Please Answer!
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each graph with its description.
the function increases on the interval (-∞, 1)
and decreases on the interval (1, ∞)
the function has a maximum at (3,1)
the function has a minimum at (1,3)
the function has a minimum at (3,1)
Answers
The matching of the quadratic functions with their features is given by the image at the end of the answer.
What are the features of a quadratic function?The first feature of the function on the problem is when it is increasing, and the definition is that it is increasing when the graph of the function is moving to the right and up on the graph, that is, when x increases, y also increases.
It is decreasing when it is moving right and down. Hence, a quadratic function increases until it's vertex, so for item 1, we want a function that is concave down, as it is increasing and then decreasing, and does the turn at x = 1, which is the third function on the second row.
The maximum and minimum points are given at the turning points, as follows:
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Answer: Its correct
Step-by-step explanation:
Right on Edmentum. Absolute legend
Related Questions
cosec 2A + cosec 4A = cot A - cot 4A
Answers
The given expression is proved by the necessary changes.
cosec 2A + cosec 4A = cot A - cot 4A
Cosec 2 A + Cot 4 A = Cosec 4 A - Cot 2 A
Taking LHS :
⇒Cosec 2 A + Cot 4 A
⇒Cosec 2 A + ( Cot 2 A )2
⇒Cosec 2 A + ( Cosec 2 A - 1 )2 ( we know:1+ Cot 2 θ = Cosec 2 θ )
⇒Cosec 2 A + Cosec 4 A + 1 - 2 Cosec 2 A
⇒ Cosec 4 A + 1 - Cosec 2 A
⇒ Cosec 4 A + 1 - ( 1 + Cot 2 A)
⇒ Cosec 4 A + 1 - 1 - Cot 2 A
⇒ Cosec 4 A - Cot 2 A
or cosec2A+cosec4A=cotA-cot4A
Hence Proved.
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engineers must consider the diameters of heads when designing helmets. the company researchers have determined that the population of potential clientele have head diameters that are normally distributed with a mean of 6.4-in and a standard deviation of 0.9-in. due to financial constraints, the helmets will be designed to fit all men except those with head diameters that are in the smallest 1.4% or largest 1.4%. what is the minimum head diameter that will fit the clientele? min
Answers
The largest head diameter that can accommodate the clientele is 8.5743
Mean, u = 6.4
Standard deviation = 0.9
We must utilize the inverse of the common normal table to obtain our values.
the smallest head width possible.
P(Z < z) = 1.4%
P(Z < z) = 0.014
P(Z < -2.0749) = 0.014
z = -2.0749
Using the z-score calculation,
(x - μ) ÷ σ = [tex]Z_{0.019}[/tex]
Let x be the heads' breath.
Making x the focus of the equation,
x = z × σ + μ
We already have:
z = -2.0749
u = 6.5
s.d = 1
Replacing numbers,
x = (-2.0749 × 1) + 6.5
x = 4.4251
The clientele requires a minimum head breadth of 4.4251.
The largest head width that can be accommodated.
P(Z > z) = 1.4%
1 - P(Z < z) = 0.014
P(Z < z) = 1 - 0.014 = 0.981
P(Z < 2.0749) = 0.981
Using the z-score calculation,
(x - μ) ÷ σ = [tex]Z_{0.019}[/tex]
Let x be the heads' breath.
Making x the focus of the equation,
x = z × σ + μ
z = 2.0749
u = 6.5
s.d = 1
Substituting figures,
x = (2.0749 × 1) + 6.5
x = 4.4251
x = 8.5743
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4. The temperature of the water in a pot on the stove is taken every 2 minutes, as shown in the
following chart.
Time (Minutes)
0
2
4
6
8
10
12
14
16
18
20
Temperature (°C)
23.2
25.1
29.2
36.8
42.5
47.6
55.9
62.7
72.4
86.1
98.3
Based on an exponential model of the data, what is the predicted temperature of the water at 7
minutes? Use the Desmos calculator to find your answer. Round your answer to the nearest tenth
of a degree.
(1 point)
Answers
Based on an exponential model of the data, the predicted temperature of the water at 7 minutes is 39.7 °C using desmos graphing calculator.
What is an exponential model of the data?Similar to how you discovered linear and quadratic models in prior chapters, exponential models can be found by fitting data to them. As you may already be aware, exponential functions take the form y = abx, where an is the value of y at x = 0 and b is the growth factor over each unit of time. Based on an equation like this one, the exponential model represents the degradation failure process: Y = deterioration; T = time; A and B = parameters to be calculated using the regression approach based on historical data. An expansion within a population that happens at the same pace across time is represented by the function of exponential growth. It is reasonable to suppose that data grows exponentially as populations double or triple in size.
Graph all the points on a graph. Then from the graph, we can find that at 7 minutes the temperature is 39.7°C.
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Answer: 38.2 degrees
Step-by-step explanation:
enter into desmos
use y1 ~ abx2
then input numbers provided
(22.9178)1.07564^7
equals 38.18049
round 38.2
what is the future amount of 12,000 invested for 5 years at 14% compounded monthly?
Answers
The total amount accrued, principal plus interest, with compound interest on a principal of $12,000.00 at a rate of 14% per year compounded 12 times per year over 5 years is $24,067.32.The amount of the initial loan, or principal, is multiplied by one plus the annual interest rate raised to the number of compound periods minus one to determine compound interest.
what is compound interest?To begin, change R from a percentage to a decimal, using the formula:
r = R/100 r = 14/100
r = 0.14 rate per year;
Next, find A by solving
A = P(1 + r/n)nt A = 12,000.00(1 + 0.14/12)(12). (5)
A = 12,000.00(1 + 0.011666666666667)(60) (60)
A = $24,067.32
Summary: The total amount accrued, principal plus interest, with compound interest on a principal of $12,000.00 at a rate of 14% per year compounded 12 times per year over 5 years is $24,067.32.
The amount of the initial loan, or principal, is multiplied by one plus the annual interest rate raised to the number of compound periods minus one to determine compound interest. You will then be left with the loan balance plus compound interest.
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Convert 17 weeks into days
Answers
Answer:
119days
Step-by-step explanation:
1 week= 7 days
take week as w
so 1w=7 or w=7
now 17 weeks=??
17w=??
w=7 so input in above statement:
17(7)=119days
Answer: 119 days
Step-by-step explanation:
We can set up a dimensional analysis problem to solve.
[tex]\displaystyle 17 \;\text{weeks}\;(\frac{7\;\text{days}}{1\;\text{week}} )[/tex]
The units of [tex]\frac{weeks}{weeks}[/tex] cancel out, leaving us with days. Since we are being asked to find days, this will leave us at the right point.
[tex]\displaystyle \frac{17*7}{1} =119\;\text{days}[/tex]
write equations for each line given the following points. Remember you must first find the slope and then determine the Y intercept, then write out the equation in slope intercept form. Remember if the Y intercept b is zero, then, there is no need to put it there, and if the slope is one, then you only need to write x, not 1 X
(-3,2) and (5,7)
Answers
The slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is: [tex]y = \frac{5}{8} x + \frac{1}{8}[/tex]
What is the slope-intercept form?One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills. There are several ways to solve the straight line equation given as,Slope-intercept formPoint slope formTwo-point formIntercept formCalculation
from ( - 3, 2) and (5, 7)
slope(m) = [tex]\frac{y_{2}- y_{1} }{x_{2}- x_{1} }[/tex]
[tex]=\frac{7 - 2}{5 - (-3)}[/tex]
[tex]= \frac{5}{8}[/tex]
from slope-intercept equation
⇒y = mx+ c
⇒( - 3, 2) , [tex]2 = \frac{5}{8} * (-3) + b[/tex]
⇒[tex]2 = \frac{15}{8} + b[/tex]
⇒[tex]2 - \frac{15}{8} = b[/tex]
⇒[tex]\frac{16+15}{8} = b[/tex]
⇒[tex]\frac{31}{8} = b[/tex]
Therefore, the slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is :
⇒[tex]y = \frac{5}{8} x +\frac{31}{8}[/tex]
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The slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is:
What is the slope-intercept form?One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line.
When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).
The equation of a line is the equation that each point on the line fulfills. There are several ways to solve the straight line equation given as,
Slope-intercept form
Point slope form
Two-point form
Intercept form
from ( - 3, 2) and (5, 7)
slope(m) = y²-[tex]y^{1}[/tex]/x²-[tex]x^{1}[/tex]
=7-(-2)/5-(-3)
=5/8
from slope-intercept equation
⇒y = mx+ c
⇒( - 3, 2) , 2=5/8*(-3)+b
⇒2=15/8+b
⇒2-15/8=b
⇒16+15/8
31/8=b
Therefore, the slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is :
⇒y=5/8x +31/8
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hi i need some help with this math problem
Answers
1 is value of x in given function.
What is the definition of a function?
An association between a value from the set of the first components of the ordered pairs and a specific value from the set of the second components is known as a function. a relationship between a set of inputs and a set of potential outputs, where each input is connected to only one possible output.f(x) = 2x + 4/6
put x = - 2 in equation
f(-2) = 2 * -2 + 4 /6
= -4 + 4 /6
= 0/6
= 1
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Please Help!
Solve the inequality and graph it’s solution.
Answers
Answer:
Step-by-step explanation:
You have to multiply both sides by 3 so its -9>-5+n. Then add each side by 5. The answer is n<-4 (D)
Answer:
D) n<-4
Step-by-step explanation:
Kenneth has c toy cars. Jennifer has 3 times as many toy cars as Kenneth. Write an expression that shows how many toy cars Jennifer has.
Answers
Answer:
3c
3c mean 3xc
but just write 3c
I NEED HELP PLEASEEEEE ASAPPPPPPP
Answers
Answer:
7x+40=180
Step-by-step explanation:
(5x+40)+(2x)=180
7x+40=180
if you were to solve
subtract 40 from each side
7x=140
divide both sides by 7
x=20
check your answer
5(20)+40+2(20)=180
100+40+40=180
this is correct
hope this helps..and with future questions if you need to solve it
To find BCD
we know that C is 40 degrees and we know that triangle is also 180
we can also see that B is a right triangle or 90 degree
so 90+40+A=180
130+A=180
subtract 130 from 180
A=50
Matteo buys a basil plant that is 22 cm tall and grows 1/2 a centimeter every day.
A. Write an equation that can be used to solve for the number of days until the plant has a height of 30 cm. Use d to represent the number of days. Label each part of your equation with what it represents.
B. How much does the plant still have to grow?
C. Solve for the value of d. What does this value represen in this problem?
PLEASE SOLVE ALL
Answers
The equation that can be used to solve for the number of days until the plant has a height of 30 cm is 22+(d-1)0.5 = 30 where d represents the number of days and the value of d is 17.
According to the question,
We have the following information:
Matteo buys a basil plant that is 22 cm tall and grows 1/2 a centimeter every day.
Now, we have the following arithmetic progression with common difference, denoted by d:
22, 22.5, 23, 23.5, ...
Formula used to find the nth term:
an = a+(n-1)d where a is the first term
A) 22+(d-1)0.5 = 30
B) The plant still have to grow 8 cm because the difference between 30 and 22 is 8 cm.
C) Value of d:
22+(d-1)0.5 = 30
22+0.5d-0.5 = 30
21.5+0.5d = 30
0.5d = 30-21.5
0.5d = 8.5
d = 8.5/0.5
d = 17
Hence, the equation that can be used to solve for the number of days until the plant has a height of 30 cm is 22+(d-1)0.5 = 30 where d represents the number of days and the value of d is 17.
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a supermarket employee wants to construct an open-top box from a 14 by 30 in piece of cardboard. to do this, the employee plans to cut out squares of equal size from the four corners so the four sides can be bent upwards. what size should the squares be in order to create a box with the largest possible volume?
Answers
The size of the squares should be 3 inches in order to create a box with the largest possible volume.
If squares of equal sizes are to be cut out from the four corners so the four sides can be bent upwards, then the length of these squares will be the height of the box. Also twice of this length subtracted from the initial length and width of the material will be the new length and width of the box, respectively.
let x = length of square to be cut = height of the box
length of the box = 30 - 2x
width of the box = 14 - 2x
The volume of the box, which is a rectangular prism, is the product of the length, height and width.
V = l x w x h
V = (30 - 2x)(14 - 2x)(x)
V = 420x - 88x² + 4x³
To obtain the largest volume possible, the first derivative of the volume should be equal to zero.
V'(x) = 0
V = 420x - 88x² + 4x³
420 - 176x + 12x² = 0
Simplify and solve for the value of x.
12x² - 176x + 420 = 0
3x² - 44x + 105 = 0
(3x - 35)(x - 3) = 0
x = 35/3 ; x = 3
Check each value.
When x = 35/3 = h
l = 30 - 2x = 20/3
w = 14 - 2x = -28/3 ( length should be positive)
When x = 3 = h
l = 30 - 2x = 24
w = 14 - 2x = 8
Hence, the length of square to be cut is 3 in.
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1 can go on saturday and 14 can go on sunday; some of them can go on both days. how many people can only go to the game on saturday? 6
Answers
Answer:
No solution
Step-by-step explanation:
The reason why I say this problem has no solution is due to the fact that it says only one person may go on Saturday yet some fraction of the people between the numbers 1 - 14 can go. We have no idea what this fraction is, leading to a paradox of multiple equations and guesses desperately trying to figure out the number. Thus, the problem has no solution.
Hope this helps.
Karl bought 1.6 pounds of oranges and 2.4
pounds of pears. They each cost $1.48 per pound
Use properties to find the total cost.
Answers
Answer:
$5.92
Step-by-step explanation:
1.6 lbs. + 2.4 lbs. = 4 lbs.
4 x 1.48 = 5.92
Since it doesn't specify whether the oranges and apples cost differently you can add both of them. Then you multiply it by 1.48 because that's the cost per pound.
Multiply 2.9x and 5x.
(Multiplying Linear Expressions LC)
14.5x2
7.9x2
14.5x
7.9x
Answers
Multiplication of 2.9x and 5x gives 14.5x²
How to multiply algebraic expressions?The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants
Given: 2.9x and 5x
To multiply 2.9x and 5x, multiply the numbers and multiply the letters:
2.9x × 5x = 2.9 × 5 × x × x = 14.5x²
Therefore, 2.9x multiplied by 5x is 14.5x²
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can you give me an answer i don't know how to do this
Answers
Answer:
It should be ≈ 6,6
calculated the angle <CAB and both are 90°. But that would mean BC is wrong
Jamie has a table top that he wants to cover in contact paper. The table top has the following dimensions. Length: 3.5 ft. Width: 3.5 ft. Height: 0.25 ft. How many square feet of contact paper does he need to cover the entire table top?
Answers
The area of the contact paper required to cover the entire tabletop is 12.25 square feet.
Jamie has a tabletop that he wants to cover with contact paper. The length, width, and height of the tabletop are 3.5 feet, 3.5 feet, and 0.25 feet, respectively. We need to calculate the area of the contact paper required to cover the entire tabletop.
Let the area of the tabletop be represented by the variable "A". We need to calculate the area of only the top surface of the table. The table is rectangular in shape. The area of the tabletop must be the product of the length and the width of the table.
A = 3.5×3.5
A = 12.25
Hence, the area of the tabletop is 12.25 square feet.
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answer the question please i would appreciate it man
Answers
The scientific notation representation is 2.6 x [tex]10^{-2}[/tex].
What is scientific Notation?Scientific notation is a way to present extremely large or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place after the decimal. This makes it challenging to represent a small number of integers in their enlarged form. We therefore employ scientific notations.
Given:
(0. 00032) (5.2 x [tex]10^6[/tex])/ 6.4 x [tex]10^5[/tex]
Now, solving the above expression
= 0.001664 x 10² / 6.4
= 0.00026 x 10²
= 2.6 x [tex]10^{-2}[/tex]
Hence, the scientific notation representation is 2.6 x [tex]10^{-2}[/tex].
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Help me for this question
Answers
Which number is greatest?
57
10
O 5. 84
51
√33, 5. 84,
0 5. 7
OV33
51
9
Answers
The greatest number among the given numbers is= 57
What are greatest numbers?largest and smallest number formation We are aware of how to list the numbers in both ascending and descending order. The highest number is created by placing the specified digits in ascending order, and the lowest number is created by placing them in descending order, as we have already learned.. A number has more places when the digit at the very left is in that position. Therefore, to increase the value of the number, the largest digit should be positioned at the very left of the number.The digit 0 is never written at the very leftmost position when one of the given digits is 0, but rather in the second place from the left to obtain the smallest number.learn more about greatest numbers click here:
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please give me the right answer on this so I can turn it in to my math teacher
Answers
Answer: 16/18 and 10/16
Step-by-step explanation: The least common denominator would be 18 and 16 because you would multiply by 2.
Hoped This Helped!
the hypotenuse of a triangle is 4x one of the legs . the other leg in 3(sqrt 5 units. find the length of the hypotenus?
Answers
The length of the hypotenuse is 4√3 units.
Given that hypotenuse is 4 times the length of one leg of a triangle. So here we can assume that length to be x. Hence the hypotenuse length is 4x. To calculate hypotenuse we have the formula a²=b² + c², where b and c are two sides of the triangle and a is the hypotenuse. If we put these values in the formula we get,
16x² = x² + (3√5)²
15x² = 45
x² = 3
x = ±√3
Since length cannot be negative, the final value of x = √3, and since the length of the hypotenuse was 4x, the final value of the hypotenuse is 4√3.
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The Venn diagam represents the
information from the following sets.
= {Prime numbers less than 38}
R = {2, 3, 5, 17, 19, 37}
S = {3, 5, 7, 11, 13, 37}
R
17 5
2
19 37
3/13
S
11
231 23
Find P(RUS)
P(RUS) =
Answers
=======================================================
Explanation:
The U refers to set union. We combine the elements of set R and set S together in one big set. Toss out any duplicates. Sorting the items is optional, but I recommend it.
R U S = {2, 3, 5, 17, 19, 37} U {3, 5, 7, 11, 13, 37}
R U S = {2, 3, 5, 17, 19, 37, 3, 5, 7, 11, 13, 37}
R U S = {2, 3, 5, 7, 11, 13, 17, 19, 37}
This list of values consist of items in set R, set S, or both.
There are 9 items in set R U S.
This is out of 12 items total in the universal set rectangle.
The probability of randomly selecting something from set R U S is 9/12 = 3/4
help meeeeeeeeeeeeeee pleaseee
Answers
The vertex of the curve is at (-2, -4) and the axis of symmetry is at -2
The curve opens downward.
from, the graph, the roots of the equation are -4 and 0
so if -4 is a root, (x + 4) is a factor and if 0 is a root, then x is a factor.
The equation of the curve is the product of the factors of the curve which is y = x(x + 4)
y = [tex]x^{2}[/tex] + 4x
the x coordinate of the vertex = -b/2a = axis of symmetry
where a is the coefficient of [tex]x^{2}[/tex] and b is the coefficient of x
so a = 1, b = 4
x coordinate of vertex = -4/2 = -2
substitute x = -2 into y = [tex]x^{2}[/tex] + 4x to find the y-coordinate of the vertex
y = [tex](-2)^{2}[/tex] + 4(-2)
y = 4 -8
y = -4
vertex is (-2, -4)
The axis of symmetry is -b/2a which is -2
The curve opens downward as the vertex is at -4
In conclusion, the vertex of the parabola is (-2, -4) and the axis of symmetry is -2 and the parabola opens downward
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State the value of the two square numbers closest to 55. Hence, show that 55 is not a square number.
Answers
Answer:
7.416 is the answer
annual revenue for corning supplies grew by 5.5% in 2007; 1.1% in 2008; -3.5% in 2009; -1.1% in 2010; and 1.8% in 2011. what is the mean growth annual rate over this period? round your answer to four decimal places. do not round intermediate calculations.
Answers
The mean yearly growth rate for this period is 0.0036.
Define annual growth rate.The average annualized return of a portfolio, asset, or cash flow over time is known as the average annual growth rate, or AAGR. The basic arithmetic mean of a set of returns is used to calculate AAGR.
The change in a measurement's value over a year is known as the annual growth rate (AGR).
The sum of the growth rates for each year divided by the total number of years yields the mean growth annual rate.
Where the annual growth rate is calculated as follows: 5.5 + 1.1 - 3.5 - 1.1 + 1.8 = 3.8%
And the total number of years is 5.
Then ,
The average annual growth rate for this time period is = 3.8/5
Over this time span, the average yearly growth rate was 0.76%.
Make a decimal conversion
= 0.76% = 0.0076
Therefore, the mean yearly growth rate for this period is 0.0036.
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You have 84,000 grams of a radioactive kind of tellurium. How much will be left after 75
minutes if its half-life is 25 minutes?
grams
Answers
Answer:
10,500 g
Step-by-step explanation:
Half-life is the length of time it takes for half of the radioactive atoms of a radionuclide to decay. In this scenario, the amount of radioactive atoms is halved after 25 minutes. After 75 minutes, then, the amount of radioactive atoms is halved three times. Therefore:
1st half-life: [tex]84000\text{ g}\div{2}=42000\text{ g}[/tex]
2nd half-life: [tex]42000\text{ g}\div{2}=21000\text{ g}[/tex]
3rd half-life: [tex]21000\text{ g}\div{2}=10500\text{ g}[/tex]
Write this ratio another way.
120/150
Answers
The ratio 120/150 represented in the simplest form is 4 : 5 .
The given ratio is 120 /150 .
Now if we write the expression in the form of the simplest ratio we have to divide the ratio by the highest common factor.
The HCF of the number is 30. Hence the ratio in simplest form will be
120÷30 : 150÷30 = 4 : 5 .
By comparing two amounts of the same unit and establishing the ratio, we can work out how much of one quantity is contained in the other. Two categories of ratios exist.
Ratio can be thought of as an ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or as the value that this fraction represents.
Ratios of counts are rational numbers that can also be rational numbers and are occasionally expressed by (non-zero) natural numbers.
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What is the additive in verse of 16 5/7?
Answers
Answer:
the additive inverse of 16 5/7 IS 26/7
Referring to the figure, find the perimeter of the regular polygon
shown. [Note: do not approximate the value of any radicals; thus, if you
obtain, for example, 45 times the square root of 3, simply type 45SQR(3)
as your final answer.]
Referring to the Fig. in Question #1, find the area of the regular polygon
shown. [Note: do not approximate the value of any radicals; thus, if you
obtain, for example, 45 times the square root of 3, simply type 45SQR(3)
as your final answer.]
Answers
Answer:
Perimeter = 18√3 = 18SQR(3)
Area = 27√3 = 27SQR(3)
Step-by-step explanation:
The sides of a regular polygon are congruent.
Therefore, as the triangle is a regular polygon, it is an equilateral triangle since its sides (and interior angles) are congruent.
The interior angles of a triangle sum to 180°. Therefore, each interior angle of the equilateral triangle is 60°.
Therefore, the right triangle formed inside the equilateral triangle by the perpendicular bisectors is a 30-60-90 triangle with hypotenuse of 6 units.
The ratio of the side lengths of a 30-60-90 triangle is b : b√3 : 2b, where:
b = shortest side opposite the 30° angle.b√3 = side opposite the 60° angle.2b = longest side (hypotenuse) is opposite the right angle.As the hypotenuse of the 30-60-90 right triangle is 6 units:
[tex]2b = 6 \implies b=3[/tex]
Therefore, the length of the longest leg of the right triangle is 3√3.
As this is half the length of one side of the equilateral triangle:
[tex]\implies \sf Perimeter = 6 \times 3 \sqrt{3}=18\sqrt{3}\; units[/tex]
Heron's Formula allows us to find the area of a triangle in terms of its side lengths.
Heron's Formula
[tex]\sf Area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]
where:
a, b and c are the side lengths of the triangle.s is half the perimeter.Given:
Each side length = 6√3 unitsHalf perimeter = 9√3 unitsSubstitute these values into the Heron's formula to calculate the area of the equilateral triangle:
[tex]\begin{aligned}\implies \sf Area &= \sf \sqrt{9\sqrt{3}(9\sqrt{3}-6\sqrt{3})^3}\\ &= \sf \sqrt{9\sqrt{3}(3\sqrt{3})^3}\\ &= \sf \sqrt{9\sqrt{3}(81\sqrt{3})}\\&=\sf \sqrt{2187}\\&=\sf \sqrt{729 \cdot 3}\\&=\sf \sqrt{729}\sqrt{3}\\&=\sf 27\sqrt{3} \;\;units^2\end{aligned}[/tex]