Rewrite the following expression using the division symbol and as a fraction: The quotient of m and 11.

The height of the nearby lemon tree is 8 feet using the property of similar triangles.

Triangles that are similar to one another in shape but differ in size are called similar triangles. Their respective sides are proportional to one another, and their corresponding angles are equal. The ratio of the corresponding sides of two triangles that are comparable is constant across all pairs of corresponding sides. Problems involving unknown lengths or heights in comparable forms can be resolved using this attribute.

The given situation represent two proportional triangles.

We know that the ratio of lengths of similar triangles are equal thus,

height of plum tree / length of plum tree's shadow = height of lemon tree / length of lemon tree's shadow

Substituting the values we have:

12 / 9 = height of lemon tree / 6

Using cross multiplication:

height of lemon tree = 12 * 6 / 9 = 8 feet

Hence, the height of the nearby lemon tree is 8 feet using the property of similar triangles.

Learn more about similar triangles here:

https://brainly.com/question/16999451

#SPJ1

A graph of Triangle ABC after a dilation with a scale factor of 1/2 and center of dilation at D (-5, 5) is shown in the image attached below.

In Geometry, dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 1/2 centered at the point D (-5, 5) by using this mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate A, we have;

Coordinate A = (1, -1)  →  (1/2(1 - (-5)) + (-5), 1/2(-1 - 5) +5)

Coordinate A = (1, -1)  →  (1/2(6) - 5, 1/2(-6) + 5)

Coordinate A' = (-2, 2).

For coordinate B, we have;

Coordinate B = (1, -3)  →  (1/2(1 - (-5)) + (-5), 1/3(-3 - 5) +5)

Coordinate B = (1, -3)  →  (1/2(6) - 5, 1/2(-8) + 5)

Coordinate B' = (-2, 1).

For coordinate C, we have;

Coordinate C = (3, -3)  →  (1/2(3 - (-5)) + (-5), 1/3(-3 - 5) +5)

Coordinate C = (3, -3)  →  (1/2(8) - 5, 1/2(-8) + 5)

Coordinate C' = (-1, 1).

Read more on dilation here: brainly.com/question/20482938

#SPJ1

The equation for the line of best fit for the table above is y = 0.96x + 3.8. This equation can be determined by using the least squares method, which is a mathematical procedure for finding the best fit line for a given set of data points.

The determination of something is the process of making a decision or arriving at a conclusion about it. Determining something can involve a variety of methods, such as research, observation, analysis, and experimentation. It can also involve the use of deductive reasoning, inductive reasoning, intuition, and intuition combined with logic.

This method involves finding the sum of the squares of the differences between the given y-values and the corresponding y-values of the line, and then minimizing this sum by varying the slope and y-intercept of the line. In this case, the best fit line is found to have a slope of 0.96 and a y-intercept of 3.8.

To learn more about determined

https://brainly.com/question/24255969

#SPJ1

The equation for the line of best fit for the table above is y = 0.4x + 3.8.

An equation is a mathematical statement that describes the relationship between two or more variables. Equations are written using an equal sign and can be used to solve for unknown values. For example, the equation 2x + 5 = 15 can be used to solve for x; in this case, x = 5.

This equation can be determined by using the two-point form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. The slope of the line can be determined by calculating the rise over run between the two points, which in this case is (6-5)/(7-3)
= 0.4.
The y-intercept of the line can then be determined by plugging in one of the points into the equation and solving for b,
which in this case is (5-0.4*3)
= 3.8.
Therefore, the equation for the line of best fit is y
= 0.4x + 3.8.

To learn more about equation
https://brainly.com/question/2228446
#SPJ1

Answer:

285°

Step-by-step explanation:

x + x + 2x + 2x + 40 + 2x + 10 = (5 - 2)180

8x + 50 = 540

8x = 490

x = 61.25

2x + 40 = 2(61.25) + 40 = 285

Answer:

Step-by-step explanation:

Interior angles in a pentagon equal 540°.

Simplify

x°,x°,2x°, (2x+40) and (2x+10) = 8x+50

Calculate x

8x + 50 = 540

8x = 540 - 50 = 490

x = 490/8

x = 61.25°

Calculate largest angle

2x + 40, where x = 61.25°

=162.5°

In linear equation, value of expression is -5 and 0.

What in mathematics is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.  

                                   Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

  -6d + 4a + 5c/5

1)

d = 1 , a = 1 , c = 3

=  -6d + 4a + 5c/5

= -6 * 1 + 4 * -1 + 5 * -3/5

= -6 -4 - 15/5

= -25/5

= -5

2)

 d = -10, a = -5 , c = -8

=    -6d + 4a + 5c/5

= -6 * -10 + 4 * -5 + 5 * -8/5

= 60 -20 - 40/5

 = 60-60/5

  = 0

Learn more about linear equation

brainly.com/question/11897796

#SPJ1

The absolute value of inequality representing the range of John's weight is | x - 156 | ≤ 8.

An absolute value inequality is an inequality that contains an absolute value expression. The absolute value of a number represents the distance between that number and zero on a number line.

An absolute value expression is a mathematical expression that contains an absolute value function, denoted by vertical bars around a number or expression. The absolute value of a number is its distance from zero on a number line, so an absolute value expression represents a positive number, regardless of whether the original number was positive or negative.

As per the given question,

If John weighed 156 pounds give or take 8 pounds ten years ago, then his weight could have been anywhere from 156 - 8 = 148 pounds to 156 + 8 = 164 pounds.

To write this as an absolute value inequality, we can let x represent John's weight, and use the absolute value to represent the distance from the mean weight of 156 pounds. The inequality would be:

| x - 156 | ≤ 8

This inequality says that the distance between John's weight (x) and the mean weight of 156 pounds must be less than or equal to 8 pounds. In other words, John's weight must be within 8 pounds of 156, which represents the range of possible weights he could have had ten years ago.

To know more about absolute value inequality, visit:

https://brainly.com/question/30201926

#SPJ1

The alternative hypothesis states the presence of an association between class level and IQ score. The statement "Not all the population 1Q means are the same" is incorrect as it does not indicate any association between the two variables. A more appropriate alternative hypothesis would be "At least one of the population IQ means will be different" which suggests that the population IQ means are not all the same and there is an association between class level and IQ score.
In more technical terms, the alternative hypothesis can be expressed as:
H1: μ1 ≠ μ2 ≠ μ3 ≠ μ4

where μ

is the population mean IQ score for Seniors. This statement suggests that at least one of the population means will be different.

for such more questions on alternative hypothesis

https://brainly.com/question/25263462

#SPJ11

The following equation can be used to represent the sentence:

7 + (x/4) = 5 where x stands for a number.

A straight line on a graph is represented by a linear equation. It has a constant slope and y-intercept, one or more variables, typically expressed by x and y. Several different real-world situations can be represented by linear equations, such as estimating the cost of goods based on the quantity purchased or calculating a car's distance traveled based on speed and time. Finding the value of the variable that causes the equation to be true is the first step in solving a linear equation. In mathematics, science, engineering, and economics, linear equations are frequently employed.

Learn more about linear equation here:

brainly.com/question/11897796

#SPJ1

Answer:

The exact value of the given trigonometric expression is undefined.

Step-by-step explanation:

Given trigonometric expression:

[tex]\dfrac{\cos\left(\dfrac{2 \pi}{3}\right)}{\tan\left(-\dfrac{7 \pi}{4}\right)}+\csc(\pi)[/tex]

To find the exact value of the given  trigonometric expression, begin by finding the exact values of each of the trigonometric functions in the expression

The exact value of cos(2π/3) is:

[tex]\implies \cos\left(\dfrac{2 \pi}{3}\right)=-\dfrac{1}{2}[/tex]

The exact value of tan(-7π/4) is:

[tex]\implies \tan\left(-\dfrac{7 \pi}{4}\right)=1[/tex]

Since the cosecant function is the reciprocal of the sine function, the exact value of csc(π) is:

[tex]\implies \csc (\pi)=\dfrac{1}{\sin(\pi)}=\dfrac{1}{0}=\textsf{unde\:\!fined}[/tex]

Therefore:

[tex]\begin{aligned}\implies \dfrac{\cos\left(\dfrac{2 \pi}{3}\right)}{\tan\left(-\dfrac{7 \pi}{4}\right)}+\csc(\pi)&=\dfrac{-\dfrac{1}{2}}{1}+\dfrac{1}{0}\\&=-\dfrac{1}{2}+\dfrac{1}{0}\\\\&=\textsf{unde\:\!fined}\end{aligned}[/tex]

The work done is 3750 Joules on the box.

To quantitatively express this concept, the work W is equal to the force f times the distance d, or W = fd. If the force is applied at an angle to the displacement, the work is W = fd cos.t.

The equation W = F * d * cos(theta), where W is the work done, F is the force applied, d is the displacement of the item, and theta is the angle between the force and displacement vectors, can be used to solve this problem.

The force in this instance is 500 N, and the distance is provided as 15 m, and the 60 degree angle between the vectors of force and displacement.

So, by changing these numbers in the equation, we obtain:

W = 500 N x 15 m x cos (60 degrees)

We can simplify this to: Applying the trigonometric identity cos(60 degrees) = 1/2

W = (500 N) * (15 m) * (1/2)

W = 3750 J.

To know more about work done visit:-

https://brainly.com/question/29050812

#SPJ1

Answer:

21.93 meters.

Step-by-step explanation:

To find when the rockets are at the same height, we need to set the two functions equal to each other and solve for x:

-4.9x² + 25x = -4.9x² + 16x + 15

Simplifying this equation, we get:

9x = 15

x = 15/9

x ≈ 1.67

Therefore, the rockets are at the same height after approximately 1.67 seconds.

To find the height at which the rockets are at the same height, we can plug this value of x into either of the two functions. Let's use Buffy's function:

f(1.67) = -4.9(1.67)² + 25(1.67)

f(1.67) ≈ 21.93

Therefore, the height at which the rockets are at the same height is approximately 21.93 meters. Rounded to the nearest hundredth, this is 21.93 meters.

The analysis of the data to obtain the confidence interval of the difference in the means indicates;

99% confidence interval for [tex]\bar x[/tex]₁ - [tex]\bar x[/tex]₂

The correct options are;

Name of Procedure

Random

10%

Normal/Large Sample

99% CI = (-0.302, 2.301)

Conclude;

We are 99% confident that the interval give in the previous step captures -0.301 to 2.301 = the true difference in mean heart height for all subject like these who listen to love songs versus classical music.

A confidence interval is a range of value that is likely to contain the true value of a population parameter with a certain degree of confidence.

The two-sample t-test can be used to construct the 99% confidence interval as follows;

([tex]\bar x[/tex]₂ - [tex]\bar x[/tex]₁) ± t(α/2, df) × √(s₁²/n₁ + s₂²/n₂)

Where;

[tex]\bar x[/tex]₂ and [tex]\bar x[/tex]₁ = The sample means of the love song and classical music groups

s₁, and s₂ = The sample standard deviations

n₁ and n₂ = The sample sizes

df = The degrees of freedom

t(α/2, df) = The value from the t-distribution table with a significance level of 0.01 and df = n₁ + n₂ - 2

The data indicates;

n₁ = n₂ = 15

[tex]\bar x[/tex]₁ = 5.07, s₁ = 1.63

[tex]\bar x[/tex]₂ = 4.07, s₂ = 1.13

Therefore, we get;

([tex]\bar x[/tex]₂ - [tex]\bar x[/tex]₁) ± t(α/2, df) × √(s₁²/n₁ + s₂²/n₂)

= (5.07 - 4.07) ± t(0.005, 28) × √(1.62²/15 + 1.13²/15)

= 1 ± 2.763 × 0.469

= 1 ± 1.301

The 99% confidence interval for the difference in the true mean heart for subjects who listen to a love song versus classical music is; (-0.301, 2.301).

The correct statement is; 99% confidence interval for [tex]\bar x[/tex]₁ - [tex]\bar x[/tex]₂

The correct statements, placed in the box are;

Name of Procedure;

Two sample interval for [tex]\bar x[/tex]₁ - [tex]\bar x[/tex]₂

Random

The volunteers are randomly selected

The random condition is met

We have a random sample of 15 subjects who listen to a love song

We have a random sample of 15 subjects who listen to classical music

10%

The 10% condition is met

15 < 10% of all subjects like these who listen to love songs

15 < 10% of all subjects like these  who listen to classical music

Normal/Large Sample

The Normal/Large condition is met

The stemplot of the classical music sample data shows no strong skewness or outliers

The stemplot of the love song music sample data shows no strong skewness or outliers

Therefore;

99% CI = (-0.301, 2.301)

Conclude;

We are 99% confident that the interval given in the previous step captures -0.301 to 2.301 = the true difference in mean heart height for all subject like these who listen to love songs versus classical music.

Learn more on the confidence intervals of population parameters here: https://brainly.com/question/29911447

#SPJ1

Answer:

7/12 pizzas have been eaten

Step-by-step explanation:

3 + 4= 7

7/12

7-12=5

5 pizzas left

Therefore , the solution of the given problem of area comes out to be the area of the resulting picture is therefore 28 units.

By calculating how much space would be needed to fully cover its exterior, its overall size can be calculated. The neighboring area is considered when selecting a comparable item for a rectangular design. The surface area of something determines its overall dimensions. The number of sides between a cuboid four trapezoidal curves determines how much water it can hold.

Here,

The following algorithm determines the area of a parallelogram:

=> Base area * height

We can write: given that the trapezoid RKMT has an area of 343 units2,

=>  Base(RKMT) x Height(RKMT) = Area(RKMT) = 343

All of the parallelogram's linear measurements (lengths and widths) are multiplied by 2/7 when it is dilated by a scale factor of 2/7. As a result, the expanded parallelogram's base and height will be as follows:

=>  base(dilated) equals base x (2/7)(RKMT)

=>  Height(dilated) = Height * (2/7)(RKMT)

The dilated parallelogram's size will be as follows:

=> Area(dilated) = base(dilated) x height(dilated)

=>  (2/7) x base(RKMT) x (2/7) x height(RKMT)

=>  (4/49) x Area(RKMT)

=> (4/49) x 343

=> 28

The area of the resulting picture is therefore 28 units2.

To know more about area visit:

https://brainly.com/question/2835293

#SPJ1

Answer: 37.85

Step-by-step explanation:

Substitute: 3.2x0.2+6.1^2

Calculate the product or quotient: 0.64+6.1^2

Calculate the power: 0.64+37.21

Calculate the sum or difference: 37.85

Answer:  37.85

pls mark brainliest

Answer:

Were sorry! Answer is not available right now check in later.

Step-by-step explanation:

If Lainey bought a set of 20 markers for $6, then the cost of one marker is $0.30.

To determine the cost of 1 marker, we need to divide the total cost of the set of markers by the number of markers in the set.

Lainey bought a set of 20 markers for $6, so the cost of the set is $6. To find the cost of 1 marker, we divide the cost of the set by the number of markers in the set:

Cost of 1 marker = Total cost of set / Number of markers in set

Cost of 1 marker = $6 / 20

Cost of 1 marker = $0.30

Therefore, the cost of 1 marker is $0.30.

In summary, to determine the cost of 1 item in a set, we divide the total cost of the set by the number of items in the set. In this case, Lainey bought a set of 20 markers for $6, so the cost of 1 marker is $0.30.

To learn more about cost click on,

https://brainly.com/question/15339820

#SPJ4

Complete question is:

Lainey bought a set of 20 markers for $6. What is the cost of 1 marker?  

We have shown that KLMN has four congruent sides and opposite sides are parallel and perpendicular, which makes KLMN a square.

What is a graph?

A diagram (such as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables.

To determine if KLMN is a square, we need to check if all four sides are congruent and if opposite angles are congruent.

We can find the length of each side using the distance formula:

KL = sqrt((10 - 6)^2 + (-5 - 0)^2) = sqrt(16 + 25) = sqrt(41)

LM = sqrt((5 - 10)^2 + (-9 - (-5))^2) = sqrt(25 + 16) = sqrt(41)

MN = sqrt((1 - 5)^2 + (-4 - (-9))^2) = sqrt(16 + 25) = sqrt(41)

NK = sqrt((6 - 1)^2 + (0 - (-4))^2) = sqrt(25 + 16) = sqrt(41)

So all four sides have the same length of sqrt(41), which is a necessary condition for a square.

To check if opposite angles are congruent, we can find the slope of each pair of opposite sides:

slope KL = (-5 - 0)/(10 - 6) = -5/4

slope MN = (-4 - (-9))/(1 - 5) = 5/4

slope LM = (-9 - (-5))/(5 - 10) = -4/5

slope NK = (0 - (-4))/(6 - 1) = 4/5

We can see that the slopes of KL and MN are negative reciprocals, as are the slopes of LM and NK. This means that opposite sides are parallel and perpendicular, respectively, which is another necessary condition for a square.

Learn more about graphs on:

https://brainly.com/question/19040584

#SPJ1

We have demonstrated that KLMN is a square since it has four congruent sides and opposite sides that are parallel and perpendicular.

What is graph?

A visual representation of the variation of one variable with relation to one or more other variables, such as a collection of dots, lines, line segments, curves, or regions.

To determine if KLMN is a square, we need to check if all four sides are congruent and if opposite angles are congruent.

We can find the length of each side using the distance formula:

KL = sqrt((10 - 6)² + (-5 - 0)²) = sqrt(16 + 25) = sqrt(41)

LM = sqrt((5 - 10)² + (-9 - (-5))²) = sqrt(25 + 16) = sqrt(41)

MN = sqrt((1 - 5)² + (-4 - (-9))²) = sqrt(16 + 25) = sqrt(41)

NK = sqrt((6 - 1)² + (0 - (-4))²) = sqrt(25 + 16) = sqrt(41)

So all four sides have the same length of sqrt(41), which is a necessary condition for a square.

To check if opposite angles are congruent, we can find the slope of each pair of opposite sides:

slope KL = (-5 - 0)/(10 - 6) = -5/4

slope MN = (-4 - (-9))/(1 - 5) = 5/4

slope LM = (-9 - (-5))/(5 - 10) = -4/5

slope NK = (0 - (-4))/(6 - 1) = 4/5

We can observe that the slopes of KL, MN, LM, and NK are all negative reciprocals. Another prerequisite for a square is that the opposing sides must be parallel and perpendicular, respectively.

Learn more about graphs on:

brainly.com/question/19040584

#SPJ1

we have

13x+6y=−30------------- > 6y=-30-13x--------------- > y=(-30-13x)/6

x−2y=−4-- > 2y=x+4-------- > y=(x+4)/2

Using a graphing tool---------- > see attached figure

the solution of the system is the point (-2.625,0688)

the best estimate pair for the solution to the system is (−2.5, 0.75)

Step-by-step explanation:

1)561

2)5

3)40

4)90

5)3

6)500

7)200

8)100

9)5

10)50

Answer:

x = 6

Step-by-step explanation:

given a line parallel to a side of a triangle and it intersects the other two sides, it divides those sides proportionally , that is

[tex]\frac{x}{x+3}[/tex] = [tex]\frac{8}{12}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )

3x = 2(x + 3)

3x = 2x + 6 ( subtract 2x from both sides )

x = 6

The equation representing the relationship between dy/dt and dx/dt that is rate at which the length of the woman's shadow is changing is equal to option C. dy/dt =4× (dx/dt).

Woman is walking towards the street lamp.

Rate at which the length of her shadow is changing as she walks.

Let us consider the height of the street lamp as h = 20 feet.

Height of the woman be w = 5 feet.

And the distance between the woman and the street lamp be x.

Length of the woman's shadow be y.

Triangles formed by the woman, the street lamp, and their shadows are similar.

Sides of similar triangles are in proportion,

This implies,

h / y = (h + w) / (x + y)

Solving for y we get,

⇒h(x + y) = y(h + w)

⇒hx + hy = hy + wy

⇒y = hx / w

Rate at which the length of the woman's shadow is changing by differentiating both sides of this equation with respect to time,

⇒ dy/dt = h(dx/dt) / w

Substitute in the values for dx/dt = 3 ft/s, h and w we get,

⇒dy/dt = (20)(3) / 5

⇒dy/dt = 60 /5

⇒dy/dt =12

⇒dy/dt = 4(3)

⇒dy/dt =4× (dx/dt)

Therefore, the rate at which the length of the woman's shadow is changing is given by option C. dy/dt =4× (dx/dt) .

learn more about length here

brainly.com/question/29292459

#SPJ4

In Python, to calculate FV (Future Value), you can use the following formula: "FV = PV * (1 + r) ^ n" Here, PV = Present Value, r = interest rate, and n = number of periods. There are different ways to implement this formula in Python, but one possible way is using a function.

Here is an example: function fv(pv, r, n): return pv * (1 + r) ** n

The function takes three arguments: pv, r, and n. Then it returns the future value computed with the formula. In your Python code, you can call the function and pass the required values. For example fv_result = fv(1000, 0.05, 10)print(fv_result)The output will be the future value of $1000 after 10 years with a 5% annual interest rate.

For more such questions on Python

https://brainly.com/question/30349021

#SPJ11

Answer:

x = -13/7

y = 54/7

Step-by-step explanation:

Y = 5x + 17                          Y = -2x + 4

5x + 17 = -2x + 4

7x + 17 = 4

7x = -13

x = -13/7

Not put -13/7 in for x and solve for y

y = 5(-13/7) + 17

y = 54/7

So, the answer is x = -13/7 and y = 54/7

Answer:   x = -13 / 7, y = 54/7

Step-by-step explanation:

To eliminate a variable, we can substitute y for 5x + 17

We get 5x + 17 = -2x + 4

7x = -13

x = -13 / 7

Substituting x into the 2nd equation y = 5 * -13 / 7 + 17

y = 119/7 - 65/7

y = 54/7

The radius of the cylinder is r = 13 cm

The radius of a cylinder is the radius of the circular base of the cylinder.

Since the volume of a cylinder is 15, 919.8 cm³. If the height is 30 cm, we require it radius.

Using the formula for volume of a cylinder V = πr²h where

Making r subject of the formula, we have that

r = √V/πh

Since

Substituting the values of the variables into the equation for the radius, we have that

r = √V/πh

r = √(15,919.8 cm³/[3.142 × 30 cm])

r = √(15,919.8 cm³/94.26 cm)

r = √168.8924 cm²

r = 12.995 cm

r ≅ 13 cm

So, the radius r = 13 cm

Learn more about radius of cylinder here:

https://brainly.com/question/30986751

#SPJ1

a. The exact value of the sum of -12 + 4 – 4/3 +4/9 – 4/27 +4/81 - … = -12/(1+1/3)  is 12/7.

b.The exact value of the sum of∑ (1/3)ⁿ = 6*1/3⁶(1/3¹¹-1)/(1/3-1)  is 3/2.

A.-12 + 4 – 4/3 +4/9 – 4/27 +4/81 - …

This is an infinite geometric series with first term a = -12 and common ratio r = 4/(-3). The sum of an infinite geometric series is given by:

S = a / (1 - r)

Substituting the values of a and r, we get:

S = (-12) / [1 - (4/(-3))]

Simplify the denominator by multiplying both numerator and denominator by (-3):

S = (-12) / [-3 - 4]

S = (-12) / (-7)

S = 12/7

Therefore, the exact value of the sum is 12/7.

B. 6*1/3⁶(1/3¹¹-1)/(1/3-1)

This is a geometric series with first term a = 1 and common ratio r = 1/3. The sum of a geometric series with n terms is given by:

S = a (1 - rⁿ) / (1 - r)

As n approaches infinity, rⁿ approaches zero and the sum converges to:

S = a / (1 - r)

Substituting the values of a and r, we get:

S = 1 / (1 - 1/3)

S = 3/2

Therefore, an expression that gives the exact value of the sum is 3/2.

Learn  more about value at https://brainly.com/question/1446179

#SPJ11

Answer: 3

Step-by-step explanation:

3rd, lands on a vowel.

Answer: The spinner lands on a vowel.

Step-by-step explanation:

Probability to land on purple section: 1/10

Probability to land on letter D: 1/10

Probability to land on vowel: 3/10 (A, E, I)

Probability to land on red section: 2/10

3/10 > 2/10 > 1/10

ABCD is a parallelogram,

a) Expression of FD in terms of m and n is equals to vector FD = ( 1/2)(m + n).

b) The value of k is equals to the 2n/(n - 2m).

According to the Parallelogram law of vector addition, if two vectors vector a and vector b represent two sides of a parallelogram in magnitude and direction, then their sum vector a + vector b = the diagonal of the parallelogram through their common point in magnitude and direction. We have a parallelogram ABCD, where vector AB

= m and vector BC = n. Point F is the midpoint of the line BD. Using the Parallelogram law, vector AB + vector BC

= vector BD = m + n

a)As we know, mid point F divides the diagonal BD into two equal parts FD, and DB. So, the expression of vector FD is

vector FD = ( 1/2) vector BD

=> vector FD = ( 1/2)(m + n)

b)Now, ADE is a straight line with AD: DE = k : 1

and vector FE = 2n - (1/2)m

vector FA = vector FD = n/2 + m/2

vector AE + vector FA = vector FE

=> vector AE = 3n/2 - m

AD : DE = k : 1 so k = 2n/(n - 2m). Hence, required value is 2n/(n - 2m).

To learn more about parallelogrm, visit :

https://brainly.com/question/20526916

#SPJ4

Complete question:

ABCD is a parallelogram where AB = m and BĆ = n В. с F is the midpoint of the line BD. a) Express FD in terms of m and n. FD = m A D E is the point such that ADE is a straight line with AD: DE = k:1 and FÈ = = 2n m b) Find the value of k. Note: Please make sure your final answer says k... Mina Minute Harian hand Question Progress.