Each hexagon tile has an area of LaTeX: 18\sqrt{3} 18 3 in.2 . Solve for x. Then find the exact length of each side of the hexagon. (Hint: Six equilateral triangles make one hexagon.)

Answers

Answer 1

Answer:

The length of the side of the hexagon is [tex]2\sqrt{3}[/tex] inches.

Step-by-step explanation:

According to this question, we have a regular hexagon with a surface area of [tex]18\sqrt{3}\,in^{2}[/tex]. From Geometry, we know that all regular hexagons can be formed by six regular triangles, since the angle of one complete revolution (360º) divided by the number of triangles is equal to the internal angle of each triangle (60º). Then, the area of each triangle is found after dividing the complete area by the number of regular triangles:

[tex]A_{\triangle} = \frac{18\sqrt{3}\,in^{2}}{6}[/tex]

[tex]A_{\triangle} = 3\sqrt{3}\,in^{2}[/tex]

The area of the triangle as a function of the length of the side of the hexagon ([tex]l[/tex]), measured in inches, is determined by this equation:

[tex]A_{\triangle} = \frac{\sqrt{3}}{4} \cdot l^{2}[/tex] (1)

If we know that [tex]A_{\triangle} = 3\sqrt{3}\,in^{2}[/tex], then the length of the side of the hexagon is:

[tex]\frac{4}{\sqrt{3}}\cdot A_{\triangle} = l^{2}[/tex]

[tex]l^{2} = \frac{4\cdot \sqrt{3}}{3} \cdot A_{\triangle}[/tex]

[tex]l = 2\sqrt{\frac{\sqrt{3}}{3}\cdot A_{\triangle} }[/tex]

[tex]l = 2\sqrt{3}\,in[/tex]

The length of the side of the hexagon is [tex]2\sqrt{3}[/tex] inches.

Each Hexagon Tile Has An Area Of LaTeX: 18\sqrt{3} 18 3 In.2 . Solve For X. Then Find The Exact Length

Related Questions

GIVING BRAINLIEST TO WHOEVER GETS QUESTION 8 AND 9 RIGHT!!

Answers

Answer:

1 toonie 1 quarter 1 dime

2 loonies 1 quarter 2 dimes 1 nickel

Step-by-step explanation:

Answer:

C

none of the others are correct for 9

Step-by-step explanation:

y = x+3 Solve by substitution. 2x + y = -6 What is the solution?​

Answers

Answer: x= -1/2y-3

Step-by-step explanation:

x = -3

plug in x+3 for the y variable.
2x + x + 3 = -6
3x + 3 = -6
3x = -9
divide by 3 on each side
x = -3

16.Speedy Rentals charges $300 per month to rent a car plus an initial deposit of $500. Thrifty Rentals charges $200 per month to rent a car plus an initial deposit of $1,000. (a)If you wanted to rent a car for 4 months, which company's cost would be lower? (b)For how many months would you have to rent a car for the price to be the same for both companies?

Answers

Answer:

A: Speedy Rentals is $100 cheaper if you only rent a car for 4 months

B: If you rented a car for 5 months then both places woulb be the same amount

Step-by-step explanation:

khan sucks 3 for 30 points
again

Answers

Answer:

D, John did not make a mistake!

Step-by-step explanation:

What is the discount given on a jacket that was originally priced $90 and is now $72?

Answers

Answer:

Step-by-step explanation:

The disCount will be the differenceb

Write an equation of the line with a slope of -7 and y-intercept of 1​

Answers

Answer:

y = -7x + 1

Step-by-step explanation:

You put it in the form y = m*x + b

Where m = the slope, so -7 and b = the y-intercept, so 1.

This means it's y = -7x + 1

Note: this answer assumes the equation can be put in slope-intercept form.

Answer:

y = -7x + 1

Step-by-step explanation:

Slope-intercept form, or y = mx + b format, is written in a way that easily reflects the slope and y-intercept of a line. The m, or the coefficient of the term with the x, represents the slope. The b represents the y-value of the y-intercept.

Therefore, substitute the number -7 and 1 in place of those variables. Since -7 is the slope, substitute in place for m. Since 1 is the y-intercept, substitute in place of b. This gives us the equation y = -7x + 1.

CAN SOMEONE PLEASE HELP ME AND TYSM IF YOU DO!!

Answers

Answer:

yes it's proportional

Step-by-step explanation:

yes i think cause it 100,100 etc

If x +9= 2, then x + 9 - 9 = 2 - 9

Answers

Answer: The answer is -16

x= -7      

Step-by-step explanation:

now that you know the value of x, rewrite the equation, if -7 + 9=2, then -7 + 9 - 9 = 2 -9. now that its easier to understand, add and subtract to get you answer, -16

Mirko made a purchase of $150.00 and was charged 8.5% tax. What is just the tax collected?

i give brainliest

Answers

Answer:

11.59

Step-by-step explanation:

Im pretty sure thats correct

((12 / 3^2) - (18 / 3^2)) x (4 / 2)

Answers

Answer:

−4/3

or -4/3x

or (Decimal: -1.333333)

Step-by-step explanation:

A bacteria colony started with 2 bacteria. The colony is growing exponentially at 10% per hour. How long will it take to have 1 million bacteria?

Answers

Answer:

the time taken for having 1 million bacteria is 137.68 hours  

Step-by-step explanation:

The computation is shown below:

y = 2 × (1.10)^x

1,000,000 = 2 × (1.10)^x

500,000 = (1.10)^x

x = log (500,000) ÷ log (1.10)

= 137.68 hours

hence the time taken for having 1 million bacteria is 137.68 hours  

Consider the following Function:
F(x)= 7x-9


If the output is 26, what is the input?

Answers

Answer:-

Input of the given function F(x) is 5.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Given:-

F(x) = 7x - 9

Output = 26

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Solution:-

According to the question the output is 26.

Hence, the above data can be written in an equation form.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ F(x) = 7x - 9 = 26

➪ 7x = 26 + 9

➪ 7x = 35

➪ [tex]\sf x = \dfrac{35}{7}[/tex]

➪ [tex]\bold\red{x = 5}[/tex]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Therefore, F(x) = 5

Which method would be appropriate to factor the polynomial below. 55x^3-40x^2 -Difference of Squares -Basic Trinomial Factoring -AC Method -Sums of Cubes -Greatest Common Factor -Factors by grouping

Answers

Answer:

Greatest Common Factor

Step-by-step explanation:

Let [tex]55\cdot x^{3}-40\cdot x^{2}[/tex], we proceed to demonstrate the appropriate form to factor the polynomial:

1) [tex]55\cdot x^{3}-40\cdot x^{2}[/tex] Given.

2) [tex](5\cdot 11)\cdot (x^2\cdot x) +[5\cdot (-8)]\cdot x^{2}[/tex] Definition of multiplication and subtraction/[tex]a^{b+c} = a^{b}\cdot a^{c }[/tex]/[tex]-a\cdot b = (-a)\cdot b[/tex]/Associative property

3) [tex](5\cdot x^{2})\cdot (11\cdot x)+ (5\cdot x^{2})\cdot (-8)[/tex] Commutative and associative properties

4) [tex]5\cdot x^{2}\cdot (11\cdot x-8)[/tex] Distributive property/Definition of subtraction/Result

Hence, we conclude that this polynomial can be factored by Greatest Common Factor.

500 meters divided by 10 days

Answers

Answer:

50 meters per day

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

i think but ur question doesnt make sen

how many solutions does this system of equations have ? PLZ HELP ASAP DUE AFTER CLASS !

Answers

Answer:

No Solution

Step-by-step explanation:

For system of equations, you must equal the equations to each other like shown below:

[tex]3x + 1 = 3x + 7[/tex]

Solve for x by subtracting 3x from both sides of the equation:

[tex]1[/tex] ≠ [tex]7[/tex]

2] The band has a ratio of boys to girls of 5 to 4. There are 171 students in the band.
(Make sure to write out in words first)

How many are boys?



How many are girls?

Give work for each

Answers

9514 1404 393

Answer:

There are 95 boys.There are 76 girls.

Step-by-step explanation:

The fraction that is boys is 5/(5+4) = 5/9. That fraction of the total is ...

  boys = 5/9 × 171 = 95

Girls are the remainder:

  girls = 171 -95 = 76

There are 95 boys and 76 girls in the band.

please help me out with this question!!
show your work!!​

Answers

The answer is 3 5/4 or 4 1/4 hope this helps

is y = 1 3 x a proportional relationship

Answers

Answer:

Yes

Step-by-step explanation:

What is a secure line of credit?

Answers

Answer:

A secured line of credit means you're promising an asset like real estate or a savings account as collateral in case you don't pay back what you owe. With an unsecured line of credit, you don't have to put down an asset as collateral to secure the loan.

please answer this question

Answers

Answer:

B

Step-by-step explanation:

trust me 100% sure

Its B me and the other guy is right

Which table shows the amount of a substance decaying at an exponential rate?

Answers

Answer:D

Step-by-step explanation:

Just trust

Susanna purchased a shirt for $5, pants for $10, and a jacket for $25. She wants to buy at least one purse for the outfit, but she wants to have something left of her original $65. How much money might she spend on the purse?

Answers

Answer:

$15 dollars left after you purchased everything except the purse.

Step-by-step explanation:

5+10+25=40

65-40=15

if you have $15 left it depends on how much the purse costs.

Say it costs $10 dollars you would have $5 left and so on

pls help me i will mark the brainlyiest thingg if you get it right

Answers

Answer:

(3x+6) degrees+(5x+4) degrees equals 90 degrees

Step-by-step explanation:

Answer:

try 3x+6+5x+4=90

sorry if it's wrong

Whatcha table shows a proportional relationship?
p 1 3 5 7 9
q 0 2 4 6 8
—————-
b 1 4 5 7 11
c 3 12 15 21 33
——————-
r 3 6 10 12 15
s 2 4 6 8 10
——————
x 1 2 3 4 5
y 9 10 11 12 13

Answers

Answer:

The answer is the second table (the one with B and C.)

Step-by-step explanation:

You know this, because the other tables are just based on patterns and the x and y values have nothing to do with each other. However, for the second table, the b value times 3 equals the c value. This is how you know the table shows a proportional relationship, and this is key to solving this problem.

Here's an image that helps demonstrate this idea:

A bakery offers a sale price of $2.70 for 3 muffins. What is the price per dozen? The price per dozen muffins

Answers

Answer:

Step-by-step explanation:

i think your asnwer would be 14 dollers but im not to sure

hope this helps

i am so sorry if i am wrong

18. On Faith's math test, she received
a 85%. If there were 40
questions on the test, how many
did she get right?

Answers

Answer: 40/10=4

That means 10% of 40 is 4.

Know that means you have to times 4 by 8

4x8=32

Now you know what 80% of 40 is.

Now we need to know what the 5% is. So if 4 is 10% . 5% must be 2.

Next we have to add 2 to 32.

32 + 2 = 34

Answer is 34

Step-by-step explanation:

How do i find what to put into the boxes??

Answers

you have to figure out what x and y are . they will both be the same most likely. Is there anything else that was with that problem?

Find the missing dimension.
The missing dimension is

inches.fill in the blank

Answers

Answer:

H= 11

Step-by-step explanation:

231 = h x 7 x 3

231 = 21h

/21    /21

H=11

Answer:

11

Step-by-step explanation:

sup my guys.
simplify.
12/232 x 24/127 =

Answers

Answer:

36/3683

Step-by-step explanation:

Your laptop battery will last for exactly 6 hours before it needs to be recharged.You have had your laptop on for
2 1/2. What fraction of your battery life remains.

Answers

Answer:

[tex]3\frac{1}{2} hours[/tex]

Step-by-step explanation:

You have to subtract 2 1/2 from 6 and that will equal 3 and 1/2.

Answer:

75%

Step-by-step explanation:

6 - 3/2 is 4.5.

So the computer has 4.5 hours.

the battery will last for 6 hours so every hour on the computer is 100/6 percentage, which is 16.6666666667.

Finally multiply 16.6666666667 and 4.5 and you will get 75%

Your final answer would be 75%

Hope it helps

Pls mark brainliest

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