In triangle $ABC$ points $D$ and $E$ lie on $\overline{BC}$ and $\overline{AC}$, respectively. If $\overline{AD}$ and $\overline{BE}$ intersect at $T$ so that $AT/DT

Answer:

\(2^1^5\)

Step-by-step explanation:

Power rule: you multiply the exponent.

Think of it this way: \(X ^3 = X \times X \times X\). In this case, \(X = 2^5\)

At this point our original number is \(2^5 \times 2^5 \times 2^5 = 2\times2\times2... \times 2\)  with 15 2s

Which is, by definition, \(2^1^5\)

A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.

A perpendicular bisector can be defined as a type of line that bisects (divides) a line segment exactly into two (2) halves and forms an angle of 90 degrees at the point of intersection.

In this scenario, we can reasonably infer that to divide the triangles into these regions, you should construct the perpendicular bisector of each segment. These perpendicular bisectors intersect and divide each triangle into three regions. The points in each region are those closest to the vertex in that region.

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Answer:y=2x+1

Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answer:

cos a = \(\frac{7}{25}\)

Step-by-step explanation:

Given

sin a = \(\frac{24}{25}\) = \(\frac{opposite}{hypotenuse}\)

tan a = \(\frac{24}{7}\) = \(\frac{opposite}{adjacent}\)

Then this is a right triangle with opposite = 24, adjacent = 7 and hypotenuse = 25 , then

cos a = \(\frac{adjacent}{hypotenuse}\) = \(\frac{7}{25}\)

After subtraction (3x+4) - (x+7), the resultant answer is 2x-3.

One of the four operations used in mathematics, along with addition, multiplication, and division, is subtraction.

Removal of items from a collection is represented by the operation of subtraction.

For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches.

So, we have:

(x+7) and (3x+4)

We have to subtract as:

(3x+4) - (x+7)

Now, subtract as follows:

(3x+4) - (x+7)

3x+4 - x-7

2x-3

Therefore, after subtraction (3x+4) - (x+7), the resultant answer is 2x-3.

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Answer:

\(2( {x + 7})^{2} + 5\)

Step-by-step explanation:

Our Standard form for each of these transformations is

\(a( {x + h)}^{2} + k\)

Insert each value into the appropriate.

K is for vertical movement

h is for horizontal

a is for stretching/compression

The solutions of the given differential equations are\(x(t) = 3(1 - e^3t)\)and \(y(t) = 3te^3t.\)

Given differential equations are:

x′=x−y

y′=4x+6y​

x(0)=−23​

y(0)=0

​The Laplace transform of the given differential equations is:

L{x′}= L{x} − L{y}

L{y′}= 4L{x} + 6

and, the Laplace transform of the initial conditions is:

L{x(0)}=−23​

L{y(0)}=0

Using the differentiation property of the Laplace transform, we get:

L{x′} = sL{x} − x(0)

L{y′} = sL{y} − y(0)

Applying Laplace transform to the given differential equations, we get:

sL{x} − x(0) = L{x} − L{y}

4L{x} + 6L{y} = L{y′}

= sL{y} − y(0)

Simplifying the above equations and substituting the initial conditions, we get:

(s-1)L{x} + L{y} = 2/3(s+3)

L{y} = sL{x}

Since x(t) and y(t) are defined using inverse Laplace transform, we need to eliminate L{x} and L{y} from above equations.

Therefore, multiplying equation (3) by (s+3)/(s-1), we get:

(s+3)L{x} - L{y} = 0

By substituting the above equation in equation (2), we get:

s(s+3)L{x} - sL{y} = 0

Therefore,

L{y} = s(s+3)L{x}

Substituting L{y} in equation (3), we get:

(s+3)L{x} - s(s+3)

L{x} = 0

\(L{x} (s+3-s^2) = 0\)

L{x} = 0 or L{x} = 3/s-3

We have already calculated that

L{y} = s(s+3)L{x}

Therefore,

\(L{y} = 3s/(s-3) - 9/(s-3)^2\)

Taking inverse Laplace transform of L{x} and L{y}, we get:

\(x(t) = 3(1 - e^3t)\\y(t) = 3te^3t\)

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Answer:

1,687.5 square millimeters

Step-by-step explanation:

There are six faces of a cuboid:

1. Top and bottom face: length x width

- Top face area = Length x Width = 15mm x 7.5mm = 112.5 square mm

- Bottom face area = Top face area = 112.5 square mm

2. Front and back face: height x width

- Front face area = Height x Width = 45mm x 7.5mm = 337.5 square mm

- Back face area = Front face area = 337.5 square mm

3. Left and right face: height x length

- Left face area = Height x Length = 45mm x 15mm = 675 square mm

- Right face area = Left face area = 675 square mm

Therefore, the total surface area of the cuboid is the sum of all six faces:

Total Surface Area = 2(Top face area + Front face area + Left face area)

= 2(112.5 square mm + 337.5 square mm + 675 square mm)

= 2(1125 square mm)

= 2250 square mm

Therefore, the surface area of the given cuboid is 2250 square mm.

Answer:

x = 11

Step-by-step explanation:

By using angle bisector theorem,

"Bisector of an angle divides the opposite side of the angle into two segments such that they are proportional to the other two sides.

\(\frac{AC}{CD}= \frac{AB}{BD}\)

\(\frac{8}{4}=\frac{x+3}{x-4}\)

8(x - 4) = 4(x + 3)

8x - 32 = 4x + 12

8x - 4x = 32 + 12

4x = 44

x = 11

Therefore, value of x is 11.

Slope intercept form become C = 10 + 0.20m

What do you mean by linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Both linear equations with one variable and those with two variables exist.

The standard form or the general form of linear equations in one variable is written as, Ax + B = 0; where A and B are real numbers, and x is the single variable.

Slope intercept form is y =  mx + c where m is the slope and c is the y-intercept.

It is given that an Uber driver charges a $10 pick-up fee plus $0.20 per mile.

Let m be the total miles.

According to question, the equation become

Total charges, C = 10 + 0.20m

Therefore, slope intercept form become C = 10 + 0.20m

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Answer

he would have gotten a marry Christmas

Step-by-step explanation:

also hope you have a good day

The Cobb-Douglas utility function satisfies the properties of local non-satiation, decreasing marginal utility for both goods, quasi-concavity, and homotheticity.

The Cobb-Douglas utility function u(x1, x2) = xi^(α) * x2^(β), where α and β are both greater than zero, satisfies the following properties:

(a) Local non-satiation:

This property states that at each point of the consumption set, there is always another bundle that is arbitrarily close and strictly preferred. Thus, the function has local non-satiation.

(b) Decreasing marginal utility for both goods 1 and 2: The marginal utility of a good measures the utility obtained by consuming one more unit of it. The marginal utility of x1 can be obtained as:

MU1 = α * xi^(α−1) * x2^(β)

The marginal utility of x2 can be obtained as:

MU2 = β * xi^(α) * x2^(β−1)

Therefore, both marginal utilities are decreasing in x1 and x2, satisfying this property.

(c) Quasi-concavity:

The Cobb-Douglas function is quasi-concave. This means that the upper contour set of any level set of the function is convex. This can be proved by taking the second partial derivative of the function and checking whether it is negative or not.

(d) Homotheticity:

The Cobb-Douglas function is homothetic. This means that its shape is independent of the total level of utility. The proof can be achieved by checking whether the function is homogeneous of degree one or not. This is true, since multiplying the inputs by any positive scalar λ leads to a proportional increase in the output.

In conclusion, the Cobb-Douglas utility function satisfies all four properties - local non-satiation, decreasing marginal utility for both goods 1 and 2, quasi-concavity, and homotheticity.

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Answer:

Undefined slope

Step-by-step explanation:

Slope , m is equal to rise/run    Or   ( y1-y2) / ( x1 -x2)

              This line is a vertical line at x = -8    And thus has undefined slope

              (Because you cannot divide by zero)

Answer:

Undefined

Step-by-step explanation:

Hey! Let's help you with your question here! I am unsure if the points are correct cause you've written each one down twice. If it does change, I will change my answer accordingly.

We're looking for a slope of the line that passes through 2 points I see! Alright, so as you would recall, most equations of a linear line are described in the form of slope-intercept form. And that being this:

\(y=mx+b\)

When we're finding for slope of the line, we're essentially just look for m. But how can we find m with only just 2 points? Well, we can! Using a formula that helps us find the slope using exactly 2 points! And that is:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Now, all we have to do is plug in the values as such and solve:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

\(m=\frac{-11-(-1)}{-8-(-8)}\)

From here, we come to a problem. If we were to solve this equation to find the slope, we will get an undefined value mainly because the denominator will equal 0 and we can't have it equal 0. So therefore, it is undefined.

Answer:

\(y=x\)

Step-by-step explanation:

Each point has the same y coord as their x, so \(y=x\)

Not that the first point works for both equations since it's the intersection between the two

Answer:

The answer is underneath!

Step-by-step explanation:

Set I is the set of ordered pairs which is a function. Choose A.

A function is a relationship between inputs where each input is related to exactly one output.

Based on the definition of function as seen above. Let's check the set of ordered pairs:

Given:

I. { (3, 7), (-1, 9), (-5, 11)}

II. { (9, -5) , (4, -5) , (-1, 7)}

III. { (-2, 1) , (3, -4) , (-2, -6)}

In set I, each input (i.e. 3, -1 and -5 ) has different output (i.e. 7, 9 and 11 ). Thus, set I is a function

In set II, two inputs (9 and 4) have the same output (i.e. -5). Thus, set II is not a function

In set III, the same input (i.e. -2 ) has different outputs (i.e. 1 and -6). Thus, set III is not a function

Therefore, the set of ordered pairs which is a function is I. So option A. is the answer

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To calculate 3/8 × 2/6 using a grid model, we need to use the following procedure:

First, represent the fraction 3/8 by shading three cells in each of the eight rows.Then, represent the fraction 2/6 by shading two cells in each of the six columns of the grid model.

Next, identify the cells that are shaded blue and textured. There are six cells where the blue shading and the texture overlap.Now count the number of cells that are shaded blue but not textured, there are 18 of them.Now count the number of cells that are textured but not shaded blue, there are 12 of them.

Finally, count the total number of cells that are shaded blue or textured.

There are 24 of them.

Thus, the product 3/8 × 2/6 is equal to the fraction of the total number of cells that are shaded blue or textured. This fraction is equal to 13/24.Therefore, the answer is B. 13/24.

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The number of the small seats is 30 while the number of the big seats is 94.

We know that from the question, Vicky is an airline attendant. Last week, she worked on flights on 3 small jets and 5 large jets, which could seat a total of 560 passengers. The week before, she was assigned to flights on 5 small jets and 2 large jets, which could seat a total of 338 passengers.

Now;

Let the number of small seats be x and the number of large seats be y

It follows that;

3x + 5y = 560 ----- (1)

5x + 2y = 338 ------(2)

If you multiply (1) by 5 and (2) by 3 we have;

15x + 25y = 2800 ------ (3)

15x + 6y = 1014 -----------(4)

        19 y = 1786

y = 1786/19

= 94

Substitute y = 94 into (1)

3x + 5(94) = 560

x = 560 -  5(94)/3

x = 30

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The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

To solve this differential equation, we can use separation of variables.

First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:

dy/dx = 1/3(sin x − xy^2)

dy/(sin x - xy^2) = dx/3

Now we can integrate both sides:

∫dy/(sin x - xy^2) = ∫dx/3

To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:

∫dy/(sin x - xy^2) = ∫du/(sin x - u)

= -1/2∫d(cos x - u/sin x)

= -1/2 ln|sin x - xy^2| + C1

For the right side, we simply integrate with respect to x:

∫dx/3 = x/3 + C2

Putting these together, we get:

-1/2 ln|sin x - xy^2| = x/3 + C

To solve for y, we can exponentiate both sides:

|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)

|sin x - xy^2| = 1/e^(2C/3 - x/3)

Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.

Case 1: sin x - xy^2 > 0

In this case, we have:

sin x - xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]

Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:

y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5

Squaring both sides and solving for C, we get:

C = 3/2 ln(1/25)

Putting this value of C back into the expression for y, we get:

y = √[(sin x - e^(x/2)/25)/x]

Case 2: sin x - xy^2 < 0

In this case, we have:

- sin x + xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(e^(2C/3 - x/3) - sin x)/x]

Again, using the initial condition y(0) = 5 and solving for C, we get:

C = 3/2 ln(1/25) + 2/3 ln(5)

Putting this value of C back into the expression for y, we get:

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]

So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:

y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5

Note that there is no solution for y when sin x - xy^2 = 0.

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The value k represents the y-intercept of a line in slope-intercept form (y = mx + k) when the value of x is zero or when it crosses the y-axis. This implies that the line cuts the y-axis at a point (0, k).

To determine the value of k, you must substitute x = 0 into the equation y = mx + k. If the value of x is zero, the equation becomes y = m(0) + k = k.

In algebra, a line can be described in numerous ways. One way to represent a line is to use the slope-intercept form, which is y = mx + k, where m is the slope and k is the y-intercept. The slope m represents the line's steepness and direction, while k represents the y-coordinate where the line crosses the y-axis.

The slope-intercept form of the equation y = mx + k is the preferred way of representing lines because it is simple to comprehend and is in a linear function's standard form. When it comes to graphing a line in this form, the y-intercept, k, provides a starting point on the y-axis.

The y-intercept is the point at which the line intersects the y-axis on the graph. Therefore, the value k represents the y-intercept of the line in slope-intercept form when the value of x is zero, or the line crosses the y-axis.

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The line cross the Y axis in y=-2

The equation of a line is Y=ax+b where a is the slope and b the y intercept of the line

we know that for x=3 => y=4 then we plug the values we know in the equation of the line:

now we use the point we know:

then solve for b

The the y intercept of the line is y=-2

A set of simultaneous equations is often known as a system of equations or an equation system. The solution of the system of equations is (4.123, 5.754) and (-1.662, 3.085).

A set of simultaneous equations, often known as a system of equations or an equation system, is a finite collection of equations for which common solutions are sought.

Inconsistent System

For a system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.

The solution of the two of the given function will be when the graph of the two the function will intersect with each other.

Using the graph the solutions are (4.123, 5.754) and (-1.662, 3.085)

Hence, the solution of the system of equations is (4.123, 5.754) and (-1.662, 3.085).

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Answer:

y=mx+b

Step-by-step explanation:

To send Kred to a Krew member, you can follow the steps provided by the Kred platform. These steps typically involve accessing your Kred account, selecting the desired recipient, specifying the amount of Kred to send, and confirming the transaction.

Sending Kred to a Krew member usually requires using the features and functionalities provided by the specific Kred platform or service. The process may vary depending on the platform, so it is recommended to refer to the official documentation or guidelines provided by the platform. Typically, you would need to log in to your Kred account, navigate to the appropriate section for sending Kred, select the intended recipient from the list of Krew members, enter the desired amount of Kred to send, review the transaction details, and confirm the transfer. The platform may also offer additional options or settings for customizing the transfer process.

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The correct option is a) 3.

Let the positive number be x.Three times the square of a certain positive number exceeds six times the number by nine can be mathematically written as:\($$3{x^2} - 6x = 9$$\)

Dividing both sides by 3, we get:\($$\frac{3{x^2}}{3} - \frac{6x}{3} = \frac{9}{3}$$$$\Rightarrow {x^2} - 2x = 3$$$$\Rightarrow {x^2} - 2x - 3 = 0$$\)

We can factorize the above quadratic equation to get:\($$(x - 3)(x + 1) = 0$$\)

By using the zero product property, we get the two roots as x = 3 and x = -1.

Since the problem statement specifies a certain positive number, the answer is x = 3.

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The inverse of f(x) is restricted to the domain x ≥ 1, since this is when\(x^2 − 2x + 1\) is always greater than 0.

To find the inverse function of f(x), we must first determine the domain of f(x). We can do this by finding the values of x where f(x) is greater than or equal to 0.

We can start by setting f(x) to 0 and solving for x:

\(x^2 − 2x + 1 = 0\)

\(x^2 − 2x + 1 − 1 = 0 − 1\)

\(x^2 − 2x = -1\)

(x − 1)(x − 1) = -1

x = 1

Therefore, the inverse of f(x) is restricted to the domain x ≥ 1, since this is when \(x^2\) − 2x + 1 is always greater than 0.

The inverse of a function f(x) is a function that "undoes" f(x). In order to find the inverse of a function, the domain of the function must first be identified. This is done by solving f(x) = 0 and determining which values of x make the equation equal to 0.In the case of f(x) =\(x^2\) − 2x + 1, the equation is equal to 0 when x = 1. This means that the inverse of f(x) is restricted to the domain x ≥ 1, since this is when \(x^2\) − 2x + 1 is always greater than 0.Once the domain of the function is restricted, the inverse function can be found by switching the x and y values, and solving for the new equation. This process can be used to find the inverse of any function, as long as the domain is appropriately restricted.

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Answer:

part a) y

-9=0.4(x-14.5)

part b) slope= 0.4

part c) 3.2 meters

final answer is y=0.4x+3.2( slope-intercept )

Step-by-step explanation:

hope that help :)

The equation of the model given written in point slope form is :

Final elevation = 50 m

Using the information given :

9 meter = 14.5 seconds - - - - (1)

20 meter = 42 seconds - - - - (2)

(20 - 9)meters = (42 - 14.5) seconds

11 meters = 27.5 seconds

Speed = 11 / 27.5

Speed = 0.4 meters per second

The equation in point slope form can be represented thus :

The initial velocity :

At y = 9 meters ; x = 14.5 seconds ; c = initial elevation

y = 0.4x + c

9 = 0.4(14.5) + c

9 = 5.8 + c

c = 9 - 5.8

c = 3.2 m

In point - slope form, the equation can be written as :

Therefore, the equation of the model written in point - slope form is : y - 9 = 0.4(x - 14.5)

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Answer:

8x+4x+9x

Step-by-step explanation:

Finding the perimeter is just adding the sides

to find the area you multiply instead

Answer:

the perimeter of the triangle is 21

Step-by-step explanation:

P=a+b+c=4+8+9=21

BRAINLIEST

Answer:

B. 183

Step-by-step explanation:

m<L = (1/2)[m(arc)KN - m(arc)KM)]

35 = (1/2)(177x - 107x)

70 = 70x

x = 1

m(arc)KN = 177x = 177

m(arc)NMK = 360 - m(arc)KN

m(arc)MNK = 360 - 177

m(arc)MNK = 183