The function f(x) = (x + 7)^2 is one-to-one and non-decreasing for any domain on the real numbers. The inverse of f(x) restricted to this domain is y = √x - 7.
To find a domain on which the function f(x) = (x + 7)^2 is one-to-one and non-decreasing, we need to determine where the function is strictly increasing or non-decreasing and has a one-to-one correspondence.
First, let's examine the graph of f(x) = (x + 7)^2 to understand its behavior. The function is a parabola that opens upward, centered at x = -7, and the vertex is the lowest point on the graph.
Since the vertex is the lowest point and the parabola opens upward, the function is non-decreasing for all x-values. Therefore, the function is non-decreasing over its entire domain.
To find a domain on which the function is one-to-one, we observe that the function is not symmetric about the y-axis. Hence, the domain can be any subset of the real numbers.
Now, let's find the inverse of f(x) restricted to this domain. Since f(x) is non-decreasing, the inverse will also be non-decreasing. The inverse function can be found by interchanging the roles of x and y in the original equation and solving for y.
Let's proceed with finding the inverse:
Start with the equation f(x) = (x + 7)^2.
Interchange x and y: x = (y + 7)^2.
Solve for y:
Take the square root of both sides: √x = y + 7.
Subtract 7 from both sides: y = √x - 7.
The inverse function of f(x) restricted to any domain on which it is one-to-one and non-decreasing is given by y = √x - 7.
Note that the domain can be any subset of the non-negative real numbers, since the square root function is defined only for non-negative values.
In summary, the function f(x) = (x + 7)^2 is one-to-one and non-decreasing for any domain on the real numbers. The inverse of f(x) restricted to this domain is y = √x - 7.
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Use Cramer's rule to solve the following equation systems A2 JA A VAL 8x1 + 9x2 + 413 = 2 11 +212 + 313 = 3 711 + 6x2 + 5/3 = 1 The solutions are x; = 4,15 = , and ; = What are All, a; and|A3/? 1. |4,1 = -60, x) = -1, and |A3= -60 2. [A1] = -78, 3) = -0.7, and |A3] = 28 3. |A1 = -60, ; = 1, and A3] = 36 4. |A 1 = -78, x = 1.25, and |A3| = 52 2. Given the function y = f(r) = 57- 4r. (a) Find the difference quotient as a function of and Ar. 1. 10.r - 4 2. 5.r? - 4r 3. 5(Ar)? - 4A: 4. 10.r + 5Ar - 4 (b) Find f'(-1) and f'(5). 1. S'(-1) = 9 and f'(5) = 105 2. f'(-1) = -14 and f'(5) = 46 3. $'(-1) = -14 and f'(5) = 105 4. f'(-1) = -19 and f'(5) = 71
1) The solutions to the equation system are x₁ = 11/39 and x₂ = -7/39.
2) The difference quotient as a function of Δr is -4.
3) f'(-1) = -4 and f'(5) = -4.
To solve the equation system using Cramer's rule, we need to find the determinant of the coefficient matrix A and the determinants of the matrices obtained by replacing each column of A with the column on the right-hand side.
The given equation system is:
8x₁ + 9x₂ = 2
11x₁ + 2x₂ = 3
7x₁ + 6x₂ = 1
Step 1: Calculate the determinant of the coefficient matrix A.
A = |8 9|
|11 2|
|7 6|
|A| = (8 * 2) - (9 * 11)
= -78
Step 2: Calculate the determinant of the matrix obtained by replacing the first column of A with the column on the right-hand side.
A₁ = |2 9|
|3 2|
|1 6|
|A₁| = (2 * 2) - (9 * 3)
= -22
Step 3: Calculate the determinant of the matrix obtained by replacing the second column of A with the column on the right-hand side.
A₂ = |8 2|
|11 3|
|7 1|
|A₂| = (8 * 3) - (2 * 11)
= 14
Step 4: Calculate the solutions x₁ and x₂ using Cramer's rule.
x₁ = |A₁| / |A|
= -22 / -78
= 11/39
x₂ = |A₂| / |A|
= 14 / -78
= -7/39
Therefore, the solutions to the equation system are x₁ = 11/39 and x₂ = -7/39.
Now, let's move on to the second part of your question regarding the function f(r) = 57 - 4r.
(a) To find the difference quotient as a function of Δr (Δr represents the change in r):
Difference quotient = (f(r + Δr) - f(r)) / Δr
Expanding and simplifying the expression:
Difference quotient = (57 - 4(r + Δr) - (57 - 4r)) / Δr
= (57 - 4r - 4Δr - 57 + 4r) / Δr
= -4Δr / Δr
= -4
Therefore, the difference quotient as a function of Δr is -4.
(b) To find f'(-1) and f'(5), we need to find the derivative of f(r) with respect to r.
f'(r) = d/dx (57 - 4r)
= -4
Substituting r = -1 and r = 5 into f'(r), we get:
f'(-1) = -4
f'(5) = -4
Therefore, f'(-1) = -4 and f'(5) = -4.
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Which correctly describes this rotation?
A. a counterclockwise rotation of 30° about point A
B. a counterclockwise rotation of 45° about point A
c. a counterclockwise rotation of 90° about point A
D. a counterclockwise rotation of 180° about point A
The number of bagels sold daily for two bakeries is shown in the table.
Bakery A Bakery B
53 34
52 40
50 36
48 38
53 41
47 44
55 40
51 39
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Why? Select the correct answer below. (5 points)
Mean for both bakeries because the data is symmetric
Mean for Bakery B because the data is symmetric; Median for Bakery A because the data is not symmetric
Mean for Bakery A because the data is symmetric; Median for Bakery B because the data is not symmetric
Median for both bakeries because the data is not symmetric
Answer:
“Mean for both bakeries because the data is symmetric.”
Step-by-step explanation:
This is correct because the numbers shown in this problem is all in the same range. Meaning that on bakery A and B there are no stray numbers, also known as outliers. No outliers means that the data is symmetric. If you search up, you can see that when the data is symmetric, you use “mean.”
also I got it right on my test
Answer:
Mean for both bakeries because the data is symmetric.
Step-by-step explanation:
Michael's dog stands 10 feet from a table, and notices a plate resting on the edge of the table. The height from the ground to the top of the table is 4 feet, and his dog's eyes are 1 foot above the ground. What is the angle of elevation from Michael's dog to the plate? Round your answer to the nearest whole degree.
Answer:
The angle of elevation is 17°.
Step-by-step explanation:
Let's draw the scenario to better understand the problem:
Focusing on the right triangle formed, it appears that we get measures of the two sides of the right triangles.
Opposite Side = 3 Ft.
Adjacent Side = 10 Ft.
To find the angle of elevation, we will be using the Targent Function:
[tex]targent \: 0 = \frac{opposite \: side}{adjacent \: side} \\ targent \: 0 = \frac{3}{10} \\ 0 = {targent}^{ - 1} ( \frac{3}{10} ) \\ 0 = 16.69924423399 = 17[/tex]
Therefore, the angle of elevation is 17°.
Reagan rides on a playground roundabout with a radius of2.5 feet. To the nearest foot, how far does Reagan travel over an angle of 4π/3 radians?
Answer:
10 feets
Step-by-step explanation:
Given that:
Angle, θ = 4π/3
Radius, r = 2.5 feets
To obtain how Far Reagan traveled, we calculate the Length of the arc, s
s = r*θ
s = 2.5 feets * 4π/3
s = 10π/3
s = 10.4719
To the nearest foot ; distance traveled by Reagan is 10 feets
i need the prosces plis is for tomorrow
Answer:
p) = 17/30 or 0.56
q) = 191/60 or 3 11/60
You have an order for an 8-gallon aquarium that is 20 in long and 10.5 in wide. How deep should the aquarium be?
Answer:
8.8
Step-by-step explanation:
i need help please thanks
Answer:
33
Step-by-step explanation:
6 * 3 = 18
8-3 = h
h = 5
A = 5 * 3 = 15
Combined:
15 + 18
33
Similar Polygons
DEFG is similar to HJKL. What is the length of LK?
A) 5
B)21
C) 80/3
D) 60
Answer:
I think it's 21. .........
A sofa is 7 feet 5 inches long. How many inches is the sofa?
89 inches!
Because each foot is 12 inches and 12*7=84 and 84+5=89!
Find the equation in slope-intercept form for the line with a slope of 5/4 and passes through the point (8, 2)
Answer:
92/37
Step-by-step explanation:
Given the points A(-2, 0), B(6, 16), C(1, 4), D(5, 4), E(2,2)2
,2
)), and F(32,−4232
,−42
), find the position vector equal to the following vectors.
AB⃗
AB
This indicates that vector 2AB has a length of 165.
Given the points A(-2, 0), B(6, 16), C(1, 4), D(5, 4), and E, let's determine the length of the vector 2AB. To begin, we must determine the distance that separates points A and B. The distance formula is as follows: Equation for distance: We can calculate d as [(x2 - x1)2 + (y2 - y1)2] using the distance formula: Spot = [(6 - (- 2))2 + (16 - 0)2] = [(6 + 2)2 + (16)2] = [(8)2 + (16)2] = [(64 + 256) = 320 = 8] Now, we can deduct the directions of point A from guide B toward decide the vector Stomach muscle:
To find 2AB, simply multiply each part of AB by 2: AB = (6 - (-2)i + (16 - 0)j = 8i + 16j 2AB = 2(8i + 16j) = 16i + 32j. Last but not least, we must ascertain the magnitude of 2AB. The extent recipe is as per the following: Size formula: Using the magnitude formula, we get: ||v|| = (v12 + v22). ||2AB|| = (162 + 322) = (256 + 1024) = (1280 + 165). This indicates that vector 2AB has a length of 165.
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a restaurant used 6.5 ounces of cheese to make 5 slices of pizza. if each slice had the same amount of cheese, how much was on each slice?
Answer:
1.3 ounces, 1.3*5 =6.5
Compare lengths. Select >, <, or = .
900 cm _ 9 m
Answer:
900 cm = 9 m
Step-by-step explanation:
9 m = 900 cm
Therefore, 9 m equals 900 cm.
help-
1. half a number, less 3, is 8
2. the area decreased by 7 is 14
Answer:
. the area decreased by 7 is 14
Yasmin ordered 20 sandwiches for the STEM club's after school meeting. Some were turkey and some were ham sandwiches. Turkey sandwiches cost $5.50 and ham costs $4.50. The total bill was $97. How many turkey sandwiches were ordered?
7 TURKEY AND 13 HAM
I USED CALCULATOR BTW
Tossing of a fair coin infinitely many times. Define (1, if head shows, X(t)= for nT
Tossing of a fair coin infinitely many times. The process X(t) can be defined as follows:
- X(t) = 1 if a head shows up at time t, where t = nT for some positive integer n.
- X(t) = 0 if a tail shows up at time t.
In the given scenario, we are considering the tossing of a fair coin infinitely many times. We want to define a process X(t) that represents the outcome of each toss at different time points.
The process X(t) is defined as 1 when a head shows up at time t, where t is a multiple of T (the fixed time interval between tosses). In other words, X(t) takes the value 1 when t is of the form nT, where n is a positive integer.
Conversely, X(t) is defined as 0 when a tail shows up at time t. This includes all time points that are not of the form nT.
The process X(t) is a representation of the outcome of the coin tosses over time. It takes the value 1 when a head shows up at time t = nT for some positive integer n, and 0 when a tail shows up. This process allows us to track the occurrences of heads at specific time intervals in the infinite sequence of coin tosses.
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PLEASE HELP!! I'll make brainliest
30 POINTS!!! HELP!!!!
If Θˆ 1 and Θˆ 2 are unbiased estimators of the same parameter θ, what condition must be imposed on the constants k1 and k2 so that k1Θˆ 1 + k2Θˆ 2 is also an unbiased estimator of θ?
The condition imposed on the constants k₁ and k₂ for k₁Θ⁻₁ + k₂Θ⁻₂ to be an unbiased estimator of θ is that their sum must equal 1.
For k₁Θ⁻₁ + k₂Θ⁻₂ to be an unbiased estimator of θ, its expected value should be equal to θ. In other words, we want to find the conditions on k₁ and k₂ such that E(k₁Θ⁻₁ + k₂Θ⁻₂) = θ.
Given that Θ⁻₁ and Θ⁻₂ are unbiased estimators of θ, we have:
E(Θ⁻₁) = θ
E(Θ⁻₂) = θ
Now, let's calculate the expected value of k₁Θ⁻₁ + k₂Θ⁻₂:
E(k₁Θ⁻₁ + k₂Θ⁻₂) = k₁E(Θ⁻₁) + k₂E(Θ⁻₂)
Since E(Θ⁻₁) = θ and E(Θ⁻₂) = θ, we can substitute these values into the equation:
E(k₁Θ⁻₁ + k₂Θ⁻₂) = k₁θ + k₂θ
To make sure this expression is equal to θ, we need:
k₁θ + k₂θ = θ
This implies that k₁ + k₂ = 1. Therefore, the condition imposed on the constants k₁ and k₂ for k₁Θ⁻₁+ k₂Θ⁻₂ to be an unbiased estimator of θ is that their sum must equal 1.
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Show explicitly that the following functions: (a) (x+at)², (b) 2e-(x-at) ², 7 satisfy the wave equation J²u(x, t) Ət² = (c) 5 sin[3 (x - at)] + (x + at). ₂d²u(x, t) dx²
Each satisfies the wave equation.
We are given the functions as follows:
(a) (x+at)², (b) 2e-(x-at) ², 7 satisfy the wave equation J²u(x, t) Ət² = (c) 5 sin[3 (x - at)] + (x + at).
₂d²u(x, t) dx²
Let us prove that they satisfy the wave equation using the formula of the wave equation. Wave equation is given by;
J²u(x, t) Ət² = ₂d²u(x, t) dx²
Applying the partial derivative to
(a) with respect to time, t, we obtain:
2a(x+at)
The second partial derivative with respect to x is as follows:
2a
By substituting these results into the wave equation, we have:
J²u(x, t) Ət² = ₂d²u(x, t) dx²
(2a(x+at)) = 2aJ²u(x, t) Ət² = 2a
Ət² = 1/J².
Thus, (a) satisfies the wave equation.
For part (b), let us begin by taking the partial derivative of the function with respect to time, t. This is given by:
-4a e^-(x-at) ²
By taking the second partial derivative with respect to x, we get:4a e^-(x-at) ²
Similar to above, we substitute these results into the wave equation as follows:
J²u(x, t) Ət² = ₂d²u(x, t) dx²
-4a e^-(x-at) ² = 4aJ²u(x, t) Ət² = -4a e^-(x-at) ²/J²
Ət² = -1/J²e^-(x-at) ².
Thus, (b) satisfies the wave equation.
For part (c), let us calculate the partial derivative with respect to t as follows:
5a cos[3(x-at)] + a
The second partial derivative with respect to x is given by:-
15a sin[3(x-at)]
By substituting these results into the wave equation, we have:
J²u(x, t) Ət² = ₂d²u(x, t) dx²
(5a cos[3(x-at)] + a) = -15a
sin[3(x-at)]J²u(x, t) Ət² = -15a
sin[3(x-at)]/(5a cos[3(x-at)] + a)
Ət² = -3 sin[3(x-at)]/(cos[3(x-at)] + 1/5).
Thus, (c) satisfies the wave equation.
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The table shows the scores of students recent test. Find the mean of the scores and round to the nearest hundredth
Answer:
Answer and work is in the pdf
Step-by-step explanation:
75+75+80+80+80+80+80+80+85+85+90+90+90+90+90+90+95+95+95+100+100+100+100+100+100
=2,425
2+6+2+6+3+8
=27
2,425/27=89.81
The mean is 89.81
Given the functions f(n)=11 and g(n)=((3)/(4))^(n-1), combine them to create a geometric sequence, a_(n), and solve for the 9 th term.
The given functions f(n) = 11 and g(n) = (3/4)^(n-1) can be combined to create a geometric sequence. The nth term of a geometric sequence is given by a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.
In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. In this case, the first term is given as 11, and the common ratio is (3/4).
The nth term of a geometric sequence is calculated using the formula a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the position of the term. By substituting the values into the formula, we can find the 9th term.
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BRAINLY TO WHOEVER HELPS AND GETS IT RIGHT
~no links pls~
Answer: A
Step-by-step explanation:
Yoshi is a basketball player who likes to practice by attempting the same three-point shot until he makes the shot. His past performance indicates that he has a 30 % 30%30, percent chance of making one of these shots. Let X XX represent the number of attempts it takes Yoshi to make the shot, and assume the results of each attempt are independent. Is X XX a binomial variable? Why or why not?
Answer:
There is no fixed number of trials, so X is not a binomial variable
Step-by-step explanation:
mama
There is no fixed number of trials, so X is not a binomial variable.
What is a binomial variable in statistics?
This is a specific kind of discrete random variable. A binomial random variable counts how regularly a specific event occurs in a fixed variety of attempts or trials.
What is a binomial data example?The binomial is a form of distribution that has possible effects (the prefix “bi” method two, or twice). as an example, a coin toss has only viable effects: heads or tails, and taking a check may want to have viable outcomes: pass or fail. A Binomial Distribution indicates both success and failure.
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Which of the following are among the five basic postulates of Euclidean geometry? Check all that apply.
A. All circles have 360 degrees
B. A straight line segment can be drawn between any two points.
C. A straightedge and compass can be used to create a triangle.
D. Any straight line segment can be extended indefinitely.
Answer:
B and D.
Step-by-step explanation:
A p e x
The following are among the five basic postulates of Euclidean geometry
A straight line segment can be drawn between any two points.Any straight line segment can be extended indefinitely.The five basic postulates of Euclidean geometry
The five (5) basic postulates are:
Any segment of a straight line connecting any two points can be drawn.You can draw and stretch any straight line to any finite length.Given a centre and radius, circles are drawn.Congruent angles are always right angles.There is a line that is parallel to the given line if a given point is not on the supplied line.Learn more about Euclidean Geometry here:
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A system of linear equations is graphed.
Which ordered pair is the best estimate for the solution to the system?
(−4, 2 1/2)
(0, −2)
(−4 1/2, 2 1/2)
(0, 7)
The best estimate for the solution to the system of linear equations among the given ordered pairs is (-4, 2 1/2).
In the context of a system of linear equations, the solution represents the values of the variables that satisfy all the equations simultaneously. To determine the best estimate for the solution, we need to evaluate each ordered pair and see which one satisfies the given system.
By substituting the values of the ordered pairs into the equations of the system, we can determine if they satisfy the equations or not. Among the given options, when substituting (-4, 2 1/2) into the system of linear equations, it is likely to result in a solution that satisfies all the equations. Therefore, it is important to consider the specific equations and the context of the problem to determine the best estimate for the solution.
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Please help and explain, please no links, thank you
Answer:
The two triangles are related by angles, so the triangles are similar but not proven to be congruent.
Step-by-step explanation:
Because the triangles have the same angles, they are congruent. The definition of congruence is if you take a shape and scale it up or down (or keep it the same) therefore, they are congruent.
Hope this helped, have a nice day
EDIT: I screwed up, I thought it was supposed to be similar. These triangles are SIMILAR not congruent. The actual answer is they are related by AAA similarity but they are similar, but they are not proven to be congruent. Hope this clears it up, and sorry.
~cloud
At a birthday party pizzas and sodas were purchased for the kids. The number of sodas bought was two more than three times the number of pizzas. Pizzas cost $9.50 each and sodas cost $1.25 each. (ANSWER A AND B PLEASEEEEEEE I REALLY NEED HELP!!!!)
A). If 8 pizzas were bought, how many sodas were bought?
B). How much was the total money would be spent on the pizza and sodas from (A)?
THANK YOU SOOOOO MUCH!!!! :))))))
Answer:
61
Step-by-step explanation:
Givens
Let the pizzas = x
Let the sodas = y
Equation
y = 3x + 2
Part A
y = 3*8 + 2
y = 24 + 2
y = 26
Part B
Sodas = 26* 1.25 = 32.50
Pizzas =9.50 * 3 = 28.50
Total for both = 32.50 + 28.50 = 61
Seth is using a large shoe box to store his baseball cards. The length of the box is 12 inches, and the height is 6 inches. If the volume of Seth's box is 288 cubic inches, how wide is the box?
Step-by-step explanation: *First, decide which volume formula to use: v = lwh
*Next, substitute in for what you do know (leave variable for unknown): 288 = 12 · w · 6
*Then simplify the side of the equation with the variable: 288 = 72 · w
*Now divide each side of the equation by 72 to solve for w:
288 ÷ 72 = w
4 in = w