A triangle has sides with lengths of 11 feet, 9 feet,
and 14 feet. Is it a right triangle?

Answer:

y=-2x+15

Step-by-step explanation:

Hi there!

We are given that m=-2, b=15, and we want to write the equation of the line, given these values

We can write the line in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept, since we are given the values of both m and b.

Since we know the values of m and b (-2 and 15 respectively), we can substitute those numbers in as the variables they equal to.

Substitute -2 as m:

y=-2x+b

Substitute 15 as b:

y=-2x+15

Hope this helps!

The coordinates of the circumcenter of the triangle with vertices A(0,0), B(0,6), and C(10,0) are (5,3).

To find the circumcenter of a triangle, we need to first find the perpendicular bisectors of the sides. The point where these three perpendicular bisectors intersect is the circumcenter.
Let's start by finding the equation of the line passing through the midpoint of AB and perpendicular to AB.

The midpoint of AB is ((0+0)/2,(0+6)/2) = (0,3). The slope of AB is (6-0)/(0-0) = undefined, so the slope of the perpendicular bisector is 0. Therefore, the equation of the perpendicular bisector of AB is y = 3.
Similarly, the midpoint of BC is ((0+10)/2,(6+0)/2) = (5,3) and the slope of BC is 0. Therefore, the equation of the perpendicular bisector of BC is x = 5.
Lastly, the midpoint of AC is ((0+10)/2,(0+0)/2) = (5,0) and the slope of AC is (0-0)/(10-0) = 0.

Therefore, the equation of the perpendicular bisector of AC is y = 0.
Now, we need to find the point of intersection of these three lines. The intersection of the perpendicular bisectors of AB and BC is (5,3), and the intersection of the perpendicular bisectors of AB and AC is (0,3).

Therefore, the circumcenter of triangle ABC is the midpoint of the line segment connecting (5,3) and (0,3), which is ((5+0)/2,(3+3)/2) = (2.5,3).
Therefore, the coordinates of the circumcenter of the triangle with vertices A(0,0), B(0,6), and C(10,0) are (5,3).

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The proportion of babies weighing between 11 and 15 pounds is approximately 0.508.

We can standardize the values of 11 and 15 using the formula:

z = (x - mu) / sigma

where x is the observed value, mu is the mean, sigma is the standard deviation, and z is the standardized score.

For 11 pounds:

z1 = (11 - 12.7) / 2.9 = -0.5862

For 15 pounds:

z2 = (15 - 12.7) / 2.9 = 0.7931

We can then use a standard normal distribution table or calculator to find the area under the curve between these standardized scores:

P(-0.5862 < Z < 0.7931) = P(Z < 0.7931) - P(Z < -0.5862)

Using a standard normal distribution table or calculator, we can find that:

P(Z < 0.7931) = 0.7867

P(Z < -0.5862) = 0.2787

Therefore:

P(-0.5862 < Z < 0.7931) = P(Z < 0.7931) - P(Z < -0.5862)

= 0.7867 - 0.2787

= 0.5080

Rounding to three decimal places, we get:

The proportion of babies weighing between 11 and 15 pounds is approximately 0.508.

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Using statistics helps us make decisions based on empirical evidence, which is obtained through data analysis and inference.

Statistics provides us with a set of tools and methods to collect, analyze, and interpret data. By applying statistical techniques, we can make decisions based on evidence derived from empirical observations and measurements.

Statistics allows us to summarize and describe data, identify patterns and relationships, and draw conclusions from samples or populations. It helps us quantify uncertainty and assess the strength of evidence supporting different claims or hypotheses.

Decision-making based on statistics involves making inferences about a larger population based on the information available from a sample. By using probability theory and statistical models, we can estimate population parameters, test hypotheses, and make predictions about future events or outcomes.

Statistics provides a systematic and rigorous framework for evaluating evidence and reducing bias in decision-making. It allows us to objectively assess the reliability and validity of information, making decisions that are informed by data-driven analysis rather than intuition or anecdotal evidence.

In summary, statistics helps us make decisions based on evidence obtained through data analysis, enabling us to draw reliable conclusions, quantify uncertainty, and make informed choices in various fields such as business, medicine, social sciences, and more.

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Using the rule of 72, startfraction 72 over t endfraction, Manuel will double his money first, in approximately 9 years. Option C is the answer.

The rule of 72 is a quick and simple way to estimate the number of years it takes for an investment to double given the

interest rate. It is calculated by dividing 72 by the interest rate.

For example, if an investment has an interest rate of 8%, it will take approximately 72 / 8 = 9 years to double the investment.

Applying this rule, we can estimate the time it will take for Sylvia's investment to double: 72 / 8 = 9 years.

And for Manuel's investment to double: 72 / 7.25 = 10 years.

Since Manuel's investment will double in approximately 9 years, he will double his money first.

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Answer:

The slope of the line between points A and B is 0.25

Step-by-step explanation:

Here in this question, we simply aim at calculating the slope of the line between two given points;

The points in question are;

A(400,40) and B(480,60)

Mathematically, the slope of the line can be calculated using the formula:

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

Where ;

x1 = 400

y1 = 40

x2 = 480

y2 = 60

Substituting the values, we have;

slope = (60-40)/(480-400) = 20/80 = 1/4 = 0.25

The first three members of the corresponding orthonormal basis of V are:

\(v0(x) = 1, \\v1(x) = sqrt(2) x, \\v2(x) = 2x2 - 1.\)

Given: V be the Euclidean space of polynomials with the inner product \((u, v) S* w(x)u(x)v(x)dx\) where \(w(x) = xe-r\).

With \(Un(x) = x", \\n = 0, 1, 2, ...\)

To determine: the first three members of the corresponding orthonormal basis of VFormula to find

Orthonormal basis of V is: {vi}, where for each \(= sqrt((ui,ui)).i.e {vi} = {ui(x)/sqrt((ui,ui))}\)

with ||ui|| \(= sqrt((ui,ui)).i.e {vi} \\= {ui(x)/sqrt((ui,ui))}\)

, where (\(ui,uj) = S*w(x)ui(x)uj(x)dx\)

Here w(x) = xe-r and Un(x) = xn

First we find the inner product of U\(0(x), U1(x) and U2(x).\\S* w(x)U0(x)U0(x)dx = S* xe-r (1)(1)dx=\)

integral from 0 to infinity (xe-r dx)= x (-e-r x - 1) from 0 to infinity

\(= 1S* w(x)U1(x)U1(x)dx \\= S* xe-r (x)(x)dx=\)

integral from 0 to infinity

\((x2e-r dx)= 2S* w(x)U2(x)U2(x)dx \\= S* xe-r (x2)(x2)dx=\)

integral from 0 to infinity\((x4e-r dx)= 24\)

We have

\((U0,U0) = 1, \\(U1,U1) = 2, \\(U2,U2) = 24\)

So the corresponding orthonormal basis of V are:

\(v0(x) = U0(x)/||U0(x)|| = 1, \\v1(x) = U1(x)/||U1(x)|| = sqrt(2) x, \\v2(x) = U2(x)/||U2(x)|| \\= sqrt(24/6) (x2 - (1/2))\\= sqrt(4) (x2 - (1/2))\\= 2x2 - 1\)

Therefore, the first three members of the corresponding orthonormal basis of V are

\(v0(x) = 1, \\v1(x) = sqrt(2) x, \\v2(x) = 2x2 - 1.\)

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Answer:

n+4=28

Step-by-step explanation:

Since n is the original members and 4 joined, n+4=28, the new members.

Answer:

  -4y²

Step-by-step explanation:

You want to simplify the expression -√(16y⁴), given that y < 0.

The square root can be simplified by removing squares from under the radical.

  \(-\sqrt{16y^4}=-\sqrt{(4y^2)^2}=\boxed{-4y^2}\)

The sign of y is irrelevant.

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The inequality that is graphed above include the following: A. y < 2x - 1

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of the dashed line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 0)/(1 - 0.5)

Slope (m) = 2

At data point (1, 1) and a slope of 2, a linear inequality for this dashed line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = 2(x - 1)

y = 2x - 1

y < 2x - 1 (since the dashed line is shaded below).

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The work done by the constant force F = 5i + 2j - 3k in moving an object along the straight line connecting the points P(1, 2, 3) and Q(1, -1, 4) in space is zero.

To calculate the work done by a force along a straight line, we use the formula:

Work = Force · Displacement

Given the force vector F = 5i + 2j - 3k and the displacement vector from P to Q, which can be calculated as D = Q - P = (1 - 1)i + (-1 - 2)j + (4 - 3)k = 0i - 3j + 1k = -3j + k, we can calculate the dot product of F and D:

Work = (5i + 2j - 3k) · (-3j + k)

The dot product is calculated by multiplying the corresponding components of the two vectors and summing them:

Work = (5 * 0) + (2 * -3) + (-3 * 1) = 0 - 6 - 3 = -9

Since the work done is equal to -9, it means that the force F does negative work in moving the object along the straight line from P to Q. In other words, the force is acting in the opposite direction of the displacement, resulting in zero net work done.

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The probability that Hannah's number is an even palindrome is 1/45.

There are 45 even palindrome numbers between 1000 and 9999, out of a total of 4500 possible 4-digit numbers.

So, the probability of Hannah writing an even palindrome number is 1/45.

A palindrome number is the same when read from left to right or right to left. There are 90 possible 2-digit palindrome numbers (11, 22, 33, etc.), and 9 possible 1-digit palindrome numbers (1, 2, 3, etc.), making a total of 99 palindrome numbers from 1 to 999. In a 4-digit number, the first and last digits must be the same for it to be a palindrome.

Therefore, the first digit has 9 choices (1-9), and the last digit also has 9 choices. The second digit can be any of the 10 digits (0-9), and the third digit can be any of the 5 remaining even digits (0, 2, 4, 6, 8).

Thus, there are 45 even palindrome numbers between 1000 and 9999.

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The function f(m, n) = 3n - 4m is not injective because different pairs of inputs (m, n) can yield the same output value. For example, f(0, 1) = f(2, 3) = -4. Therefore, the function is not one-to-one.

The function f(m, n) = 3n - 4m is surjective because for every integer z, there exist inputs (m, n) such that f(m, n) = z. To verify this, we can rewrite the function as 3n - 4m = z and solve for (m, n) in terms of z. Rearranging the equation, we have 3n = 4m + z. Since m and n can take any integer values, we can choose m = z and n = 0, which satisfies the equation. Thus, for any integer z, there exists a pair of inputs (m, n) that maps to z. Therefore, the function is onto or surjective.

In summary, the function f(m, n) = 3n - 4m is not injective but it is surjective

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Answer: d

Step-by-step explanation:

Answer:

x=18

Step-by-step explanation:

Hey There!

So if you did not know all of the angles in a triangle will add up to equal 180

So we use the equation

180=2x+3x+5x

and solve for x

step 1 combine like terms

2x+3x=5x

5x+5x=10x

so now we have

180=10x

step 2 divide each side by 10

180/10=18

therefore x = 18

hope this helps and if you have any more questions feel free to ask :)

The volume of the solid generated by revolving the triangle about the -axis is (8π/3).

The region enclosed by the -axis, the line y = 2, and the curve y = -x is a triangle with base 2 and height 2.

To find the volume of the solid generated by revolving this triangle about the -axis, we can use the method of cylindrical shells.

The volume of each shell is given by the formula:

V = 2πr * h * δr

where r is the distance from the -axis to the shell, h is the height of the shell, and δr is the thickness of the shell.

We can express r as a function of y, since each shell corresponds to a vertical slice of the triangle:

r = y

The height of each shell is given by the difference between the -axis and the curve y = -x:

h = 2 - (-x) = 2 + x

Finally, the thickness of each shell is δr = dy.

Therefore, the volume of the solid is:

V = ∫[0,2] 2πy * (2 + y) dy

= 2π ∫[0,2] (2y + y^2) dy

= 2π [y^2 + (1/3)y^3] |[0,2]

= (8π/3)

Therefore, the volume of the solid generated by revolving the triangle about the -axis is (8π/3).

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Answer:

I can't see the sign between 2 and (1/3)^3 in the last question, it's a bit blurry. You should send it again.

Step-by-step explanation:

please mark BRAINLIEST

Answer:

look at the photo I have sent

you wearing a mask right now???

General solution of the given differential equations are as follows:

18. xy' = 2y + x³ cos x

The given differential equation is of the form xy′ − 2y = x³ cos x

This is a linear differential equation of first order, so the general solution can be written as

y(x) = e^(∫P(x)dx)(∫Q(x)e^(-∫P(x)dx)dx + C)

Where P(x) = -2/x and Q(x) = x³ cos x

Now, we have to solve the equation by using integrating factor= e^(∫-2/xdx)

= e^(-2lnx) = 1/x

²Multiplying throughout by the integrating factor gives(x^{-2}y)' = x cos x

Integrating with respect to x,

we gety(x) = (-1/3)x^{-3} cos x + (1/9) x^3 sin x + C/x219. y' + y cotx

= cos x

The given differential equation is of the form y′ + P(x)y = Q(x),

where P(x) = cot x

Now, the integrating factor can be found by using the formula= e^(∫P(x)dx)

= e^ln(sin x)

= sin x

Multiplying throughout by the integrating factor gives(sin x y)' = cos x Integrating with respect to x,

we gety(x) = sin x + Ccos x20.

y'= 1 + x + y + xy,

y(0) = 0The given differential equation is of the form y′ + P(x)y = Q(x),

where P(x) = 1 + x

Now, the integrating factor can be found by using the formula= e^(∫P(x)dx)

= e^(∫(1 + x)dx)

= e^(x + x²/2)

Multiplying throughout by the integrating factor gives(e^{x + x²/2} y)'

= e^{x + x²/2} (x + 1)

Integrating with respect to x, we gety(x) = e^{-x-x^2/2} ∫e^{x+x^2/2} (x + 1)dx + Ce^{-x-x^2/2}21.

xy' = 3y + x⁴ cos x, y(2л) = 0

The given differential equation is of the form xy′ − 3y = x⁴ cos x

This is a linear differential equation of first order, so the general solution can be written as y(x)

= e^(∫P(x)dx)(∫Q(x)e^(-∫P(x)dx)dx + C)

Where P(x) = -3/x and

Q(x) = x⁴ cos x

Now, we have to solve the equation by using integrating factor= e^(∫-3/xdx)

= e^(-3lnx) = 1/x³

Multiplying throughout by the integrating factor gives(x³y)' = x cos x Integrating with respect to x,

we get y(x) = (-1/3)x^{-3} cos x + (1/9) x^3 sin x + C/x³22.

y' = 2xy + 3x² exp(x²),

y(0) = 5

The given differential equation is a first-order linear differential equation of the form y′ + P(x)y = Q(x),

where P(x) = 2x and Q(x)

= 3x² exp(x²)

Now, the integrating factor can be found by using the formula= e^(∫P(x)dx) = e^(∫2xdx) = e^(x²)

Multiplying throughout by the integrating factor gives(e^{x²} y)'

= 3x² e^(2x²)Integrating with respect to x,

we gety(x) = ∫3x² e^(2x²) e^{-x²} dx + Ce^{-x²}y(x)

= (3/2) ∫2x e^{x²} dx + Ce^{-x²}y(x)

= (3/4) e^{x²} + Ce^{-x²}23.

xy' + (2x − 3) y = 4x⁴

The given differential equation is a first-order linear differential equation of the form y′ + P(x)y = Q(x),

where P(x) = (2x − 3)/x and Q(x) = 4x³

Multiplying throughout by the integrating factor, e^(∫(2x-3)/xdx), gives(xy)'e^(-3lnx) + y(x)e^(-3lnx)

= 4x³e^(-3lnx)Multiplying by x^{-3} throughout both sides of the equation, we have(x^{-2}y)' - 3x^{-2}y = 4x

Integrating both sides,

we get y(x) = x^3 - (16/5) x^{-2} + C/x^3

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Answer:

15+2i

Step-by-step explanation:

Hi there!

We are given the following expression:

(7-4i) + (8+6i)

And we want to write it as a complex number in standard form

Standard form is a+bi, where a is the real part of the number and bi is the imaginary part of the number.

We can open up the parentheses on the expression

7-4i+8+6i

Now combine the like terms (add 8 and 7 together, then add -4i and 6i together)

15+2i

The complex number is now in standard form

Hope this helps!

Answer:  resultant

Step-by-step explanation:

The statement is True only for independent events and False otherwise. The statement "p (A ∩ B) = p(A). p(B)" is not always true for any two events A and B defined on a sample space S of an experiment.

This equation only holds true if A and B are independent events, meaning that the occurrence of one event does not affect the probability of the other event happening. In other words, p(A|B) = p(A) and p(B|A) = p(B).

If A and B are dependent events, meaning that the occurrence of one event affects the probability of the other event happening, then the equation does not hold true. In this case, the probability of A and B occurring together (p(A ∩ B)) would be less than the product of the probabilities of A and B occurring separately (p(A).p(B)).

Therefore, the statement is not always true and depends on whether A and B are independent or dependent events.

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Answer:

Existen 6 formas posibles de cambiar un billete de 5000 por monedas de 200 y 500.

Step-by-step explanation:

En primer lugar, se determina el mínimo común múltiplo de 500 y 200. Si se multiplica a 500 por 2 y a 200 por 5, se encuentra que el mínimo común múltiplo es 1000. Entonces, se encuentra las siguientes dos conclusiones:

1) Se requiere dos monedas de 500 para obtener 1000.

2) Se requiere cinco monedas de 200 para obtener 1000.

Para determinar todas las formas posibles sin considerar el orden de las monedas, se requiere estudiar tres escenarios:

(i) Todas las monedas son de 200.

(ii) Todas las monedas son de 500.

(iii) Hay monedas de 200 y 500.

Caso 1 - Todas las monedas son de 200:

Es evidente que solo existe una forma.

Caso 2 - Todas las monedas son de 500:

Es evidente que solo existe una forma.

Caso 3 - Hay monedas de 200 y 500:

Existen las siguientes formas:

- 1000 en monedas de 200, 4000 en monedas de 500.

- 2000 en monedas de 200, 3000 en monedas de 500.

- 3000 en monedas de 200, 2000 en monedas de 500.

- 4000 en monedas de 200, 1000 en monedas de 500.

En resumen, existen 4 escenarios.

Finalmente, existen 6 formas posibles de cambiar un billete de 5000 por monedas de 200 y 500.

Answer:

Answer is x=-2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The answer is C which is 2

a)The linear equation is C=25n + 2500 to produce n 3000 toys, b) The total cost to produce 3000 toys is $77,500, c) With $32500, a total of 1200 toys can be produced in Pinwheel Industries.

An equation is a mathematical statement with an equal symbol (=) between the algebraic expression. Equations with a degree of one are called linear equations. It is the straight line's equation. Whenever values are substituted for the unknown values in linear equations, the solutions produce values that make the equation true. Since there is only one variable, there is only one solution. For instance, the equation x + 2 = 0 has just one solution, which is x = -2. In the case of the two-variable linear equation, however, the solutions are determined as the Cartesian coordinates of a point on the Euclidean plane.

The three different types of linear equations are: 1) Standard Form

2) The slope intercept form

3)Point Slope Form

How to solve?

A) Linear equation y=mx+b,

C (total cost) = y and n (number of toys) =x.

C=25n + 2500

B) Put n=1750

C= 25(3000) + 2500

C= $77,500

C)

32500= 25n +2500

30000=25n

n = 1200

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Answer:

50

Step-by-step explanation:

this can be solved by ratio   15/x = 30/100.  Cross multiply and solve for x.  The answer is 50.