perimeter and volumen, please help its important ​

The Sine, Cosine and Tangent of the angles are sin(28) = 0.4695, cos(28) = 0.8829 and tan(28) = 0.5318

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

The triangle

Where, we have

tan(28) = 21/x

This means that

x = 21/tan(28)

Evaluate

x = 39.49

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

tan(28) = 21/39.49

tan(28) = 0.5318

Also, we have

sin(28) = 21/√(39.49² + 21²)

sin(28) = 0.4695

Lastly, we have

cos(28) = 39.49/√(39.49² + 21²)

cos(28) = 0.8829

Hence, the Sine, Cosine and Tangent of the angles are sin(28) = 0.4695, cos(28) = 0.8829 and tan(28) = 0.5318

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Given statement solution is :- To find the area of the shaded region, we first need to determine the shapes involved and their respective areas.  A general process that you can apply to various scenarios, Identify the shapes , Break down the region, Calculate individual areas.

To find the area of the shaded region, we first need to determine the shapes involved and their respective areas. Without a specific diagram or description, I'll provide a general process that you can apply to various scenarios.

Identify the shapes: Examine the diagram and determine the shapes that make up the shaded region. These shapes can include rectangles, triangles, circles, or combinations of them.

Break down the region: If the shaded region consists of multiple shapes, break it down into simpler, recognizable shapes. This step is crucial for accurately calculating the total area.

Calculate individual areas: Determine the area of each shape by using the appropriate formulas. Here are some common formulas:

Rectangle: Area = length × width

Triangle: Area = (base × height) / 2

Circle: Area = π × radius²

Sum the individual areas: Add up the areas of all the individual shapes to find the total area of the shaded region.

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Answer: 600000

Step-by-step explanation: just multiply it man

Answer:

446.95m²

Step-by-step explanation:

10+9+13.45=32.5

32.5x11=356.95

9x10=90

356.95+90=446.95

Answer: it stand for 3 million or 3,000,000

Step-by-step explanation:

Answer:

million

Step-by-step explanation:

millions always have six 0's behind it

The expression 3j + 21 represents the sum of triple the number "j" and 21. It accounts for multiplying "j" by 3 and then adding 21 to the product. This equation allows us to calculate the desired sum when the specific value of "j" is known.

To find the sum of triple the number "j" and 21, we need to multiply "j" by 3 and then add 21 to the result.

Let's break it down step by step:

Multiply "j" by 3: This can be represented as 3 * j, or simply 3j.

Add 21 to the result: We take the product from step 1 (3j) and add 21 to it, resulting in 3j + 21.

In summary, the expression 3j + 21 represents the sum of triple the number "j" and 21. It accounts for multiplying "j" by 3 and then adding 21 to the product. This equation allows us to calculate the desired sum when the specific value of "j" is known.

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In a group of 7 participants, each person shakes hands with 6 other participants, resulting in a total of 42 handshakes.  To determine the number of participants that will make 45 handshakes in total, we need to find a number that satisfies the given condition. Let's assume that the number of participants is 'n.'

In a group of 'n' participants, each person shakes hands with (n-1) other participants since they don't shake hands with themselves. Therefore, the number of handshakes in a group of 'n' participants can be calculated by the formula: n x (n-1).

We need to find the value of 'n' that satisfies the equation n x (n-1) = 45.

Expanding the equation, we get [tex]n^2 - n - 45 = 0.[/tex]

By factoring or using the quadratic formula, we can solve this equation to find two possible values for 'n': n = -6 or n = 7.

Since the number of participants cannot be negative, we discard the negative solution and consider n = 7.

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A graph that represents the absolute function f(x) = |x + 4| - 3 is shown on the coordinate plane attached below.

In Mathematics and Geometry, an absolute value function is a type of function that contains an expression, which is placed within absolute value symbols, and it measures the distance of a point on the x-axis to the x-origin (0) of a graph.

By critically observing the transformed absolute value function f(x) = |x + 4| - 3, we can reasonably infer and logically deduce that the parent absolute value function g(x) = |x| was vertically shifted (translated) downward by 3 units and horizontally shifted (translated) to the left by 4 units, in order to produce it as follows;

g(x) = |x|

f(x) = |x + h| - k

f(x) = |x + 4| - 3

In conclusion, we would use an online graphing tool to plot the given absolute value function f(x) = |x + 4| - 3 as shown in the graph attached below.

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It should be noted that there will always be two people in attendance who have the same number of friends at the party using the pigeonhole principle.

The pigeonhole principle states that if you have n pigeons and m pigeonholes, and n > m, then at least one pigeonhole must contain more than one pigeon.

In this case, we have n people at the party, and there are m = n - 1 possible numbers of friends that a person can have. This is because a person can either know 0, 1, 2, ..., or n - 1 other people.

Since n > m, the pigeonhole principle tells us that at least two people at the party must have the same number of friends.

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Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

This equation can be factored as:

(2x + 5)(x - 2) = 0

Setting each factor equal to zero, we get:

2x + 5 = 0 => 2x = -5 => x = -5/2

x - 2 = 0 => x = 2

Therefore, the x-intercepts of the graph of f(x) are x = -5/2 and x = 2.

Part B: The vertex of the graph of f(x) can be determined using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c = 0).

In this case, a = 2 and b = -1. Plugging these values into the formula, we have:

x = -(-1) / (2 * 2) = 1/4

To determine if the vertex is a maximum or a minimum, we can examine the coefficient of the x² term. Since the coefficient a is positive (a = 2), the parabola opens upwards, and the vertex represents a minimum point

Therefore, the vertex of the graph of f(x) is (1/4, f(1/4)), where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Part C: To graph f(x), we can follow these steps:

Plot the x-intercepts: Plot the points (-5/2, 0) and (2, 0) on the x-axis.

Plot the vertex: Plot the point (1/4, f(1/4)) as the vertex, where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Determine the direction of the graph: Since the coefficient of the x² term is positive, the graph opens upwards from the vertex.

Determine additional points: Choose a few x-values on either side of the vertex and calculate their corresponding y-values by substituting them into the equation f(x). Plot these points on the graph.

Draw the graph: Connect the plotted points smoothly, following the shape of the parabola. Ensure the graph is symmetrical with respect to the vertex.

The answers obtained in Part A (x-intercepts) and Part B (vertex) provide crucial points to plot on the graph, helping us determine the shape and position of the parabola.

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The x-intercepts from the graph attached are

The vertex  from the graph attached is

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

x = (-b ± √(b² - 4ac)) / (2a)

a = 2, b = -1, c = -10

Plugging these values into the quadratic formula:

x = (-(-1) ± √((-1)² - 4 * 2 * (-10))) / (2 * 2)

x = (1 ± √(1 + 80)) / 4

x = (1 ± √81) / 4

x = (1 ± 9) / 4

x₁ = (1 + 9) / 4 = 10 / 4 = 2.5

x₂ = (1 - 9) / 4 = -8 / 4 = -2

Therefore, the x-intercepts of the graph of f(x) are 2.5 and -2.

Part B

To find the coordinates of the vertex, we can use the formula:

x = -b / (2a)

x = -(-1) / (2 * 2) = 1 / 4 = 0.25

we substitute this value back into the original function:

f(0.25) = 2(0.25)² - 0.25 - 10

f(0.25) = 0.125 - 0.25 - 10

f(0.25) = -10.125

Therefore, the vertex of the graph of f(x) is located at (0.25, -9.125).

Part C: The steps to graph f(x) include:

Plotting the x-intercepts: Based on the results from Part A, we know that the x-intercepts are 2.5 and -2. We mark these points on the x-axis.

Plotting the vertex: Using the coordinates from Part B, we plot the vertex at (0.25, -9.125). This represents the minimum point of the graph.

Drawing the shape of the graph: Since the coefficient of the x² term is positive, the graph opens upward. From the vertex, the graph will curve upward on both sides.

Additional points and smooth curve: To further sketch the graph, we can choose additional x-values and calculate their corresponding y-values using the equation f(x) = 2x² - x - 10. Plotting these points and connecting them smoothly will give us the shape of the graph.

By using the x-intercepts and vertex obtained in Part A and Part B, we have the necessary information to draw the graph accurately and show the key features of the quadratic function f(x)

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To create a graph, label the horizontal axis from 0 to 8 cm (1 cm = 0.5 m) and the vertical axis from 0 to 2 cm (1 cm = 500). Plot the points (2m, 400) as (4 cm, 1.6 cm) and (4m, 200) as (8 cm, 0.8 cm), then connect them with a line.

To create a graph with the provided scale, follow these steps:

1. Establish the horizontal axis: Label the axis from 0 to 8 cm, where each mark represents 1 meter. This means that 2 cm on the graph corresponds to 1 meter.

2. Set up the vertical axis: Label the axis from 0 to 2 cm, where each mark represents 500. This implies that 2 cm on the graph corresponds to 500.

3. Convert the given data points to fit the graph's scale:

For the point (2m, 400):

On the horizontal axis, 2 meters will be represented by 4 cm.

On the vertical axis, 400 will be represented by (400/500) * 2 cm = 1.6 cm.

For the point (4m, 200):

On the horizontal axis, 4 meters will be represented by 8 cm.

On the vertical axis, 200 will be represented by (200/500) * 2 cm = 0.8 cm.

4. Plot the converted points on the graph:

Place a point at (4 cm, 1.6 cm) to represent the point (2m, 400).

Place a point at (8 cm, 0.8 cm) to represent the point (4m, 200).

5. Connect the points with a line:

Draw a straight line to connect the two plotted points.

By following these steps, you will create a graph that visually displays the relationship between the given data points, adhering to the specified scale. Remember to provide appropriate titles and labels for the graph axes.

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Answer:

0.339, or approximately 33.9%

Step-by-step explanation:

We can solve this problem using Bayes' theorem. Let F denote the event that the selected student is female, and J denote the event that the selected student is taking Japanese classes. We want to find the probability of F given J, which we can write as P(F|J).

Using the law of total probability, we can decompose the probability of J as follows:

P(J) = P(J|F)P(F) + P(J|M)P(M)

where M denotes the event that the selected student is male. We can calculate the probabilities on the right-hand side of this equation as follows:

P(J|F) = 0.1 (from the problem statement)

P(F) = 0.51 (from the problem statement)

P(J|M) = 0.2 (from the problem statement)

P(M) = 0.49 (from the problem statement)

Plugging in these values, we get:

P(J) = 0.10.51 + 0.20.49 = 0.149

Now we can use Bayes' theorem to find P(F|J):

P(F|J) = P(J|F)P(F) / P(J)

Plugging in the values we calculated earlier, we get:

P(F|J) = 0.1*0.51 / 0.149 = 0.339

Therefore, the probability that the selected student is female given that they attend Japanese classes is 0.339, or approximately 33.9%.

Hope this helps!

a) The ratio of the number of large items in the store relative to the total number of items is given as follows: 2/5.

b) The percentage is given as follows: 40%.

The ratio and the percentage are obtained applying the proportions in the context of the problem.

40 out of 100 items are large items, hence the ratio is given as follows:

40/100 = 2/5.

The percentage is then given as follows:

2/5 x 100% = 40%.

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For question 3.) The three ratios for the marked angle would be =9.45:sin90°, 5:sinB, 8:sinA

For question 3.)

To determine the three ratios, the sine rule needs to be obeyed and the formula is written below as follows;

Sine rule:

a/sinA = b/sinB = c/sinC

where;

a = 8

A = sinA

b = 5

B = SinB

c = 9.45

C = Sin 90°

The three ratios;

= 9.45:sin90°; 5:sinB; 8:sinA

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The value of x is 9 cm, and angle O is 0 degrees.

To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:

(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:

LN = 12 cm

NK = 6 cm

KM = 8 cm

Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.

Using the Law of Cosines, we can write the equation for side NM (x):

x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)

We don't know the value of angle N yet, so we need to find it using the Law of Sines.

(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

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

In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.

We can write the equation for angle O:

sin(O) / 8 = sin(N) / 6

Now, let's solve these equations step by step to find the values of x and angle O.

To find angle N, we can use the Law of Sines:

sin(N) / 12 = sin(180 - N - O) / x

Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:

sin(N) / 12 = sin(O) / x

Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):

sin(N) / 12 = (6 / 8) * sin(N) / x

Now, we can solve this equation for x:

x = (12 * 6) / 8 = 9 cm

So, the value of x is 9 cm.

To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:

sin(O) / 8 = sin(N) / 6

sin(O) / 8 = sin(O) / 9

9 * sin(O) = 8 * sin(O)

sin(O) = 0

This implies that angle O is 0 degrees.

Therefore, the value of x is 9 cm, and angle O is 0 degrees.

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The figure for the given question is provided here :

Each letter should be matched to its correct term as follows;

1. A ⇔ Efficiency.

2. B ⇔ Impossible.

3. C ⇔ Inefficiency.

In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;

Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;

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The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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a.

The estimated total cost of the grocery items is $36.

b.

The actual total cost of the grocery items is $35.82.

for part a.

We will round each price to the nearest dollar:

$5.12 =  $5

$3.07 = $3

$7.11 = $7

$1.67 = $2

$13.18=  $13

$5.67 = $6

Summing them up, we have:

$5 + $3 + $7 + $2 + $13 + $6 = $36

the estimated total cost of the grocery items is $36.

for part b.

We will calculate the actual total cost of the grocery items by using a calculator:

$5.12 + $3.07 + $7.11 + $1.67 + $13.18 + $5.67 = $35.82

In conclusion, we will find the  actual total cost of the grocery items as $35.82.

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The function that expresses the cost of fencing the region: Cost(x) = 36x + 39y

Let's assume the length of the two opposite sides of the rectangular region with material costs of $18 per linear foot is x, and the length of the other two sides (including the side with material costs of $21 per linear foot) is y.

The total cost can be calculated as follows:

Cost = Cost of three sides with $18 per linear foot + Cost of the fourth side with $21 per linear foot

Since the perimeter is equal to 2 times the sum of the lengths of the two opposite sides (x), we have:

Cost of three sides = 2 * (x + y) * $18

The cost of the fourth side with $21 per linear foot is equal to the length of that side (y) multiplied by the cost per linear foot:

Cost of the fourth side = y * $21

we can express the total cost of fencing the region in terms of the length x of the two opposite sides:

Cost = 2 * (x + y) * $18 + y * $21

Simplifying this expression, we get the function that expresses the cost of fencing the region:

Cost(x) = 36x + 39y

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Answer:

To find the values of the other three angles in a pentagon given that the sum of all angles is 450 degrees and one angle is 150 degrees, we can use the fact that the sum of the angles in any polygon with n sides is (n-2) * 180 degrees.

Let's denote the other three angles as A, B, and C.

The sum of the angles in a pentagon is given as 450 degrees, so we have:

150 + A + B + C = 450

We know that the sum of the angles in a pentagon is (5-2) * 180 = 540 degrees, so we have another equation:

A + B + C = 540

Now we have a system of two equations with two variables. We can solve this system to find the values of A, B, and C.

The correct subtraction should be:

(150 + A + B + C) - (A + B + C) = 540 - 450

Simplifying the equation, we have:

This equation is not valid, which means that the values given for the sum of angles and one angle are inconsistent with a pentagon. The sum of the angles in a pentagon should be 540 degrees. Please ensure the accuracy of the provided values.

The graph has: A. order 2 rotational symmetry about the origin.

In Mathematics and Geometry, the order of rotational symmetry of any geometrical shape can be defined as the number of times in which the geometrical shape can be rotated around a full (complete) circle and still look the same.

As a general rule in geometry, a geometrical shape with number of sides (n) has "n" lines of symmetry and its order of rotational symmetry is equal to "n."

Based on this rule, we can reasonably infer and logically deduce that the order of rotational symmetry for this graph is equal to 2.

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1) sin 36 = 0.5878

cos 34 = 0.8290

tan 86 = 14.3007

2) A  = 37°

B  = 23°

C  = 2°

3) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

4) The measure of angle A is: ∠A = 39.6°

5) The length of side x is: x = 39.5 mm

The six trigonometric ratios of a right angle triangle are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

cot x = 1/tan x

sec x = 1/cos x

cosec x = 1/sin x

1) sin 36 = 0.5878

cos 34 = 0.8290

tan 86 = 14.3007

2) A = sin⁻¹0.6018 = 37°

B = cos⁻¹0.9205 = 23°

C = tan⁻¹0.0349 = 2°

3) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

4) The measure of angle A is gotten from:

∠A = cos⁻¹ (47/61)

∠A = 39.6°

5) The length of side x using trigonometric ratios is:

21/x = tan 28

x = 21/tan 28

x = 39.5 mm

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Answer: The digit in the hundreds place is 100 times greater than the digit in the hundredths place.

To understand this, consider a number like 5.253. The digit in the hundreds place is 5, while the digit in the hundredths place is 3. The value of the digit in the hundreds place (5) is 100 times greater than the value of the digit in the hundredths place (0.03).

Therefore, the correct answer is:

A: 100

You should buy approximately 1.067 kilograms of apples at $10.20 per kilogram in order to have the kilogram of fruit cost $8.15.

Let's assume that Sally bought x kilograms of apples at $10.20 per kilogram.

The total cost of bananas is given as AED 7.35 per kilogram, and Sally bought 1.4 kilograms of bananas. So, the cost of the bananas is:

Cost of bananas = AED 7.35 * 1.4 = AED 10.29

The total cost of apples is given by the equation:

Cost of apples = $10.20 * x

The total cost of the fruits combined should be AED 8.15 per kilogram. So, the equation becomes:

Total cost of fruits = (Cost of bananas + Cost of apples) / (1.4 + x) = AED 8.15

Substituting the known values, we have:

(10.29 + 10.20 * x) / (1.4 + x) = 8.15

Cross-multiplying and simplifying, we get:

10.29 + 10.20 * x = 8.15 * (1.4 + x)

Expanding the equation, we have:

10.29 + 10.20 * x = 11.41 + 8.15 * x

Rearranging the equation, we get:

10.20 * x - 8.15 * x = 11.41 - 10.29

1.05 * x = 1.12

Dividing both sides by 1.05, we find:

x = 1.12 / 1.05

x ≈ 1.067

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The choice that shows a set of data that could be represented by the box plot below is (B)1,3,6,8,10,12,13,13,16,18,19

In the box plot, a left whisker extends from 1 to 6, therefore, the least value is 1.

The box extends from 6 to 16 and is divided into 2 parts by a vertical line segment at 12. Therefore:

The lower quartile is 6

The median is 12

The upper quartile is 16

The right whisker extends from 16 to 19, therefore the highest value is 19.

The set of data that satisfies these conditions where the numbers in bold are the 5- number summary is

1,3,6,8,10,12,13,13,16,18,19The correct option is B.

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Which data set could be represented by the box plot shown below? A horizontal boxplot is plotted along a horizontal axis marked from 0 to 20, in increments of 1. A left whisker extends from 1 to 6. The box extends from 6 to 16 and is divided into 2 parts by a vertical line segment at 12. The right whisker extends from 16 to 19. All values estimated. Choose 1 answer: Choose 1 answer: (Choice A) A 1,3,6,8,10,12,13,13,16,18,201,3,6,8,10,12,13,13,16,18,201, comma, 3, comma, 6, comma, 8, comma, 10, comma, 12, comma, 13, comma, 13, comma, 16, comma, 18, comma, 20 (Choice B) B 1,3,6,8,10,12,13,13,16,18,191,3,6,8,10,12,13,13,16,18,191, comma, 3, comma, 6, comma, 8, comma, 10, comma, 12, comma, 13, comma, 13, comma, 16, comma, 18, comma, 19 (Choice C) C 1,3,6,8,10,11,13,13,18,18,191,3,6,8,10,11,13,13,18,18,191, comma, 3, comma, 6, comma, 8, comma, 10, comma, 11, comma, 13, comma, 13, comma, 18, comma, 18, comma, 19 (Choice D) D 1,3,6,8,10,11,13,13,16,18,191,3,6,8,10,11,13,13,16,18,19

Answer:

24m

Step-by-step explanation:

If we imagine this situation as a right angled triangle, 25m is the hypotenuse, 7m is the height and we need the base length

so by Pythagoras thorium we can say that [tex]\sqrt[2]{25^2 -7^2}[/tex]= base length

which is= 24

Based on the information, the minimum value is 15, and the maximum value is 30.

To find Q1: Calculate the position of Q1 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (25).

Position = (22 + 1) * (25 / 100) = 5.75 (rounded to 6)

Take the average of the values at positions 6 and 7 to find Q1.

Q1 = (18 + 19) / 2 = 18.5

To find Q2 (the median): Calculate the position of Q2 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (50).

Position = (22 + 1) * (50 / 100)

= 11.5 (rounded to 12)

The value at position 12 is the median.

Q2 = 21

To find Q3: Calculate the position of Q3 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (75).

Position = (22 + 1) * (75 / 100) = 16.5 (rounded to 17)

Take the average of the values at positions 17 and 18 to find Q3.

Q3 = (28 + 29) / 2 = 28.5

The minimum value is 15, and the maximum value is 30.

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The decimal 0.36 can be represented as a fraction in simplest form as 9/25. It can also be expressed as a repeating decimal using a variable.

a) 0.36 can be represented as a fraction in simplest form by using place value to identify the denominator. The number 3 is in the hundredths place value position.

Thus, the denominator is 100. 36 is in the numerator position.

Therefore, 0.36 in fraction form is 36/100 which simplifies to 9/25.

b) 0.36 can be represented as a fraction in simplest form by identifying the denominator based on place value.

In this case, 6 is in the thousandths place value position, so the denominator is 1000. 36 is in the numerator position. Thus, 0.36 in fraction form is 36/1000 which can be simplified to 9/250.

c) To write 0.36 as a fraction in simplest form, the place value of each digit needs to be considered. 3 is in the tenths place value position and 6 is in the hundredths place value position.

Therefore, 0.36 in fraction form is 36/100 which simplifies to 9/25.The decimal 0.36 can be represented in fraction form as 36/100 or 9/25.

To determine the fraction in simplest form, the denominator must be reduced to its lowest possible value without changing the numerator. The decimal 0.36 with a line on top of 3 and 6 represents a repeating decimal.

To express this number as a fraction, a variable is used.

In this case, the variable x is equivalent to 0.36. By setting up a proportion and solving for x, the answer can be found.

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The length of the segment AC is 15 units and the coordinate of point B is (-6, 7)

The length of the segment DF is √68  units and the coordinate of point E is (-6, -5)

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

A = (-10, 10) and (2, 1)

The length AC is then calculated as

AC = √[Δx² + Δy²]

So, we have

AC = √[(-10 - 2)² + (10 - 1)²]

Evaluate

AC = 15

The point B is calculated using

B = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

Where

m : n = 1 : 2 & x, y are the coordinates of A and B

Substitute the known values in the above equation, so, we have the following representation

B = 1/3 * (1 * 2 + 2 * -10, 1 * 1 + 2 * 10)

Evaluate

B = (-6, 7)

Hence, the coordinate of point B is (-6, 7)

Here, we have

(-10, -6) and (-2, -4)

The length DF is then calculated as

DF = √[Δx² + Δy²]

So, we have

DF = √[(-10 + 2)² + (-6 + 4)²]

Evaluate

DF = √68

The point E is calculated using

E = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

Where

m : n = 1 : 1 & x, y are the coordinates of E and F

So, we have

E = 1/2 * (1 * -2 + 1 * -10, 1 * -4 + 1 * -6)

Evaluate

E = (-6, -5)

Hence, the coordinate of point E is (-6, -5)

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