PLEASE HELP!


In the figure, ∠1 ≅ ∠2, ∠3 ≅ ∠4, and TK ≅ TL. You can justify the conclusion that ∆TKS ≅ ∆TLR by the _____
SAS Postulate
ASA Postulate
AAS Theorem
SSS Postulate

The error message "Difference order N must be a positive integer scalar" is indicating that there is an issue with the input argument for the diff function.

The diff function is used to calculate the difference between adjacent elements in a vector.
In the code you provided, the line that is causing the error is:
f_prime0 = diff(f,x0,xinc);
To fix this error, you need to ensure that the input arguments for the diff function are correct.

To fix this problem, you need to look at the code in the Newton_Raphson_tutorial function and possibly also the Tutorial_m function. You probably get an error when computing the derivative with the 'diff' function.

However, we can offer some general advice on how to fix this kind of error. The error message suggests that the variable N used to specify the difference order should be a positive integer scalar.

Make sure the variable N is defined correctly and has a positive integer value.

Make sure it is not assigned a non-integer or non-scalar value.

Make sure the arguments to the diff function are correct.

The diff function syntax may vary depending on the programming language or toolbox you are using.

Make sure the variable to differentiate ('f' in this case) is defined and suitable for differentiation.

Make sure that x0 and xinc are both positive integer scalars, and that f is a valid vector or matrix.
Additionally, it's important to check if there are any other errors or issues in the code that could be causing this error message to appear.

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The graph of h against m is plotted in form of a curve.

Given:

A tree branch is observed to bend as the fruit growing on it increases in size.

The height h in metres of the branch end above the ground is closely approximated by the function \(h=2-0.2*1.60^{0.2m}\) where m is the estimated mass, in kilograms, of fruit on the branch.

We have to sketch the graph of h against m.​

The x-axis represents the mass in kg while the y-axis represents the height of the branch above the ground in metres.

Hence a curved graph is obtained by plotting the function.

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Answer: \(x \leq 12\)

Step-by-step explanation:

\(3(x-3) \leq 27\\\\x-3 \leq 9\\\\x \leq 12\)

Step-by-step explanation:

To solve the inequality 3(x - 3) ≤ 27, we can use the following steps:

Distribute the 3 on the left side of the inequality: 3x - 9 ≤ 27

Add 9 to both sides of the inequality: 3x ≤ 36

Divide both sides of the inequality by 3: x ≤ 12

Therefore, the solution to the inequality is x ≤ 12.

This solution is valid for any value of x less than or equal to 12, including 12.

Examples of values that satisfy this inequality are:

x = -6, -4, -2, 0, 2, 4, 6, 8, 10, 11, 12

x = -1, -0.5, 0.1, 4.5, 8.9, 12

Note that the solution set is a set of real numbers, that includes all x that are less or equal than 12.

os(-θ) = √3/2 Since cos(θ) = cos(-θ), we have: cos(θ) = √3/2. To find all solutions in the interval [0, 2π), we look for angles θ for which cos(θ) = √3/2: θ = π/6 or θ = 11π/6,  in the interval [0, 2π) are θ = π/6 and θ = 11π/6.

To simplify the equation cos(θ) cos(2θ) + sin(θ) sin(2θ) = square root of 3 over 2, we can use the Addition Formula for cosine:

cos(A + B) = cos(A) cos(B) - sin(A) sin(B)

We notice that the left side of the equation has the same form as the right side of the formula, with A = θ and B = θ. Therefore, we can rewrite the left side as:

cos(θ + θ) = cos(2θ)

Similarly, using the Addition Formula for sine:

sin(A + B) = sin(A) cos(B) + cos(A) sin(B)

we can rewrite the left side of the equation as:

sin(θ + θ) = sin(2θ)

Substituting these expressions back into the original equation, we get:

cos(2θ) + sin(2θ) = √3/2

Now we can use the Pythagorean identity:

sin^2(A) + cos^2(A) = 1

to solve for sin(2θ) and cos(2θ):

sin^2(2θ) + cos^2(2θ) = 1

sin^2(2θ) = 1 - cos^2(2θ)

sin(2θ) = ±√(1 - cos^2(2θ))

Substituting this into the equation above, we get:

cos^2(2θ) ± √(1 - cos^2(2θ)) = √3/2

We can solve this equation for cos^2(2θ) using algebraic manipulation:

cos^2(2θ) = (√3 ± √(3 - 4cos^2(2θ)))^2 / 8

Simplifying, we get:

4cos^4(2θ) - 3cos^2(2θ) + 1/4 = 0

This is a quadratic equation in cos^2(2θ), which we can solve using the quadratic formula:

cos^2(2θ) = [3 ± √(9 - 16/4)] / 8

cos^2(2θ) = (3 ± √7) / 8

Taking the square root and remembering that cos(2θ) is positive for θ in the first and fourth quadrants, we get:

cos(2θ) = ±√[(3 ± √7) / 8]

Finally, using the formula cos(2θ) = 2cos^2(θ) - 1, we can find the values of cos(θ):

cos(θ) = ±√[(3 ± √7) / 16] + 1/2

These are the solutions for cos(θ) in the interval [0, 2π).

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The angle between the lines passing through (2, 5) and (4, -3), and (1, -2) and (3, 4) is approximately -32.7 degrees.

Example 1:

Find the angle between the lines with equations y = 2x + 3 and y = -3x + 1.

Solution:

To find the angle between the lines, we need to determine the slopes of the two lines.

The slope-intercept form of a line is y = mx + b, where m is the slope.

Comparing the given equations, we can see that the slopes of the lines are m1 = 2 and m2 = -3.

Using the angle between two lines formula, the angle θ between the lines is given by the equation:

tan(θ) = |(m2 - m1) / (1 + m1m2)|

Substituting the values, we have:

tan(θ) = |(-3 - 2) / (1 + (2)(-3))|

= |-5 / (1 - 6)|

= |-5 / -5|

= 1

To find the angle θ, we take the inverse tangent (arctan) of 1:

θ = arctan(1)

θ ≈ 45°

Therefore, the angle between the lines y = 2x + 3 and y = -3x + 1 is approximately 45 degrees.

Example 2:

Determine the angle between the lines with equations 3x - 4y = 7 and 2x + 5y = 3.

Solution:

First, we need to rewrite the given equations in slope-intercept form (y = mx + b).

The first equation: 3x - 4y = 7

Rewriting it: 4y = 3x - 7

Dividing by 4: y = (3/4)x - 7/4

The second equation: 2x + 5y = 3

Rewriting it: 5y = -2x + 3

Dividing by 5: y = (-2/5)x + 3/5

Comparing the equations, we can determine the slopes:

m1 = 3/4 and m2 = -2/5

Using the angle between two lines formula:

tan(θ) = |(m2 - m1) / (1 + m1m2)|

Substituting the values:

tan(θ) = |((-2/5) - (3/4)) / (1 + (3/4)(-2/5))|

= |((-8/20) - (15/20)) / (1 + (-6/20))|

= |(-23/20) / (14/20)|

= |-23/14|

To find the angle θ, we take the inverse tangent (arctan) of -23/14:

θ = arctan(-23/14)

θ ≈ -58.44°

Therefore, the angle between the lines 3x - 4y = 7 and 2x + 5y = 3 is approximately -58.44 degrees.

Example 3:

Find the angle between the lines passing through the points (2, 5) and (4, -3), and (1, -2) and (3, 4).

Solution:

To find the angle between the lines, we need to determine the slopes of the two lines using the given points.

For the first line passing through (2, 5) and (4, -3):

m1 = (y2 - y1) / (x2 - x1)

= (-3 - 5) / (4 - 2)

= -8 / 2

= -4

For the second line passing through (1, -2) and (3, 4):

m2 = (y2 - y1) / (x2 - x1)

= (4 - (-2)) / (3 - 1)

= 6 / 2

= 3

Using the angle between two lines formula:

tan(θ) = |(m2 - m1) / (1 + m1m2)|

Substituting the values:

tan(θ) = |(3 - (-4)) / (1 + (-4)(3))|

= |(3 + 4) / (1 - 12)|

= |7 / (-11)|

= -7/11

To find the angle θ, we take the inverse tangent (arctan) of -7/11:

θ = arctan(-7/11)

θ ≈ -32.7°

Therefore, the angle between the lines passing through (2, 5) and (4, -3), and (1, -2) and (3, 4) is approximately -32.7 degrees.

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as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

\(\stackrel{f(x)}{y}~~ = ~~2x^2+4x\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~2y^2+4y} \\\\\\ x=2(y^2+2y)\implies \cfrac{x}{2}=y^2+2y\impliedby \begin{array}{llll} \textit{now let's complete the square}\\ \textit{to make it a perfect square trinomial}\\ \textit{by using our good friend, Mr "0"} \end{array} \\\\\\ \cfrac{x}{2}=y^2+2y(+1^2-1^2)\implies \cfrac{x}{2}=y^2+2y+1-1\implies \cfrac{x}{2}=(y^2+2y+1)-1\)

\(\cfrac{x}{2}+1=(y^2+2y+1^2)\implies \cfrac{x}{2}+1=(y+1)^2\implies \sqrt{\cfrac{x}{2}+1}=y+1 \\\\\\ \sqrt{\cfrac{x+2}{2}}=y+1\implies \sqrt{\cfrac{x+2}{2}}-1=y~~ = ~~f^{-1}(x)\)

Answer:

\(y=60\textdegree\)

Step-by-step explanation:

The Tangent-Secant Interior Angle Measure Theorem states that the measure of an angle formed by a tangent and a secant of a circle at the point of tangency is equal to half of the measure of its intercepted arc.

Therefore, \(y=\frac{1}{2} *120\textdegree = \bf 60\textdegree\). Hope this helps!

The expected value for each roll is \((1+2+3+4+5+6)/6 = 3.5.\)

The average of Brandon's rolls, we simply add up all the results and divide by the number of rolls:
\((1+2+2+3+4+6+2+1+5+6+1+6+2+6+4+6+2+6+4+6)/20 = 3.6\)
So the average of Brandon's rolls is 3.6.
Now we need to count how many times he rolled above the average. To do this, we simply count how many rolls were greater than 3.6:
4, 6, 5, 6, 6, 4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 6, 4, 6
There were 18 rolls that were greater than 3.6, so Brandon rolled above the average 18 times.
In summary, Brandon rolled a six-sided die 20 times and recorded the results in a table. To find out how many times he rolled above the average, we first calculated the average roll to be 3.6. We then counted how many times he rolled above this value and found that he did so 18 times.

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Answer:

use symbolab

Step-by-step explanation:

Answer:

D. x=10

Step-by-step explanation:

6 - 4 = 2

5 x 2 = 10

10/5 + 4 = 6

:)

The solution set of the equation 3X=-6/1-X for x # 1 is {-2,1)

3x = -6/(1-x)

3x(1-x) = -6

3x – 3x2 = -6

Taking 3 as common from both sides

x –x2 = -2

x2 – x +2 =0

Using factorisation method we will get two factors

Factoring quadratics is a method of expressing the quadratic equation ax2 + bx + c = 0 as a product of its linear factors as (x - k)(x - h), where h, k are the roots of the quadratic equation ax2 + bx + c = 0. This method is also is called the method of factorization of quadratic equations. Factorization of quadratic equations can be done using different methods such as splitting the middle term, using the quadratic formula, completing the squares, etc.

( x – 2)(x+1)=0

So, x = 2 , -1

Now, when x ≠ 1

The solution of the equation will vary from {-2,1) .

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According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

At one classroom for economics and another for other topics, they dumped 122 stamped envelopes with addresses and $20 bills inside each.

Let the money returned = R

economics classes = E

other classes = O

a). The following gives the probability statement for the overall percentage of the money returned: 100.P (R)

b). The probability statement that the percentage of money recovered from economics classes is 100.P(R|E)

c). The probability statement that displays the percentage of money returned from the other classes is 100.P(R|O).

d). No, because P(R) is not equal to P(R|E), the money returned is not independent of the classes.

e).  According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

The complete question is:

Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped 122 stamped, addressed envelopes with $20 cash in two different classrooms (one economics, one not) on the George Washington campus. Of these, 42% were returned overall. From the economics class 51% of the envelopes were returned. From the other class 36% were returned.

From

the business, psychology, and history classes 31% were returned.

Let: R = money returned; E = economics classes; O = other classes

a. Write a probability statement for the overall percent of money returned.

b. Write a probability statement for the percent of money returned out of the economics classes.

c. Write a probability statement for the percent of money returned out of the other classes.

d. Is money being returned independent of the class? Justify your answer numerically and explain it.

e. Based upon this study, do you think that economists are more selfish than other people? Explain why or why not. Include numbers to justify your answer.

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To determine the 90% confidence interval for the mean repair cost of VCRs, we need to find the critical value for constructing the interval. The sample data consists of 1414 randomly selected VCRs, with a sample mean repair cost of $55.95 and a sample standard deviation of $18.89.

The critical value is determined based on the desired confidence level and the sample size. In this case, we want a 90% confidence interval, which means we need to find the critical value that leaves 5% in the tails of the distribution (since the remaining 90% will be in the interval).

Using a standard normal distribution table or a calculator, the critical value for a 90% confidence level is approximately 1.645 (rounded to three decimal places). This value represents the number of standard deviations away from the mean that includes 90% of the distribution.

In the next step, we will use this critical value along with the sample mean, standard deviation, and sample size to calculate the confidence interval for the mean repair cost of the VCRs.

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Answer:

They should walk on a bearing of 59.4 degrees

Step-by-step explanation:

Given

\(South = 4.2km\)

\(West = 7.1km\)

Required

The bearing back to the base

The given question is illustrated with the attached image.

To do this, we simply calculate the measure of angle a using:

\(\tan(a) = \frac{Opposite}{Adjacent}\)

\(\tan(a) = \frac{7.1}{4,2}\)

\(\tan(a) = 1.6905\)

Take arctan of both sides

\(a = \tan^{-1}(1.6905)\)

\(a = 59.4^o\)

The bearing that the scout should work is N59.4W for the shortest distance

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let  A represent the angle that the scouts walk

tan∠A = 4.2/7.1

A = 30.6°

The bearing that the scout should work is N59.4W (90 - 30.6) for the shortest distance

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Answer:

y ≥ 62

Step-by-step explanation:

Give Me Brainllest plz T - T

The answer of the given question is positive linear relationship.

If the value of the sample covariance between the two random variables x and y equals 14.67, then we can conclude that x and y have a positive linear relationship.

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If the value of the sample covariance between the two random variables x and y equals 14.67, we can conclude that x and y have a positive linear relationship or association

Covariance measures the direction and strength of the relationship between two variables. A positive covariance indicates that as the values of x increase, the values of y tend to increase as well, and vice versa. In other words, there is a tendency for the variables to move in the same direction.

However, the value of covariance alone does not provide information about the strength or the exact nature of the relationship. To determine the strength and statistical significance of the relationship, additional analysis, such as calculating the correlation coefficient or performing hypothesis tests, may be necessary.

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Answer:

-10 = a

Step-by-step explanation:

17 = a - 3 - За

Combine like terms

17 = -3 -2a

Add 3 to each side

17+3 = -3-2a+3

20 = -2a

Divide by -2

20/-2 = -2a/-2

-10 = a

Answer:

a=-10

Step-by-step explanation:

17= -3-2a

17+3=-2a

20=-2a

a=-10 hope I helped

The mean of a random variable is a measure of its central tendency and represents the average value it takes.

To find the mean of the given random variable X, we multiply each possible value of X by its corresponding probability and sum them up. In this case, we have three possible values for X: 0, 1, and 2. The probabilities associated with these values are 0.7, 0.1, and 0.2, respectively.

To calculate the mean, we multiply each value of X by its probability and sum them up:

Mean = (0 * 0.7) + (1 * 0.1) + (2 * 0.2) = 0 + 0.1 + 0.4 = 0.5

Therefore, the mean of the random variable X is 0.5, rounded to two decimal places.

The mean of 0.5 indicates that, on average, the random variable X takes a value close to 0.5. However, since X is a discrete random variable, it can only take one of the three possible values: 0, 1, or 2. The mean serves as a summary statistic that represents the "typical" value of X in terms of its probability distribution.

It's important to note that the mean of a random variable does not necessarily have to be one of the possible values that the random variable can take. It is a weighted average of all possible values, where the weights are the probabilities assigned to each value.

In this case, the mean of 0.5 indicates that, on average, X is closer to the value 0 than to 1 or 2, since the probability of X being 0 is 0.7, which is higher than the probabilities of 1 (0.1) and 2 (0.2).

Therefore, the mean of the random variable X is 0.5, indicating its central tendency based on the given probability distribution.

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Answer:  60

Step-by-step explanation:

Answer:60

Step-by-step explanation:

((−8)(15) (-1/2) =60

Answer

It is the equation of the plane that passes through the point (0, -2, 1) and is orthogonal to the line x = -5 + 4t, y = 2 - 5t, with a coefficient of x equal to 4.

Step-by-step explanation:

We can start by finding the direction vector of the line x = -5 + 4t, y = 2 - 5t. We can see that the direction vector of the line is <4, -5, 0>.

Now, we want to find a normal vector to the plane that is orthogonal to the direction vector of the line. The cross product of two vectors is orthogonal to both of them, so we can take the cross product of the direction vector of the line and any other vector in the plane to get a normal vector to the plane.

Since we want the coefficient of x to be 4, we can choose the vector <4, 0, a> for some scalar a. To make this vector orthogonal to the direction vector of the line, we can take the cross product:

<4, -5, 0> x <4, 0, a> = <-5a, -16, 20>

This vector is normal to the plane and has a coefficient of x equal to -5a. We want this to be equal to 4, so we solve for a:

-5a = 4

a = -4/5

So the normal vector to the plane is <-4, -16, 20/5> = <-4, -16, 4>.

Now, we can use the point-normal form of the equation of a plane to write the equation of the plane. The equation is:

-4(x - 0) - 16(y + 2) + 4(z - 1) = 0

Simplifying this equation, we get:

-4x - 16y + 4z + 16 = 0

And that is the equation of the plane that passes through the point (0, -2, 1) and is orthogonal to the line x = -5 + 4t, y = 2 - 5t, with a coefficient of x equal to 4.

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The entire garden needs to be fence for a total of $156.

Given that,

A fence is required to entirely enclose a garden that is 15 by 24 feet in size. Each foot of fencing costs $2.

To find : The overall cost of fencing the garden?

Dimensions are given by 15 feet and 24 feet

Cost per foot is $2

Total perimeter of garden is given as 2(l+b)

P = 2(l+b)

P= 2(15+24)

P = 78 feet

1 feet = $2

78 feet = 78 * 2 = $156

Therefore, the total cost required to fence the entire garden is $156

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Answer:

-1.1, 6.1

Step-by-step explanation:

-2X^2+10X+14=0

(-2X^2+10X+14)/-2=0

X^2-5X-7=0

Then use the quadratic formula because you can't factor

Fill in the equations and solve. One should have the plus and the other should have the minus and that's how you get the 2 different answers.

A=1

B=-5

C=-7

The solutions of the equation −2x²+10x=−14 is -1.1 and 6.1.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that;

−2x²+10x=−14

Now,

Move the constant term to the right side of the equation. For example:

−2x2+10x=−14

−2x2+10x+14=0

Divide both sides of the equation by the coefficient of x2. In this case, the coefficient is -2. For example:

−2−2x2+10x+14​=−20​

x2−5x−7=0

Write the equation as x² - 5x + ___ - ___ - 7 = 0, leaving two blanks for the constant term.

To find the constant term, divide the coefficient of x by 2 and square it. In this case, -5/2 = -2.5 and (-2.5)² = 6.25. So we fill in the blanks with 6.25 and get x² - 5x + 6.25 - 6.25 - 7 = 0.

(x - 2.5)² - 6.25 - 7 = 0

(x - 2.5)² - 13.25 = 0.

(x - 2.5)² = 13.25.

x - 2.5 = ±√13.25.

Add 2.5 to both sides of the equation: x = 2.5 ±√13.25.

Use a calculator to approximate the solutions and round to the nearest tenth: x ≈ -1.1 or x ≈ 6.1.

Therefore, by the given equation the answer will be -1.1 and 6.1.

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The system of equations with no solutions is the second one:

3x - 7y = 22

4.5x - 10.5y = 44

When we have a system of linear equations, the only case where the system has no solutions is when both of the lines are parallel lines (thus, the lines never intercept).

So we need to identify the system of linear equations where the lines are parallel.

If you look at the second system of equations, we have:

3x - 7y = 22

4.5x - 10.5y = 44

We can multiply the first equation by 1.5 to get:

1.5*(3x - 7y) = 1.5*22

4.5x - 10.5y = 33

Then the system is:

4.5x - 10.5y = 33

4.5x - 10.5y = 44

We can see that these lines are parallel,and thus, this system has no solutions.

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Answer:

Correct option: A

Step-by-step explanation:

The angle BDC inscribe the arc mBC, so we have that:

mBDC = (1/2) * mBC

mBDC = (1/2) * 118 = 59°

From the secants relation in a circle, we have that:

mA = (1/2) * (mBC - mDE)

35 = (1/2) * (118 - mDE)

70 = 118 - mDE

mDE = 48°

The sum of the arcs is 360°, so we have:

mBC + mCD + mDE + mBE = 360

118 + mCD + 48 + 76 = 360

mCD = 360 - 118 - 48 - 76 = 118°

The angle mCBD inscribes the arc mCD, so we have:

mCBD = (1/2) * mCD = (1/2) * 118 = 59°

The angles mCBD and mBDC are equal, so the triangle is isosceles.

Correct option: A

Answer:

The answer is  11

Step-by-step explanation:

Answer:x=18

Step-by-step explanation:

3(x-5)=x+21

Distribute the 3

3x-15=x+21

Add 15 to each side

3x=x+36

Subtract x from each side

2x=36

Divide each side by 2

x=18

Answer:

P = 11/135 = 0.0815

Step-by-step explanation:

we can said that:

So, there are 124 people that use the gym, the pool or the track. This is calculated using the information above as:

14 + 18 + 21 + 22 + 14 + 16 + 19 = 124

Finally, there are 11 ( 135 - 124 = 11 ) people that don't use any facility, so the probability that a person doesn't use any facility is:

P = 11/135 = 0.0815

Answer:

0.0815

Step-by-step explanation:

Answer:

5 × (20+3) it ez math bro 5 th grade

The graphs show that Function composition is not commutative. This is observed from the graph of the compositions f(g(x)) and g(f(x)), which are not symmetrical about the y-axis. In other words, the order of function composition matters.

Based on the given information, the correct statements are:

1. f(g(x)) = g(f(x)) for at least one value of x. This means that there is at least one value of x for which the compositions f(g(x)) and g(f(x)) are equal.

3. f(g(0)) = 5 and g(f(–2.5)) = 5. This indicates that when plugging in specific values, f(g(0)) and g(f(–2.5)) both evaluate to 5.

4. Both f(g(x)) and g(f(x)) have the same domain. The domain of a function refers to the set of all possible input values. In this case, both compositions have the same domain.

5. The graphs show that function composition is not commutative. This is observed from the graph of the compositions f(g(x)) and g(f(x)), which are not symmetrical about the y-axis. In other words, the order of function composition matters.

Therefore, the correct answer is: 1, 3, 4, 5.

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