MATHEMATICS MIDDLE SCHOOL

a square is constructed on each side of an equilateral triangle, and segments are drawn between adjacent external vertices of the three squares to form hexagon ABCDEF as shown. If the equilateral triangle has sides of length √3 - 1 units, what is the perimeter of the hexagon ABCDEF?

Answers

Answer 1

Answer:

Answer:

$P=6\ units$

Step-by-step explanation:

we know that

The perimeter of the hexagon is equal to

$P=AB+BC+CD+DE+EF+FA$

Remember that

$AB+CD=EF=(√(3)-1)\ units$

$BC=DE=FA$ ----> is the length base of an isosceles triangle

The perimeter is equal to

$P=3(√(3)-1)+3BC$

Find the length side BC

Let

x ----> the measure of the vertex angle in the isosceles triangle

The measure of the vertex angle in the isosceles triangle is equal to

$90^o+60^o+90^o+x=360^o$

$x=120^o$

Applying trigonometric property

In the right triangle of the attached figure

$cos(30^o)=(BC/2)/(√(3)-1)$ ----> by CAH (adjacent side divided buy the hypotenuse

Remember that

$cos(30^o)=(√(3))/(2)$

substitute

$(√(3))/(2)=(BC/2)/(√(3)-1)$

$BC=(3-√(3))\ units$

Find the perimeter

$P=3(√(3)-1)+3(3-√(3))$

$P=3√(3)-3+9-3√(3))$

$P=6\ units$

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I just want to see if my answer is correct, I haven't done volume in a long time!

Answers

You did it right because 12 x 2 = 24 x 8 = 192

yes your answer is correct

A school has 764 students. Of the students, 118 are in third grade. Whichequation can be used to find s, the total number of students in all of the other
grades?
s – 118 = 764
118 + s = 764
s – 764 = 118
764 + 118 = 8

Answers

The total number of students in all other grades can be represented by the equation 118 + s = 764.

What is an equation?

'In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting themwith the equal to sign.'

According to the given problem,

Total number of students = 764

Number of students in third grade = 118

Let s be the number of students in all other grades,

⇒ s + 118 = 764

⇒ s = 764 - 118

⇒ s = 646 students

Hence, we can conclude, the number of students in all other can be represented by the equation 118 + s = 764.

Learn more about equations here: brainly.com/question/10413253

#SPJ2

Answer:

118+s=764 is the correct answer.

PLEASE HELPPPP!!!!!! Events A and B are mutually exclusive. Events B and C are non-mutually exclusive. Which Venn diagram could represent this description? Image for option 1 Image for option 2 Image for option 3 Image for option 4

Answers

Answer:

The answer is the attached figure

Step-by-step explanation:

* Lets explain mutually exclusive and non-mutually exclusive

- The mutually exclusive means events cannot happen at the

same time

# P(A or B) = P(A) + P(B)

- The non-mutually exclusive means they have at least one

outcome in common

# P(A or B) = P(A) + P(B) - P(A and B)

* Lets solve the problem

∵ Events A and B are mutually exclusive

∵ Circle A represents the event A

∵ Circle B represents the event B

∴ There is no intersection between the two circles A and B

∵ Events B and C are non-mutually exclusive

∵ Circle C represents the event C

∴ There is an intersection between the two circles B and C

* The answer is the attached figure

Answer: D. image 4.

Just did assignment.

I need help with finding the answer of 21 laps in 7 minutes

Answers

I'm not sure if that's what you mean, but I assume you might want to know how long did it take to make one lap if someone did 21 laps in 7 minutes.

If so, just divide 7 by 21:

7 ÷ 21 = 0.3333333... (repeating decimal) or 1/3 as a fraction.

It means that one lap took 1/3 of a minute (20 seconds).

If that's not what you meant, please specify the question :)

What set of reflections and rotations would carry rectangle ABCD onto itself? Rectangle formed by ordered pairs A at negative 4, 1, B at negative 4, 2, C at negative 1, 2, D at negative 1, 1. (4 points) Reflect over the y-axis, reflect over the x-axis, rotate 180°
Rotate 180°, reflect over the x-axis, reflect over the line y=x
Reflect over the x-axis, rotate 180°, reflect over the x-axis
Rotate 180°, reflect over the y-axis, reflect over the line y=x

Answers

Answer: The correct option is

(A) Reflect over the y-axis, reflect over the x-axis, rotate 180°.

Step-by-step explanation: Given that the co-ordinates of the vertices of rectangle ABCD are A(-4, 1), B(-4, 2), C(-1, 2) and D(-1, 1).

We are to select the set of reflections and rotations that would carry rectangle ABCD onto itself.

We see that if a point (x, y) is first reflected across Y-axis, its co-ordinates becomes

(x, y) ⇒ (-x, y).

Now, if the new point is reflected across X-axis, then its co-ordinates becomes

(-x, y) ⇒ (-x, -y)

and finally if we rotate the point by 180 degrees, its co-ordinates becomes

(-x, -y) ⇒ (x, y).

That is, after these three transformations, each of the vertex of rectangle ABCD, that is, A(-4, 1), B(-4, 2), C(-1, 2) and D(-1, 1) come back to its original position.

Thus, the required set of reflections and rotations would carry rectangle ABCD onto itself is

Reflect over the y-axis, reflect over the x-axis, rotate 180°

Option (A) is CORRECT.

Answer:

Step-by-step explanation:

Reflect in the y-axis.

this takes it to the first quadrant.

Reflect in the x-axis.

To the fourth quadrant

Rotate through through 180 degrees.

Back to its original location.

Write a division problem story with 53 as the divisor and 2,491 as the dividend. Solve.

Answers

Answer:

Rick had 2,491 reward points in an online video game. He wanted to split his points with 53 other players in the game. How many points does each player receive.

Answer :

2,491 ÷ 53 = 47

Check your answer : 47 * 53 = 2,491

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