∆ABC is divided into three smaller triangles and one quadrilateral. Area of ∆AFE is 4, Area of ∆AFC is 9, area of ∆DFC is 7. Find the area of quadrilateral BEFD.

ABC Is Divided Into Three Smaller Triangles And One Quadrilateral. Area Of AFE Is 4, Area Of AFC Is 9,

Answers

Answer 1

The area of quadrilateral BEFD is 15.32units²

How to find the area of quadrilateral BEFD?

Let the area of  ∆ABC be A

Let the area of ∆AFE be X

Let the area of ∆AFC be Y

Let the area of ∆DFC be Z

Using Ladder theorem:

1/A + 1/Y = 1/(X+Y) + 1/(Y+Z)

Since X = 4, Y = 9 and Z = 7, we have:

1/A + 1/9 = 1/(4+9) + 1/(9+7)

1/A + 1/9 = 1/13 + 1/16

1/A = 1/13 + 1/16 - 1/9

1/A = 53/1872

A = 1872/53

A = 35.32

area of  ∆ABC = area of ∆AFE + area of ∆AFC + area of ∆DFC + area of quadrilateral BEFD

35.32 = 4 + 9 + 7  + area of quadrilateral BEFD

35.32 = 20 + area of quadrilateral BEFD

area of quadrilateral BEFD = 35.32 - 20

area of quadrilateral BEFD = 15.32unit²

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Related Questions

Ellie ha been training for the Cedar Ridge Off-Road Race. The firt week he trained, he ran 3 day and took the ame two route each day: 2. 5 mile on a path in the wood in the morning and a longer route at the park in the afternoon. By the end of the week, Ellie had run a total of 24 mile. Which equation can you ue to find how many mile, x, Ellie ran each afternoon

Answers

The Distance that Ellie ran each evening is 16.5 miles for a entirety week.

How to find the number of miles?

We can use the following equation to find how many miles, x, Ellie ran each afternoon:

x + 2.5(3) = 24

Here, x represents the number of miles Ellie ran each afternoon, 2.5 represents the number of miles she ran each morning, and 3 represents the number of days she trained. The total number of miles she ran, 24, is on the right side of the equation.

To solve for x, we can start by simplifying the left side of the equation:

x + 7.5 = 24

Then, we can subtract 7.5 from both sides:

x = 16.5

So, Ellie ran 16.5 miles each afternoon.

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How do you find the missing side of an obtuse triangle?

Answers

Answer:

Using the cosines law

Step-by-step explanation:

So, we need to find the length of the other side, we will use the version of the Cosine Rule where a2 is the subject of the formula, which is given by, a2=b2+c2−2bccosA, Side a is the one we are trying to find. Sides band care the other two sides, and angle Ais the angle opposite side a. c2=a2+b2−2abcosC

What is the solution to the system Y 3x 7 and 6x 2y 12?

Answers

The system of equations y = 3x - 7 and 6x - 2y = 12 has no solution. That is the lines of the equation is parallel.

To solve a system of equations, you can use substitution or elimination.

One method to find the solution for this system of equations is substitution. To use this method, you can solve one equation for one variable in terms of the other variable, and then substitute this expression into the other equation.

Solving for y in the first equation:

y = 3x - 7

Then substitute the result in the second equation:

6x - 2(3x - 7) = 12

6x - 6x + 14 = 12

14 = 12

That clearly is not true and this system of equations has no solution.

--The question is incomplete, answering to the question below--

"What is the solution to the system y = 3x - 7 and 6x - 2y = 12?

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How do you solve 3 composite functions?

Answers

To solve 3 composite functions, you would need to break each function down into its individual components. Then, you would need to combine each component one at a time, starting with the outermost function and working your way inwards.

1. Break each function down into its individual components. This may involve splitting them into simpler functions such as polynomials, exponentials, trigonometric functions, and so on.

2. Start with the outermost function and combine each component one at a time. Make sure to apply the order of operations to each step in order to get the correct result.

3. Evaluate the combined function. This means solving for the output of the function, which may involve plugging in values for certain variables.

4. Repeat the same process for the other two functions.

5. When you have evaluated all three functions, you can combine the results of each to get the answer to the composite functions.

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What is a statistical question Musa can ask about the club?
How many hours does a member usually spend gardening each month?
How many members were at yesterday's club meeting?
How many gardens are on the school's property?
How much money did the club raise at last week's fundraiser?

Answers

Answer:

Step-by-step explanation:

Miranda is buying yarn so she can crochet scarves for her family. She likes the Furry Fibers brand best. At the store, she finds a 7-ounce roll of Furry Fibers yarn for $8. 33 and a 16-ounce roll for $18. 72. Which size roll is the better value?

Answers

The size roll which is the better value is $1.17 per ounce.

To determine which size roll is the better value, we need to compare the price per ounce of each roll.

To find the price per ounce of the 7-ounce roll, we divide the total cost by the number of ounces: $8.33 ÷ 7 ounces = $1.19 per ounce.

To find the price per ounce of the 16-ounce roll, we divide the total cost by the number of ounces: $18.72 ÷ 16 ounces = $1.17 per ounce.

Since $1.17 per ounce is less than $1.19 per ounce, the 16-ounce roll is the better value. It is cheaper per ounce than the 7-ounce roll.

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What does 5a+10a equal to?

Answers

Answer:

15a

Step-by-step explanation:

5a + 10a = 15a

Explain if the ordered pairs represent a function or not.
(1,2)(1,3)(2,4)(3,6)(0,0)(-1,4)

Answers

Not a function, the x values have different y values. In order for it to be a function, all the x values must have specific y values

Why it is called irrational?

Answers

The number √2 is called an irrational number because the value of √2 = 1.41421356... and the the value is non terminating and non repeating .

What are Irrational Numbers ?

The Numbers whose vales are Non Repeating and Non Terminating are called as Irrational Numbers ,

also the numbers that cannot be expressed on the form of [tex]\frac{p}{q}[/tex] are called as Irrational Numbers .

the number is given as √2 ;

we know that the values of √2 is = 1.41421356... ,

we see that the the value is non terminating and the numbers after decimal point are non repeating ,

Therefore  , the number √2 is an irrational number .

The given question is incomplete , the complete question is

Why the number √2 is called a Irrational Number ?

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Can anyone help me solve this equation: x^{2} +5x+6=0

Answers

Answer: x= -2, -3

Step-by-step explanation: Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

b. Consider a circle with centre O and radius of 4 units. The distance of point P is 2 units from centre. Find the distance of inverse of point P' from the centre O.​

Answers

The distance of the inverse of point P' from the centre O is also 4 units. This is because the inverse of a point is the point on the opposite side of the circle from the original point, and the radius of the circle is 4 units. Therefore, the distance of the inverse of point P' from the centre O is also 4 units.

How can you determine if the length of the 3 sides would make a triangle?

Answers

we can use the Triangle inequality Theorem a theorem in Euclidean geometry that states any two triangle sides added together must be greater than or equal to the third side

How to Determine if Three Side Lengths Are a Triangle?

It's simpler than it seems to determine whether a triangle has three side lengths. The Triangle Inequality Theorem, which asserts that the sum of a triangle's two side lengths is always greater than the third side, will suffice. You will have a triangle if this holds true for each of the three possibilities of increased side lengths.

1 . Triangle Inequality Theorem

smaller than the total of the first two sides. You will have a valid triangle if this holds true for each of the three possible combinations. To confirm that the triangle is feasible, you will need to go through each of these combinations one at a time. Theorem a+b > c, a+c > b, and b+c > a can alternatively be thought of as an inequality. The triangle has sides of lengths a, b, and c.

In this case, a, b, and c are each equal to seven.

2. Check to see if the sum of the first two sides is greater than the third

Check to see if the sum of the first two sides is greater than the third adding the sides a and b yields 17, which is larger than 5, or 7 plus 10. It can alternatively be considered as 17 > 5.

3. Check to see if the sum of the next combination of two sides is greater than the remaining side

just see if the sum of sides a and c are greater than the side b.[4] This means you should see if 7 + 5, or 12, is greater than 10. 12 > 10,

4. Check to see if the sum of the last combination of two sides is greater than the remaining side.

Check to see if side b and side c added together are greater than side a. To accomplish this, you must determine whether 10 Plus 5 is greater than 7. The triangle is complete on all sides since 10 + 5 = 15 and 15 > 7.

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Find the range, mean, median and mode for the scores. Round to the nearest tenth when necessary.a.40; 75.5; 75; 75c.40; 74.5; 75; 100b.35; 75.5; 75; 75d.40; 74.5; 75; 75

Answers

Range: (Largest Number) - (Smallest Number)

Answer: 100 - 35 = 65

Mean: (Add up all the numbers) divided by (Amount of numbers)

Answer: 1080/16 = 67.5

Median: (Put all the numbers in numerical order and find the one in the middle)

Answer: 75

Mode: (Most seen number)
Answer: 75

How to find the legs of a 45 45 90 triangle given the hypotenuse?

Answers

If the hypotenuse is given to the 45 45  90 triangles, the leg of the triangle is calculated after dividing the hypotenuse by [tex]\sqrt{2}[/tex].

The 45, 45, and 90 triangle is a type of isosceles triangle where the two legs are the same as each other and other non-right angles are both 45 degrees. Most of the time, Pythagoras' theorem is used for finding out the missing legs and hypotenuses of 45, 45, and 90 triangles.

If the leg of the triangle is equal to a, then:

The second leg is also equal to a;The hypotenuse is a√2;The area is equal to a²/2; andThe perimeter equals a(2 + √2).

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Find the theoretical probability that a 12-month calendar is turned to the month of May or the month of June. Write your answer as a fraction in simplest form.

Answers

Probability that the calendar turned to month of May or June is 1/6.

What is Probability?

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Total number of months = 12

Suppose that a calendar is turned.

Probability that the calendar turned to month of May = 1/12

Probability that the calendar turned to month of June = 1/12

Probability that the calendar turned to month of May or June = 1/12 + 1/12

                                                                                                      = 2/12

                                                                                                      = 1/6

Hence the probability that the calendar turned to month of May or June is 1/6.

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What is a truth table in logic gate?

Answers

The Truth Table in logic gate is  used to specify the output of the logic gate for all possible combinations of the input signals. , it is the breakdown of all the possible truth values returned by the logical expression.

What is Truth Table ?

The truth table is a tabular representation of all combinations of values for inputs and their respective outputs.

It can be called as a mathematical table which shows all possible outcomes that would occur from all the possible scenarios that are considered as  factual.

Truth tables are generally used for the logic problems as in Boolean algebra and electronic circuits.

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Answer:

Step-by-step explanation:

A truth table for a logic gate is the table that specifies the logic value/state of the output of the gate for all possible combinations of the logic states of all inputs.

Let's take the example of the AND gate with two logic inputs A and B and one output Y.

A    B    Y

0    0    0

0    1     0

1     1     1

1    0     0

This is the truth table for the AND gate.

35 POINTS Complete the sentence.
Statistics is the result of __________ data.

Answers

Answer:

analysis (i got to put a bunch of random stuff here cs the limit)

Find the volume of a cube if its area of four walls is 16 cm square.

Answers

[tex] \longmapsto \: side = \frac{16}{4} = 4 \\ \longmapsto volume = 4 {}^{3} = 64[/tex]

Darius has a cylindrical can that is completely full of sparkling water. He also has an empty cone-shaped paper cup. The height and radius of the can and cup are shown.



Darius pours sparkling water from the can into the paper cup until it is completely full. Approximately, how many centimeters high is the sparkling water left in the can?

Answers

Answer: 6.2

Step-by-step explanation:

For the equation f(x) = -3x7 + 2x- 1, identify the vertex, line of symmetry, and y intercept

Answers

The vertex of the equation is (0, -1), the line of symmetry is x = 0 and the y-intercept is (0,-1).

For the equation f(x) = [tex]-3x^7[/tex] + 2x - 1, the vertex is the highest or lowest point on the parabola and it can be found by completing the square method.

To find the line of symmetry, we can set the function equal to zero and solve for x. The x-coordinate of the vertex is the same as the line of symmetry.

The y-intercept is the point at which the parabola crosses the y-axis, and it can be found by setting x equal to zero and solving for y.

The vertex of the parabola:

The equation is in form f(x) = a[tex](x-h)^2[/tex] + k, where a is -3, h is the x-coordinate of the vertex and k is the y-coordinate of the vertex. In this case, h = 0 and k = -1.So the vertex is (0, -1)

The line of symmetry:

We can set the function equal to zero and solve for x:[tex]-3x^7[/tex] + 2x - 1 = 0The x value that makes the equation equal to zero is x = 0So the line of symmetry is x = 0

The y-intercept:

We can set x equal to zero and solve for y: f(0) = [tex]-3(0)^7[/tex] + 2(0) - 1 = -1So the y-intercept is (0, -1)

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Evaluate the expression 5(x – 6 + 3x)2 – 6 where x = 2.

Answers:

1: 974

2: 14

3: -16

4: 26

Answers

So the expression evaluates to 14 when x = 2.

To evaluate the expression, we first substitute x = 2 into the expression:

5(2 - 6 + 3*2)^2 - 6

There are two methods for solving simultaneous linear equations: graphical methods and algebraic methods. The algebraic technique includes the substitution method as one of its categories.

The value of one variable from one equation is substituted in the second equation using the substitution method. In this manner, a pair of linear equations is reduced into a single linear equation with only one variable, which can then be solved quickly.

Next, we simplify the expression inside the parentheses:

=5(2 - 6 + 6)^2 - 6

=5(2)^2 - 6

=5*4 - 6

=20 - 6

=14

So the expression evaluates to 14 when x = 2.

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(Find the value of): 2m x 2-m

Answers

4-m is the value of this

Which graph matches the system of equations

2x+3y=5
4x−5y=−1


Responses

Answers

The graph of equation is in image.

What are linear equations?

When a linear equation is graphed, it always results in a straight line because each term has an exponent of 1. This is why it is referred to as a "linear equation."

There are linear equations with one and two variables, respectively.

Given equations

2x + 3y = 5

4x - 5y = -1

For equation 1

2x + 3y = 5

The table of values appears as follows

x    1     -2    4

y    1      3    -1

Coordinates for equation 2

4x - 5y = -1

The table of values as thus

x    1     2    -4

y    1     1.8   -3

And the intersection point of equation is (1, 1)

Hence the graph of equation is intersecting at (1, 1).

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12. Which set of ordered pairs below is a function?

Answers

Answer:D. 1 and 2

Step-by-step explanation:

Domain cannot repeat

What are the properties of the graph of a function?

Answers

The properties of the graph of a function include domain, range, symmetry, asymptotes, intercepts, increasing or decreasing, continuity, smoothness, behaviour at infinity and shape.

1) Domain: The set of all input values (x-values) that produce a valid output (y-value) for the function.

2) Range: The set of all output values (y-values) that can be produced by the function for any valid input value in the domain.

3) Symmetry: A graph may be symmetric with respect to the x-axis, y-axis, or origin.

4) Asymptotes: A line that the graph of a function gets arbitrarily close to, but never touches.

5) Intercepts: The points where the graph of a function crosses the x- and y-axes.

6) Increasing or Decreasing: A function can be increasing over a certain interval, decreasing over a certain interval, or both.

7) Continuity: A function is continuous if its graph has no breaks or gaps.

8) Smoothness: A function is smooth if its graph has no sharp corners or links.

9) Behavior at Infinity: The behavior of a function at positive or negative infinity can be determined by analyzing the degree and leading coefficient of its equation.

10) Shape: The shape of a graph can be used to classify functions as linear, quadratic, exponential, logarithmic, etc.

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Data was collected for 40 randomly selected honey bee hives on a farm: The number of parasites found in each hive was recorded: The data is summarized in the histogram below. 10 [ 10 15 20 25 30 35 40 45 50 parasites in hive What is the maximum possible number of parasites for the class containing the value 27? Note: Each class contains its lower class boundary, but not its upper class boundary. maximum =

Answers

The maximum possible number of parasites for the class containing the value 27 is 29

The data for 40 randomly selected honey bee hives on a farm is summarized in the histogram below.

From given histogram we have the classes as:

10 - 15, 15 - 20, 20 - 25, 25 - 30, 30 - 35, 35 - 40, 40 - 45, 45 - 50

To find: the maximum possible number of parasites for the class containing the value 27

The class that contains the value 27 is 25 - 30

Given that each class contains its lower class boundary, but not its upper class boundary.

So, the maximum possible number of parasites for the class containing the value 27 would be 29 as 30 is not part of class 25 - 30

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which is the correct comparison of solutions for 2(5-x) > 6 and 22 > 2(9+x)?

Answers

The correct comparison of solutions for the expression is x < 2

How to determine the correct comparison of solutions for the expression

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

2(5-x) > 6 and 22 > 2(9+x)

Rewrite the expression properly

So, we have the following representation

2(5 - x) > 6 and 22 > 2(9 + x)

Divide both sides of the expressions by 2

So, we have the following representation

5 - x > 2 and 11 > 9 + x

Subtract both sides of the expression by the constant term

This gives

-x > -3 and 2 > x

Rewrite as

x < 3 and 2 > x

So, we have

x < 3 and x < 2

When combined, we have

x < 2

Hence, the solution is x < 2

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Northlake High School has two lunch periods. Students can eat their lunch in the cafeteria or on an outside patio. About 35% of students who have first lunch eat outside. Compare this with the percentage of second-lunch students who eat outside.


Select the true statement.


A. A smaller percentage of second-lunch students (24%) eat outside.


B. A greater percentage of second-lunch students (39%) eat outside.


c. A greater percentage of second-lunch students (41%) eat outside.


D. A smaller percentage of second-lunch students (18%) eat outside.


A / P / E / X

Answers

B. A greater percentage of second-lunch students (39%) eat outside.

From the table above, the percentage second-lunch students who eat outside is calculated as follows:

%= number of students who eat outside/total number of students who have second lunch × 100/1

%=18/46 x 100/1

%=39.1%

What is Percent

Percent is usually used to describe data in percentage form. This mathematical science is often used when calculating population percentages, discounts, interest rates, and so on. Percent is a number that represents part or all of the value or goods by forming a ratio of one hundred. Percent has an infinitely high value, while its lowest value is 0 percent. The amount of the percentage is denoted by "%".

History of Percent Numbers

This number was born in ancient Rome to be precise from the collection of auction taxes by using a fraction of 1/100 of the auction value or called centesima rerum venalium. the percent symbol has changed several times. Originally the Latin word percento was used. However, in the next generation, the word percento was changed to two symbols, namely the word per which changed to "/" and cento which changed to "00". Until finally the symbol "%" was known.

Percent formula

The simple formula for calculating percent is: Percentage (%) = (Total parts)/(Total amount) X 100%. The general percentage formula for calculating the percentage of a number that is considered as part of the whole is written in percent or 100%.

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make N the subject of formulaP=N+2/d

Answers

Answer:

N = Pd - 2

Step-by-step explanation:

P = N + 2/d

Pd = N + 2

Pd - 2 = N

N = Pd - 2

Select the correct answer. Which logarithmic equation is equivalent to this exponential equation? 2,400=7,500 (10) ^ -x

Answers

The logarithmic equation that is equivalent to this exponential equation 2,400=7,500 (10) ^ -x is [tex]x = -log_{10} \frac{8}{25}[/tex]. Option C

How to solve for the equation

from the question we have:

2400 = 7500(10)⁻ˣ

we would have to transform the equation that we have here into the logarithm form.

This is written as:

[tex]\frac{2400}{7500}=10^-^x[/tex]

from here we are to reduce the division

hence we would have:
[tex]10^-^x = \frac{8}{25}[/tex]

-x = log₁₀8/25

then

[tex]x = -log_{10} \frac{8}{25}[/tex]

option c is correct

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