I need the simplified form

The shortest path from a vertex to the opposite side is an altitude, but the designer used a median. The foundation should be located at the orthocentre.

In order to obtain the shortest side, they actually want the shortest pathways from each side to the opposing vertex, as seen in the triangle below, which shows the medians drawn from each angle to the middle of the opposite side.

In its place, you would draw a straight line the shortest distance from the vertex to the opposite side, add a perpendicular, and then do the same thing here, draw a straight line out of a perpendicular, and then pulled down it, a perpendicular; this center, where they all come together, is referred to as the ortho center. In order to respond to the query, I will say that the point of concurrency would be the shortest route from the vertex to the opposite. Go precisely across to the side.

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A. Prospective observational studies involve collecting data from participants before an event or outcome occurs, while retrospective observational studies collect data after the event has already taken place.

A prospective observational study is a type of observational study that involves collecting data from participants before an event or outcome occurs. This type of study is used to predict and measure outcomes in the future.

In this type of study, the researcher can control the variables, such as when and how the data is collected, and can also observe the effects of any changes in the environment.

On the other hand, a retrospective observational study is a type of observational study that involves collecting data after an event or outcome has already taken place. This type of study is used to study the causes of a given outcome.

In this type of study, the researcher looks back in time and collects data from the past. This type of study is more limited than a prospective observational study, since the researcher cannot control the variables of the study or observe any changes in the environment.

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Answer:

yES, THIS IS CORRECT THE ANSWER IS 2

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

[tex]f(3)[/tex] represents the value of [tex]f(x)[/tex] when [tex]x=3[/tex].

[tex]f(3)=2+3(3)^2=29[/tex]

Answer:

 [tex]x=-\frac{3}{2}\\[/tex]

Step-by-step explanation:

We must isolate x in this equation. To do that, we can multiply both sides by [tex]\frac{3}{2}[/tex].

[tex](\frac{3}{2})(\frac{2}{3})x=-1(\frac{3}{2})[/tex]

[tex]x=-\frac{3}{2}[/tex]

The derivative of the function is

A) dw/dz=z^5 (7z-18)

B) dh/dx=192x^11+36x^5-6x^2+19

C) dy/dx=24x^2-38x-15

In mathematics, the derivative of a function measures the sensitivity to change of the function value with respect to a change in its argument. It is the rate of change of a function with respect to a variable.

A) w = z^7 – 3z^6 + 14

dw/dz=7z^6-18z^5

dw/dz=z^5 (7z-18)

B) h(x) = 16x^12 + 6x^6 – 2x^3 + 19x – 7

dh/dx=192x^11+36x^5-6x^2+19

C) y = (8x + 5)(x^2 – 3x)

dy/dx=  d/dx  [8x+5]*〖(x〗^2-3x)+(8x+5)*d/dx[x^2-3x]

dy/dx=(8*  d/dx  [x}+d/dx[5])*〖(x〗^2-3x)+(8x+5)*(d/dx[x^2]-3 d/dx[x])

dy/dx=(8*1+0)(x^2-3x)+(8x+5)(2x-3*1)

dy/dx=8(x^2-3x)+(2x-3)(8x+5)

dy/dx=24x^2-38x-15

Note: The question is incomplete. The complete question probably is: Find the derivative of the following function: A) w = z^7 – 3z^6 + 14 B) h(x) = 16x^12 + 6x^6 – 2x^3 + 19x – 7 C) y = (8x + 5)(x^2 – 3x).

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The value of each part is AC = 18 cm, CD = 54 cm, DE = 108 cm, and

EB = 72 cm.

A collection of numbers and operations is an expression in mathematics. The following are the parts of a math expression that do a math operation:

Operands: Operands are the numbers that an operation uses. The terms that are given to the operands vary according to the kind of operation.

Operator: An operator is the symbol that denotes a math operation, such as: division, addition, subtraction, and multiplication.

Given length of wooden plank AB is 252 cm

divides it into four parts by inserting the points C, D and E

parts of plank are AC, CD, DE, EB

CD = 3AC,

DE = 2CD, and DE = 2(3AC) = 6AC

EB = 4AC

AB = AC + CD + DE + EB

substitute the values,

AB = AC + 3AC + 6AC + 4AC

252 = 14AC

AC = 252/14 = 18cm

CD = 3AC = 3(18) = 54 cm

DE = 6AC = 6(18) = 108 cm

EB = 4AC = 4(18) = 72 cm

Hence length of each part is AC = 18 cm, CD = 54 cm, DE = 108 cm, and

EB = 72 cm.

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a) The data modeling in this problem is an exponential function.

b) The function is defined as follows: y = 1.5(2)^x.

c) The rate of change from x = 2 to x = 4 is of 4.

The general format for an exponential function is presented as follows:

y = a(b)^x.

For which the parameters are given as follows:

From the data, when x increases by one, the output y is multiplied by two, hence the rate of change is given as follows:

b = 2.

Hence, when x increases by two, as is the case from x = 2 to x = 4, the rate of change is given as follows:

b² = 2² = 4.

When x = 1, y = 3, hence, applying the recursion of the rate of change, the parameter a is given as follows:

a = 3/2 = 1.5.

Meaning that the function is defined as follows:

y = 1.5(2)^x.

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The correct statement regarding the proportion is given as follows:

Both Kurt and Maria are right, because 3,585 should be rounded up to 3,600, and 21% of this amount can be approximated by either finding 10% of 3,600 and multiplying the result by 2 or by finding One-fifth of 3,600.

A proportion is a fraction of a total amount.

The total amount is of 3585, and 21% of the goal has been reached, hence the amount reached is obtained as follows:

0.21 x 3585 = $752.85.

Both Kurt or Maria took different routes, rounding the amount to 3600, and then obtaining 20% of it, which is equivalent to one-fifth. 20% can also be obtained as twice of 10%, hence both are correct, and the fourth statement is correct.

The missing text is given as follows:

Kurt and Maria’s high school is having a newspaper drive.The goal is to collect 3,585 pounds of newspapers. So far, 21% of the goal has been reached.

Kurt estimated the number of pounds of newspapers collected by finding 10% of 3,600 and then multiplying the result by 2.

Maria estimated the number of pounds of newspapers collected by finding One-fifth of 3,600.

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There were 10 different combinations to the multiple choice questions.

Combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” The combination means “Selection of things”, where the order of things has no importance.

It is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.

[tex]C_{n,r} = \frac{n!}{(n-r)! r!}[/tex]

where n = 5

r = 3

[tex]C_{5,3} = \frac{5!}{(5-3)!3!} \\= \frac{5!}{2!3!}[/tex]

= [tex]\frac{5(4)(3!)}{2!3!}[/tex]

= 20/2

= 10 ways

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The tangent function is a trigonometric function used to calculate angles and the relationships between them.

This function is also known as the “slope of a curve” and measures the rate of change of the angle with respect to the x-axis. In its most basic form, the tangent function is expressed as tanθ, which is interpreted as the ratio between the length of the opposite side of angle θ and the length of the adjacent side. The graph of the tangent function is a periodic curve with a range of [-π/2,π/2]. It has many uses in mathematics and physics, such as the calculation of derivatives, integration, and interpolation.

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The simplification of the expression −5.55− 8.55c+ 4.35c by combining the like terms is - 5.55 - 4.20c.

Like terms can be defined as terms which has the same variable and power.

For instance,

4a + 5a²

They are not like terms, though they have the same variable a but different power of 1 and 2 respectively.

So,

−5.55− 8.55c+ 4.35c

The like terms are - 8.55c and + 4.35c

−5.55− 8.55c+ 4.35c

= - 5.55 - 4.20c

Consequently, - 5.55 - 4.20c is the simplification of −5.55− 8.55c+ 4.35c.

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Answer:

Step-by-step explanation:

The coordinates of point R are (5.17, 7.33), which is answer choice C.

To find the coordinates of point R, we can use the formula for finding the coordinates of a point that divides a line segment into a given ratio:

R = [(1 - ratio) * A + ratio * B] / (1 + ratio)

In this case, the ratio is 1 : 5, which means that point R divides the line segment EF into a ratio of 1 : 5. The coordinates of points E and F are (4, 8) and (11, 4), respectively. Plugging these values into the formula, we get:

R = [(1 - (1/6)) * (4, 8) + (1/6) * (11, 4)] / (1 + (1/6))

= [(5/6) * (4, 8) + (1/6) * (11, 4)] / (6/6)

= [(20/6, 40/6) + (11/6, 4/6)] / (6/6)

= [(20/6 + 11/6, 40/6 + 4/6)] / (6/6)

= [(31/6, 44/6)] / (6/6)

= [(31/6)/(6/6), (44/6)/(6/6)]

= (31/6, 44/6)

= (5.17, 7.33)

Thus, the coordinates of point R are (5.17, 7.33), which is answer choice C.

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The coordinates of point r to be (5.17, 7.33) which is in option c.

To calculate the coordinates of point r, we must first determine the length of each section of the line segment. To do this, we can use the distance formula. The distance formula is given by d = √( (x2-x1)^2 + (y2-y1)^2 ). Using this formula, we can calculate the length of the line segment connecting points e and f to be 7 units.

We can then use the ratio of 1:5 to calculate the length of each segment. The length of the section starting at e is 1/6 of the total distance (7 units). The length of the section starting at f is 5/6 of the total distance (7 units).

To find the coordinates of point r, we can use the midpoint formula. The midpoint formula is given by (x, y) = ( (x1 + x2)/2, (y1 + y2)/2 ). Using this formula, we can calculate the coordinates of point r to be (5.17, 7.33). Therefore, the correct answer is c. (5.17, 7.33).

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To evaluate an integral by interpreting it in terms of area, one should first sketch the region indicated by the integrand and limits of integration. Once the region is visualized, the integral can be thought of as the total area under the curve of the integrand within the given limits. If the integrand is a sum, the integral is the sum of the areas under each individual curve, provided they exist.

To evaluating an integral by interpreting it in terms of area is a powerful technique that allows you to visualize the problem and understand the meaning of the integral. By sketching the region indicated by the integrand and limits of integration, you can gain a better understanding of what the integral represents. The integrand is the function whose area is being calculated, and the limits of integration are the boundaries of the region over which the integral is being taken. The integral can be thought of as the total area under the curve of the integrand within the given limits.

For example, consider the definite integral of a function f(x) between the limits of a and b. This integral represents the area between the curve of the function f(x) and the x-axis, between the values of x = a and x = b. By sketching this region, you can visualize the area being calculated and understand the meaning of the integral. It's also important to note that when the integrand is a sum, the integral is the sum of the areas under each individual curve, provided they exist. This allows you to break down a complex function into simpler parts and evaluate them separately.

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Seating arrangements that can be made, if rotations and reflections of each seating arrangement are not considered different is 24.

The combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” The combination means “Selection of things”, where the order of things has no importance.

Total number of couples = 3

No. of seating in Circular table = 8

Total number of ways they can be seated =3*8 = 24

Thus, Seating arrangements that can be made, if rotations and reflections of each seating arrangement are not considered different is 24.

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The number of possible arrangements he can make = 24

Assume that George and his wife seated opposite to each other.

Then there would be six open seats for three other couples.

The first woman of them can be seated in six ways.

Using combination formula, we can write it as

6C1 = 6

And her husband sits opposite to her.

Now the next woman can be seated in six ways.

Using combination formula, we can write this as

4C1 = 4

And her husband sits opposite to her.

Now the last woman can be take any seat from the remaning 2 seats and her husband sits opposite to her.

Since rotations and reflections of each seating arrangement are not considered different, there are 6 × 4 = 24 possible seating arrangements.

Therefore, there would be 24 possible seating arrangements.

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All the possible values of each expression is given as an inequality as;

0 < a - b < 4

We are given the inequalities of the domain and range as;

2 < a < 5

1 < b < 2

Thus, we can say that the maximum value of a - b will be the difference between the maximum value of a and the minimum value of b to give;

(a - b)max = 5 - 1

(a - b)max = 4

Similarly, minimum value of a - b will be the difference between the maximum value of b and the minimum value of a to give;

(a - b)min = 2 - 2

(a - b)min = 0

Thus, all possible values would be expressed as;

0 < a - b < 4

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Answer: Daren

Step-by-step explanation:

The rate for Daren is 8.55 kph, while Umberto is 9.5 kph.

Find the total miles for Daren and Umberto:

8,55 x 3,5 = 29,925

9,5 x 3 = 28,5

Daren will run more kilometers than Umberto because the distance running is more than Umberto's.

The interpretation that the likelihood that the first question will be true is (a) Likely

From the question, we have the following parameters that can be used in our computation:

Probability value

The value of the probability and the notation is given as

P(true) = 0.8

As a general rule of probability, we have

Using the above as a guide, we have the following:

The value of P(true) = 0.8 is greater than 0.5

This that the probability is likely

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Answer: A its that easy

Step-by-step explanation:

The property that will be used to solve the equation given, is the Division Property of Equality.

According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0.

An example is:

6 / 3 = 6 / 3

2 = 2

This means that to find the value of x in -5x = 15, the Division Property of Equality, allows us to divide both sides by - 5:

- 5 x / - 5 = 15 / - 5

x = - 3

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The statement which is true about the two functions include the following: A. Function B has a greater rate of change.

In Mathematics, the rate of change is sometimes referred to as slope or gradient and it can be calculated by using this formula;

Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change, m = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the rate of change of the value of y with respect to the value of x in function B, which represents a line that is passing through the data points (3, 3) and (6, 13):

Rate of change, m = (13 - 3)/(6 - 3)

Rate of change, m = 10/3 or 3.33.

From function A (y = 3x - 6), we can logically deduce that the rate of change is equal to 3.

In conclusion, we can logically deduce that the rate of change of function B (m = 3.33) is greater than the rate of change of function A (m = 3).

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Answer:

X/3 < -9

(x/3) 3 < -9(3)

x < -27

Step-by-step explanation:

Using the provided values and making an equivalent equation and equating the equation to solve for the number of books required to break even, The answer is 97 books should be produced and sold.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.

There are three ways to solve systems of linear equations :

required equation,

10300 + 12x = 118.25x

solving for x , we get,

106.25x = 10300

x=10300/106.25

=97

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The side length of PQ = 5.6 unit and angle C = arc sin [sin A (0.70)]

The mathematical law that shows the relationship between the size of an angle and opposite side length of a triangle is called sine rule. It is an equation that express the ratio of the side length of a triangle to the sine of the opposite angle.

The laws can be shown as

a/ sin A = b /sin B = c /sin C

Given, triangle ABC ≈ triangle PQR

for the triangle PQR, PR = 8

angle Q = 63 degrees

angle R = 38.5 degrees

we need to determine the length PQ

as per the sine rule for triangle PQR

PQ/ sin R = PR / sin Q

PQ = PR × sin R / sin Q

PQ = (8 × sin 38.5) / sin 63

PQ = 5.59

PQ = 5.6 unit

As triangle ABC ≈ triangle PQR

AB/PQ = BC/PR = AC / QR

and sin A / sin Q = sin B/ sin P = sin C /sin R

sin C = (sin A / sin Q) × sin R

sin C = sin A (0.70)

C = arc sin [sin A (0.70]

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Answer:

7.35 miles

Step-by-step explanation:

Example: [tex]\frac{66}{6} = 11[/tex]

Given 1 week = 7 days.

Given the athlete has ran 8.5 miles on Sunday, the remaining distance to run is:

[tex]52.6-8.5\\=44.1 miles[/tex]

Distance to run each day for the remaining 6 days is:

[tex]\frac{44.1}{6} \\=7.35 miles[/tex]

First, we will solve the equation of the hyperbola for y:

9x^2 - 4y^2 = 36

4y^2 = 9x^2 - 36

y^2 = (9/4)x^2 - 9

y = ±√((9/4)x^2 - 9)

In math, what is a parabola?

Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve.

We only need to consider the right half of the hyperbola because of the symmetry,

the line x=3 is the vertical asymptote of the hyperbola, so we need to find the y-coordinates of the hyperbola when x=3

y = ±√((9/4)3^2 - 9)

y = ±√(9/49 - 9)

y = ±√(27 - 9)

y = ±√18

The area of the region is given by the definite integral of y with respect to x between the limits of x = 3 and x = infinity.

∫y dx = ∫√18 dx = 3/2 * √18 * x^(3/2) from 3 to infinity

The area of the region is infinite as the integral is evaluated from x = 3 to infinity.

It's important to note that the method of evaluating the definite integral is not valid in this case as the integral is of an improper kind and it does not converge to a finite value.

It's impossible to draw a reference rectangle for this problem as the area of the region is infinite.

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Step-by-step explanation:

(6 - W)/(10+10)= (6 - W)/20= 2

6 - W= 40

-W= 34

W= -34

Answer:

line can be described by the equation y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.

Since we are given that the line has a slope of 1 and includes the point (10, 10), we can plug these values into the equation to solve for the y-intercept. We get:

10 = 1 * 10 + b

b = 10 - 10

b = 0

So the equation of the line is y = x + 0, or simply y = x.

Since we are also given that the line includes the point (u, 9), we can substitute this value for y in the equation of the line to solve for u. We get:

9 = x

x = 9

Therefore, the value of u is 9.

Uday Tahlan

line that includes the points (-10, W) and (10, 6) has a slope of I. What is the value of w?

Can someone please help me?

Thank you!

To find the value of W, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

Since we are given that the line includes the points (-10, W) and (10, 6) and has a slope of I, we can use these two points to find the value of W.

First, we can plug in the coordinates of one of the points and the value of the slope into the equation to solve for the y-intercept. Let's use the point (10, 6):

6 = I * 10 + b

b = 6 - 10I

Then, we can plug the values of the slope and y-intercept into the equation and solve for W using the coordinates of the other point (-10, W):

W = I * (-10) + (6 - 10I)

= -10I + 6 - 10I

= 6 - 20I

Therefore, the value of W is 6 - 20I.

Answer:

C

Step-by-step explanation:

C It makes the line become steeper. When the coefficient in front of x is increased, the slope of the line becomes larger, so the line becomes steeper. The other responses are not correct.

SSS congruence rules states that if three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

The SSS (Side-Side-Side) congruence rule states that if three sides of one triangle are equal to the three sides of another triangle, equal, and the two triangles share the same dimensions then the two triangles are congruent. This means that all of the angles and sides of the two triangles are In order for two triangles to be congruent according to the SSS congruence rule, the lengths of the three corresponding sides of the two triangles must be equal. If all three of these conditions are met, then the two triangles are congruent and can be used to solve a variety of geometric problems.

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The SSS congruence rule is rule that is used to prove two triangles congruent . Its full form is Side-Side-Side Congruence .

The Two Triangles can be called as  Congruent Triangles if their sides have same length and the angles also have the same measure.

One of the 4 rules in proving the triangles congruent is SSS .

The SSS Congruence Rules also called as (Side-Side-Side) Rule means that if all the three sides of one triangle are equal to the corresponding three sides in the other triangle ,

then we can say that the two triangles are congruent by SSS (Side-Side-Side) Rule .

Therefore , The SSS Congruence rule means Side-Side-Side Congruence .

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