ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively. What is the area of the quadrilateral EBFD ?

Answers

Answer 1

Answer: Given : - Square ABCD with side 3. E and F as midpoints.
To find : - area of EBFD

Solution : - We have, area of square ABCD = 3 x 3 = 9 units.

Thus, (ar)EBFD = ar ABCD - ar DAE - arDCF

arDAE = 1/2 x base x height

=1/2 x 1.5 x 3 ( AE is 1/2 of AB = 1.5, DA is altitude)
= 2.25

arDFC = 1/2 x base x height
= 1/2 x 1.5 x 3 (FC is 1/2 of BC, DC is altitude)
= 2.25

Thus, (ar) EBFD = arABCD - arDAE - arDCF

= 9 - 2.25 - 2.25

= 4.5 units.

Thus, area of quad EBFD is 4.5 units.

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N ∈ lNWe set A= n(n²+11)
Show that A is divisible by 3
( n is natural number )
please try to help me in this i need it tomorrow plz...

Answers

@Konrad509's answer was fantastic.

What you first need to know is this. 3 consecutive natural numbers multiplied by each other, for instance: (1*2*3) or (2*3*4) or (3*4*5) or (4*5*(2*3)) can be described using the abstract expression:

(n-1)n(n+1)

-------------

Now:

A=n(n²+11),

and:

n(n²+11)

=n(n²-1+12)

=n³-n+12n

=n(n²-1)+12n

=n(n+1)(n-1)+12n

=(n-1)n(n+1)+(4*3)n

-------------------------

So:

A=(n-1)n(n+1)+(4*3)n

Therefore, A is divisible by 3.

$n(n^2+11)=\nn(n^2-1+12)=\nn(n^2-1)+12n=\n(n-1)n(n+1)+12n$

$(n-1)n(n+1)$ is the product of 3 consecutive natural numbers, so it has be to divisible by 3.

$12n$ is also divisible by 3 because 12 is divisible by 3.

If both elements of the sum are divisible by 3 so the sum itself is divisible by 3 as well.

How do you do transversal of parallel lines??

Answers

Well what you have to do is first you have to create two parallel lines. You just draw a line straight through them to create a ton of angles that correspond with each other. That is basically what transversal parallel lines are.

For the equation: 6a-(2a+4)=11-3(a-2), what is the value of a ?

Answers

Answer:

a = 7/2

Step-by-step explanation:

Step 1: Write equation

6a - (2a + 4) = 11 - 3(a - 2)

Step 2: Solve for a

Distribute: 5a - 2a - 4 = 11 - 3a + 6
Combine like terms: 3a - 4 = 17 - 3a
Add 3a to both sides: 6a - 4 = 17
Add 4 to both sides: 6a = 21
Divide both sides by 6: a = 7/2

Final answer:

The variable 'a' in the given equation is 3. First, simplify both sides of the equation, then isolate 'a' by adding and subtracting the same terms on both sides. Finally, divide to find 'a'.

Explanation:

The first step to solve the equation 6a-(2a+4)=11-3(a-2) is simplifying both sides. On the left-hand side, distribute the negative sign into the parenthesis, resulting in 6a - 2a - 4. Simplifying this gives 4a - 4. On the right-hand side, distribute the negative 3 into the parenthesis, resulting in 11 - 3a + 6. Simplifying this gives -3a + 17.

So, the simplified equation is 4a - 4 = -3a + 17. To isolate the variable a on one side, add 3a to both sides to get 7a - 4 = 17. Then add 4 to both sides to get 7a = 21. Finally, divide both sides by 7 to get a = 3.

Learn more about Solving Equation here:

brainly.com/question/18322830

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Which statement is true about a model of a prime polynomial? It cannot be modeled with a rectangle. It can be modeled with a square. It cannot be modeled with all positive tiles. It can only be modeled with an odd number of tiles. please help me

Answers

The correct answer is:

It cannot be modeled with a rectangle.

Explanation:

When using area tiles to represent polynomials, we arrange the tiles into a rectangle in order to find the factors of the polynomial.

Since the area of a rectangle is found by multiplying length and width, if we find the "length" and "width" of the polynomial rectangle, we have the factors that multiply to make up that polynomial.

However, if a polynomial is prime, its only factors are 1 and itself. This means the "length" would be the polynomial itself, and the "width" would be 1. This means we cannot arrange the polynomial into a rectangle.

Answer:

A : it cannot be modeled with a rectangle

Step-by-step explanation:

edge 2020 . good luck !

An algebraic equation is an equation that includes:a.
no variables
c.
one or more variables
b.
only one variable
d.
just numbers

Answers

An algebraic equation includes one or more variables.

One or more variable

What is the domain of f(x)?What is the range of f(x)?
How is the domain and range of this function different from the other functions you have seen in this topic?