale factor 4.
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students in a statistics class are conducting a survey to estimate the mean number of units students at their college are enrolled in. the students collect a random sample of 46 students. the mean of the sample is 12.5 units. the sample has a standard deviation of 1.8 units. what is the 95% confidence interval for the average number of units that students in their college are enrolled in? assume that the distribution of individual student enrollment units at this college is approximately normal.
Answers
The 95% confidence interval for the average number of units that students in their college are enrolled in is (11.46,12.53)
We are given the number of students, n = 46, and the mean of the sample which is x= 12.5, and the standard deviation of the sample which is s= 1.8 , the formula we are referring to for calculating the confidence interval which is :
x ± t (s/√(n))
since for this case, the degree of freedom is one less than the mean, which is 45, the critical value for the confidence of 95% with the degree of freedom of 45 is 2.015
x + t(s/√(n)) = 12.5 +2.015*(1.8/6.78)= 12.53
x - t(s/√(n))= 12.5 -2.015*(1.8/6.78)= 11.46
The interval is (11.46,12.53)
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Write an equation of the line in point-slope form that passes through the given points in the table. Then write the equation in slope-intercept form.
X
15
20
25
30
35
y
175
210
245
280
315
Answers
Steps
Put into 2 point formula
210–175/20-15 = 35/5 =7
Put into point slope formula
Y-175=7(x-15)
Y-175=7x-105
Y=7x+70
How do you do this
8×+3x+4+5y+2
Answers
Step-by-step explanation:
8x + 3x + 4 + 5y + 2
combine x terms:
11x + 4 + 5y + 2
combine numbers:
11x + 5y + 6
[Please comment if you want the answer specifically for x or y.]
Answer:
8x+3x+4+5y+2
11x+9y+2
20xy+2
=22xy
help I don't understand it
3x+4=9x+3
Answers
Answer:
x = 1/6.
Step-by-step explanation:
3x+4=9x+3
STEP 1: Subtract 4 from both sides...
3x+4 -4 = 9x+3 -4
3x = 9x-1
STEP 2: Subtract 9x from both sides...
3x - 9x = 9x-1 -9x
-6x = -1
STEP 3: Divide both sides by -6x...
-6x / -6x = -1/ -6x
x = 1/6x.
REMEMBER: 2 negatives are equal to positive.
1. Find the standard form of a parabola passing through (1, 0), (2, -3), and (3,-10).
Hint: Use quadratic regression to find the standard form.
Answers
The standard form of a parabola passing through (1, 0), (2, -3), and (3,-10) is y = -2x² + 3x - 1
Define Parabola
A symmetrical open plane curve created when a cone and a plane that runs perpendicular to its side collide. Ideally, a projectile travelling under the pull of gravity will travel along a curve similar to this one.For parabolas that open either up or down, the standard form equation is y = ax² + bx + cThe equation of parabola in standard form is y = ax² + bx + c
We have given the points,
(1, 0), (2, -3), and (3,-10)
Let's put each point in parabola equation and form three equation as,
Equation for point (1, 0)
0 = a * (1)² + b * 1 + c
a + b + c = 0 --------------------eq(i)
Now, equation for point(2, -3)
-3 = a * (2)² + b * 2 + c
4a + 2b + c = -3 --------------------eq(ii)
And, equation for point (3, -10)
-10 = a * (3)² + b * 3 + c
9a + 3b + c = -10 ---------------------eq(iii)
Now, we have three equation let's put them together
a + b + c = 0 --------------------eq(i)
4a + 2b + c = -3 --------------------eq(ii)
9a + 3b + c = -10 ---------------------eq(iii)
Now, form equation which is of two variable.
For that, we take first two equation and subtract eq(ii) from eq(i)
4a+2b+c = -3
a + b + c = 0
- - - -
------------------------
3a + b = -3 ---------------eq(a)
Now, subtract eq(iii) from eq(ii)
9a + 3b + c = -10
4a + 2b + c = -3
- - - -
------------------------
5a + b = -7 ------------------eq(b)
Now, we get eq(a) and eq(b) consist of two variable.
3a + b = -3 ---------------eq(a)
5a + b = -7 ----------------eq(b)
Now, solve this equation simultaneously and find the value of a and b.
3a + b = -3
5a + b = -7
- - -
----------------
-2a = 4
a = -2
put a = -2 in eq(a) to find b
3a + b = -3
⇒3 * -2 + b = -3
⇒-6 + b = -3
⇒b = 3
We get the values of a and b. And, left with value of c for that just put the a and b value in eq(i) and find c
a + b + c = 0
-2 + 3 + c = 0
c = -1
Now, we get all the necessary values for equation.
Next, just put a, b and c values in parabola equation.
y = ax² + bx + c
y = -2x² + 3x - 1
Hence, the standard form of a parabola passing through (1, 0), (2, -3), and (3,-10) is y = -2x² + 3x - 1
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Create a table to show how the number of days is related to
the number of hours. Show at least 5 days,
24
b.
Is the relationship proportional?
c. Write an equation for the relationship.
Answers
Proportionality denotes a linear relationship between two quantities or variables.
A. Table is mentioned below.
B. Yes, it is a proportional relation.
C. y = 1/24 x
What is meant by proportional?A linear relationship between two quantities or variables is referred to as proportionality. If one quantity doubles in size, the other does as well; if one variable decreases to one-tenth of its previous value, the other does as well.If the ratio or relationship between y and x is the same or constant, the quantities are proportional: y/x = k, where k is the proportionality constant.When two quantities are proportional, it means that as one increases, so does the other, and the ratio of the quantities remains constant across all values.Consider a circle's circumference and diameter; the ratio of the two values equals pi.Therefore,
Part C : We know that,
1 day = 24 hours,
⇒ 1 hour = 1/24 day
As a result, the number of days in x hours (say y) = hours number of days in each hour
⇒ y = 1/24 x
Which is an equation of line.
Part A :
Hours 1 2 3 4 5
Days 1/24 1/12 1/8 1/6 5/24
Part B :
∵ a line passes through the origin always shows a proportional relation,
Since, for (0, 0),
0 = 1/24 (0) ( True )
i.e. there is a proportional relation between number of days and number of hours.
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16-2t=5t+9 One solution was found : t = 1 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation
Answers
Answer
Step-by-step explaination:
This is an algebraic equation. We have to solve it like this......
16-2t=5t+9
-5-2t=-16+9
-7t=-7
Ans: -7t=-7
Compare and Explain: Are they equivalent?
3 hours worked for $12; 9 hours worked for $36
Answers
Answer:
Yes they are equivalent.
Step-by-step explanation:
$12 divided by 3 is $4
$36 divided by 9 is also $4
Therefore they are equivalent.
Your welcome
Answer:
Yes!
Step-by-step explanation:
You divide 3 by 12 because that's how much they work for an hour. That means they make $36 for 9 hours.
12 ÷ 3 = 4
36 ÷ 9 = 4
They have the same answer which makes them equivalent.
Solve for n:-
[tex]\sf n - 3n = 14 - 4n[/tex]
Answers
Answer:
n = 7
Step-by-step explanation:
The equation is,
→ n - 3n = 14 - 4n
Now the value of n will be,
→ n - 3n = 14 - 4n
→ -2n = 14 - 4n
→ -2n + 4n = 14
→ 2n = 14
→ n = 14/2
→ [ n = 7 ]
Hence, the value of n is 7.
One online bookstore charges $10 per book and $8 for shipping. Another online bookstore charges $12 per book and offers free shipping. For what number of books is the cost the same ?
Answers
Answer:
The number of books bought in each store would be 4 The amount spent will be the same in either store.
Step-by-step explanation:
Comment
The question has to make the assumption that no matter how many books are bought from store 1, the shipping charge is 8 dollars. Otherwise there is no solution.
Givens
Book1: 10 and 8 dollars total for shipping
Book2: 12 dollars, no shipping costs.
Equation
12x = 10x + 8 Subtract 10x from both sides
Solution
12x - 10x = 10x - 10x + 8 Combine
2x = 8 Divide both sides by 2
2x/2 = 8/2
x = 4