Can someone help me figure this out: Factor 12y^2-27? I keep getting the steps confused.

Answers

Answer 1

Factor out the gcf first.

3(4y^2-9)

The binomial inside is a perfect square so keep factoring.

3(2y+3)(2y-3)

The pair of binomials cannot be further factored so stop there.

Related Questions

Confused. Please help thank you!

Answers

#6 is using using ratios:

7/2x+4 = 4/x+3 =

8x+16 =7x+21 =

8x=7x+5 =

x=5

AC = 2(5)+4= 14 + 5+3=8, 14+8 =22

ratio of known sides 9/4 =2.25 now multiply other 2 sides by 2.25

7*2.25 = 15.75

9*2.25=20.25

perimeter = 9 +15.75+20.25 = 45

Mateo is studying a human hair with a diameter of 6.5 x 10^-4 inches and a horse hair with a diameter of 1.3 x 10^-3 inches. Which statement is true?

A.The horse hair is 2 times as thick as the human hair.

B.The horse hair is 5 times as thick as the human hair

C.The human hair is 2 times as thick as the horse hair

D.The human hair is 5 times as thick as the horse hair

Answers

[tex] \cfrac{1.3*10^{-3}}{6.5*10^{-4}}= 0.2*10^1=2[/tex]

A.The horse hair is 2 times as thick as the human hair.

Answer:

A.The horse hair is 2 times as thick as the human hair.

Step-by-step explanation:

We have been given that Mateo is studying a human hair with a diameter of [tex]6.5\times 10^{-4}[/tex] inches and a horse hair with a diameter of [tex]1.3\times 10^{-3}[/tex] inches.

Since proportions states that two fractions are equal, So we will use proportions to solve our given problem.

[tex]\frac{\text{Diameter of horse hair}}{\text{Diameter of human hair}}=\frac{1.3\times 10^{-3}}{6.5\times 10^{-4}}[/tex]

[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{-3}}{6.5\times 10^{-4}}\times \text{Diameter of human hair}[/tex]

Now we will quotient rule of exponents to simplify our given problem.

[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{-3--4}}{6.5}\times \text{Diameter of human hair}[/tex]

[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{-3+4}}{6.5}\times \text{Diameter of human hair}[/tex]

[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{1}}{6.5}\times \text{Diameter of human hair}[/tex]

[tex]\text{Diameter of horse hair}=\frac{13}{6.5}\times \text{Diameter of human hair}[/tex]

[tex]\text{Diameter of horse hair}=2\times \text{Diameter of human hair}[/tex]

We can see that the diameter of horse hair is 2 times the diameter of human hair. Therefore, the horse hair is 2 times as thick as the human hair and option A is the correct choice.

Roger owns a one acre piece of land . The length of the land is 484 feet. What is the width of his property

Answers

1 acre = 43560 square feet

43560 = 484 * X

X=43560/484 = 90

the width = 90 feet

Answer:

90 feet

Step-by-step explanation:

How many ways can 8 books be arranged on a shelf? Show all of your work for full credit.

Answers

Answer:

40,320.

Step-by-step explanation:

We are asked to find the number of ways in which 8 books could be arranged on a shelf.

The 1st could be arranged in 8 ways. Since one place is filled, so 2nd book could be arranged in 7 ways.

Similarly, the 3rd book could be arranged in 6 ways as first two places are already taken. This process will go on.

So the 8 books can be arranged in [tex]8\times 7 \times 6\times5\times4\times3\times2\times1=8![/tex]

[tex]8!=40,320[/tex]

Therefore, 8 books could be arranged in 40,320 ways.

The number of ways to arrange 8 books on a shelf is 40,320.

We have to determine

How many ways can 8 books be arranged on a shelf?

According to the question

There is total number of books is 8.

Then,

The arranging the way of 8 books also be 8.

If one of the 8 books is placed in the first place, only 7 of them can be placed in 2nd place. In 3rd place, only 6 of them can be placed.

This continues all the way to 1.

A permutation is an arrangement of objects in a particular way.

Then,

The number of ways to arrange 8 books on a shelf is,

[tex]= 8!\\ \\ = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\\ \\ =40,320 [/tex]

Hence, The number of ways to arrange 8 books on a shelf is 40,320.

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How do I find the terms?

Answers

A(n+1) = A(n)+4 <--- is a way to say, to get the next term, ADD 4 to the current one, whist A(1) = -2, is a way to say, the first term is -2.

[tex]\bf n^{th}\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ d=4\\ a_1=-2\end{cases} \\\\\\ \begin{array}{llll} term&value\\ ------&------\\ 2&a_2=-2+(2-1)4\\ 3&a_3=-2+(3-1)4\\ 4&a_4=-2+(4-1)4\\ 5&a_5=-2+(5-1)4 \end{array}[/tex]

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

A(n)= 1/4 * A(n) is just a way of saying, you get the next term by multiplying the current one by 1/4, and A(1) = 8, simply means the first term's value is 8.

[tex]\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=\frac{1}{4}\\ a_1=8 \end{cases} \\\\\\ \begin{array}{llll} term&value\\ ------&------\\ 2&a_2=8\left( \frac{1}{4} \right)^{2-1}\\\\ 3&a_3=8\left( \frac{1}{4} \right)^{3-1}\\\\ 4&a_4=8\left( \frac{1}{4} \right)^{4-1}\\\\ 5&a_5=8\left( \frac{1}{4} \right)^{5-1}\\ \end{array}[/tex]

A jacket that regularly cost $40 is on sale for $32 what is the percent decrease in the price of the jacket?

Answers

from 40 to 32, is just 8 bucks, so the jacket went from 40 to 8, so is discounted by 8 bucks.

now, if we take 40 to be the 100%, how much is 8 off of it in percentage?

[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 40&100\\ 8&x \end{array}\implies \cfrac{40}{8}=\cfrac{100}{x}[/tex]

solve for "x".

20% off the $40 dollar jacket.

To which part of the prism are the arrows pointing

Answers

The arrows are pointing in the vertices of the prism. Vertices are the corners of an object which faces are the 2 dimensional sides of an object and the edges are the lines link 2 vertices. Vertex classically defines a corner or a point where lines met. Vertex is likewise from time to time used to designate the 'top' or high point of to some degree. Another example such as the vertex of an isosceles triangle which is the 'top' angle conflicting its base.

Melanie is flying from washington,
d.c., to seattle. her flight leaves at 10
a.m. when her plane lands, the pilot announces that it is 2 p.m. in seattle. how long did her flight take

Answers

In order to answer this, you must know how to read or tell time. I'm sure you do. The typical format of time is the 12-hour format. That is 12 hours in the morning and 12 hours in the afternoon. You just simply have to count from 10 in the morning, until you reach 2 in the afternoon. That would be 11, 12, 1 and 2. You passed 4 numbers in the clock. Therefore, her flight took 4 hours.

f(x) = 16x4 – 81 = 0 Select all of the zeroes of the function.
3/2
-3/2
3/2i
-3/2i

Answers

the way to figure this one out is move the 81 over to the other side so you have the equation 16x^4 = 81. Since 81 is not divisible by 16 you have to think of another way to simplify. 16 is a perfect square, x^4 is a perfect square, and 81 is a perfect square. So take the square root of both sides to begin the simplification. 4x^2 = 9. Divide both sides by 4 to get x^2 = 9/4. 9 and 4 are both perfect squares, so undo the square on the x by taking the square root of both sides: x = +/- 3/2.

Here we want to find all the zeros of the function f(x) = 16*x^4 - 81.

The zeros are:

x = 3/2x = -3/2x = (3/2)*ix = (-3/2)*i

First, for a given function f(x), we define the zeros as the values of x such that:

f(x) = 0.

Then we must solve:

f(x) = 16*x^4 - 81 = 0

Solving this for x leads to:

16*x^4 = 81

x^4 = 81/16

x^2 = ±√(81/16) = 9/4

x = ±√±(9/4) = ±3/2 and ±(3/2)*i

So there are 4 zeros, and these are:

x = 3/2x = -3/2x = (3/2)*ix = (-3/2)*i

Where the two complex zeros come from evaluating the second square root on -9/4.

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Which expression is equivalent to 34 ⋅ 3−9?

1 over 3 to the 13th power
1 over 3 to the 5th power
35
313

Answers

313 because you multiply then you subtract

Answer:

b.1 over 3 to the 5th power.

Step-by-step explanation:

We are given that an expression

[tex]3^4\cdot 3^{-9}[/tex]

We have to find that which expression is equivalent to given expression

[tex]3^4\cdot 3^{-9}[/tex]

We know that [tex]a^b+a^c=a^{b+c}[/tex]

Using this identity

Then, we get [tex]3^4\cdot 3^{-9}=3^{4-9}=3^{-5}[/tex]

[tex]3^4\cdot 3^{-9}=\frac{1}{3^5}[/tex]

Using [tex]a^{-b}=\frac{1}{a^b}[/tex]

Hence, option b is true.

Answer:b.1 over 3 to the 5th power.

If you have a $1 bill a 5 bill a 10 bill and a 20 bill how many different sums of money

Answers

You need to find every combinaison of bills.

ex : $1 + 10$ or 5$+10$

I takes for ever to list all the possibilities so you need to think about probabilities to chose a bill.

For each bill, you can add it to your sum or not; so it gives you 2 possibilities; you do that for each bill and you multipliate each what gives you :

2 * 2 * 2 * 2 = 16 different sums

Are the traingles congruent? Why or why not?

Yes, A ≅ D and AB ≅ DE
Yes, they are congruent by either AAS or ASA.
No, C is not congruent to any angle in DEF.
No, the congruent sides do not correspond.

Answers

the answer is A)
Yes, A ≅ D and AB ≅ DE

Yes , A ≅ D and AB ≅ DE

Yes, they are congruent by either AAS or ASA.

What are Congruent Triangles?

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

• Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

• Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

• A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

From the given data ,

AB ≅ DE

and , ∠BAC = 33°

∠EDF = 33°

Therefore by rules of congruent triangles

The two angles are the same and the corresponding sides are same

Hence , The two triangles ΔABC and ΔDEF are congruent

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How old am i if i was born in 05/22/1965?

Answers

Subtract the year you were born in from this year.

2017 - 1965 = 52

And since May already passed (05/22), you're birthday already passed.

So you are 52 years old if you were born in 05/22/1965.

Answer:

In 2021 you would be 56 or 55 years old

Step-by-step explanation:

2021-1965=56 or the other way you could do it 52+4 because the other person said you would be 52 in 2017 so 4 years after you would be 55 or 56

(20 points) You are writing a research paper on plant cells. You got 48,600,000 results on the online search. How do you write 48,600,000 in scientific notation?

Answers

i'm pretty sure the answer is D

[tex]48,600,000=4.86*10,000,000 = 4.86*10^7[/tex]

Grade 12 data!!

18% of a population eats yogurt daily. What is the probability that, in a group of 10 people, 4 of them eat yogurt daily?
0.0032 0.072 0.067 0.00032

Answers

my opinion is 0.0032 hope it helps

Answer:

The probability that, in a group of 10 people, 4 of them eat yogurt daily is 0.067

Step-by-step explanation:

In this case we can apply a Binomial distribution in which there are n events and every event have a probability p to get a success. Then, the probability of x is:

[tex]P(x)=nCx*p^{x}*(1-p)^{n-x}[/tex]

Where x is the number of people who eat yogurt daily, n is the total number of people and p is the probability of eats yogurt daily.

Additionally nCx is calculated as:

[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]

So, for the question we know that:

n=10

p=0.18

x=4

Replacing this values on the equation, we get:

[tex]P(4)=10C4*0.18^{4}*(1-0.18)^{10-4}[/tex]

P(4)=0.067

Finally, the probability that, in a group of 10 people, 4 of them eat yogurt daily is 0.067

Perform the following food service calculation. Size of juice can = 54 oz. Portions of juice served = 6 oz. Number of cases used = 2 Number of cans per case = 12 How many guests can be served? 54 216 1,944 7,776

Answers

2 cases x 12 cans = 24 cans

24 cans x 54 oz per can = 1296 oz

1296 oz / 6 oz per serving = 216 guests served

Answer: 216 guests.

Step-by-step explanation: We are given total number of cases = 2 Number of cans.

Number of cans per case = 12 cans.

Total number of cans in 2 cases = 2 cases × 12 cans = 24 cans

Each can contain = 54 oz of juice.

24 cans would contain total = 24 cans × 54 oz per can = 1296 oz juice.

Number of oz per serving = 6 oz.

Total number of guests can be served = 1296 oz / 6 oz per serving = 216 guests.

The function f(x) is represented by this table of values .Match average rate of change of f(x) with corresponding intervals

Answers

Note:
If fx(x) changes from f(x₁) to f(x₂), the rate of change is
Rate = [f(x₂) - f(x₁)]/(x₂ - x₁)

From the table, we can compute rates of change as follows:
Change in x Change in f(x) Change in x Rate
----------------- -------------------- ----------------- ---------
[-4,-2] 0 - (-12) = 12 0 - (-2) = 2 6
[-2, 1] 3 - 0 = 3 1 - (-2) = 3 1
[-3, 1] 3 - (-5) = 8 1 - (-3) = 4 2
[-4, 0] 4 - (-12) = 16 0 - (-4) = 4 4

You give your friend a head start of 20 feet in a race. A linear equation representing your friend’s progress (in feet) after x seconds is y = 9x + 20. A linear equation representing your progress (in feet) after x seconds is y = 9x. Will you catch up to your friend? Explain.

Answers

No. You are running the same speed as your friend and your friend has a head start.
By looking at the equation : The two lines does not have an intersection point .

To catch up to your friend or not in a race explained with equations and steps.

The question is: Will you catch up to your friend? Explain.

Step-by-step explanation:

Friend's progress equation: y = 9x + 20

Your progress equation: y = 9x

To catch up, set the equations equal: 9x + 20 = 9x

Solve for x: 20 = 0 (This equation has no solution)

You will not catch up to your friend.

Cannon took out a mortgage for $85,290 on his new house. If the interest rate is 8.5 percent and the loan is for 25 years, how much will he pay monthly if he must pay $8.05 per $1,000?

Answers

Number of thousands on the amount of the loan is
85,290÷1,000=85.29

Monthly payment is
85.29×8.05=686.58

Answer:

The answer is $686.584

Step-by-step explanation:

Given is, Cannon pays $8.05 per month for every $1,000, so we have a ratio: 8.05 / 1000

Now, we will find the second ratio which is an unknown payment per month over the price: x / 85290

Equaling them to solve for x :

[tex]\frac{8.05}{1000}=\frac{x}{85290}[/tex]

[tex]1000x=8.05*85290[/tex]

[tex]1000x = 686584.50[/tex]

So, x = 686.584

Hence, the answer is $686.584

The table below shows the surface area y, in square feet, of a shrinking lake in x days:

Time (x)
(days) 5 10 15 20
Surface area (y)
(square feet) 90 85 70 61

Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and surface area of the lake. [Choose the value of the correlation coefficient from −1, −0.98, −0.5, −0.02.] (4 points)

Part B: What is the value of the slope of the graph of surface area versus time between 15 and 20 days, and what does the slope represent? (3 points)

Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)

Answers

The scatter graph of the data is shown in the first picture below

The 'line of best fit' shows a negative gradient

Part A: The most likely coefficient is -0.98.
If the coefficient is -1, then each point would be exactly on the straight line (which they are not as shown on the graph). The graph however still shows a strong negative coefficient. It can be seen from the close distance of each point from the line of best fit. So -0.5 and -0.02 is unlikely as they show weak negative correlation

Part B: Refer to the second picture to see the horizontal and vertical distance between day 15 and day 20

The horizontal distance is 5 units
The vertical distance is read between 61 and 71.5, hence it's 10.5
The slope = Vertical distance ÷ Horizontal Distance = 10.5÷5 = 2.1
The 'downhill' slope shows a negative gradient, hence the value of the slope is -2.1
The value of the slope shows that the surface area of the lake shrinks by 2.1 for every one day

Part C: The data in the table represents the relation between two variables. Since one variable doesn't cause the change in the other variable, the data table represents correlation rather than a causation.

Assume that all chickens have 4725 feathers. if it takes you 5.6 seconds to pluck 24.8 feathers, how many hours would it take you to defeather 7728 chickens? answer in units of hours.

Answers

This question needs to be solved in steps rather than all at once. That being said, will start by find "feathers per second" or f/s.

So it takes 5.6 seconds to plucks 24.8 feathers. To find f/s we needs to find 24.8 divided by 5.6 which is 4.429f/s.

Now we need to find how long it will take to pluck one entire chicken. Since it takes us one second to pluck 4.429 feathers, we need to divide 4,725 by 4.429 to find how many seconds it will take us to pluck an entire chicken. This value is 1,066.832 seconds.

Since it takes us 1,066.832 seconds to pluck one chicken, it will take us
7,728 • 1,066.832 seconds to pluck 7,728 chickens. This value is 8,244,477.696 seconds.

To convert seconds to hours, we need to divide by 60 to get minutes and then divide by 60 again to reach our desired unit of measurement: hours

8,244,477.696 / 60 / 60 = 2,290.133 hours

Final answer:

It would take approximately 2284.722 hours to defeather 7728 chickens.

Explanation:

To find out how many hours it would take to defeather 7728 chickens, we need to consider the time it takes to pluck a certain number of feathers. We are given that it takes 5.6 seconds to pluck 24.8 feathers. First, we find the time it takes to pluck one feather by dividing the time by the number of feathers: 5.6 seconds ÷ 24.8 feathers = 0.2258 seconds per feather.

Next, we find the total number of feathers on 7728 chickens by multiplying the feather count per chicken by the total number of chickens: 4725 feathers/chicken × 7728 chickens = 36,396,000 feathers.

Finally, we find the total time it would take to defeather all the chickens by multiplying the time per feather by the total number of feathers: 0.2258 seconds/feather × 36,396,000 feathers = 8,224,996.8 seconds. Converting this to hours, we divide by the number of seconds in an hour: 8,224,996.8 seconds ÷ 3600 seconds/hour ≈ 2284.722 hours.

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Alicia drove 265 miles in 5 hours What is the average rate that she traveled 49 miles per hour 51 miles per hour 53 miles per hour 55 miles per hour

Answers

265 / 5 = 53 miles per hr

Simplify.

6m+7n+5m−3n

15mn

11m + 10n

m + 10n

11m + 4n

Answers

to simplify combine all like terms

6m +5m = 11m

7n-3n = 4n

so it would be 11m+4n

ms johnson and ms smith were folding report cards to send home to parents. the ratio of the number of report cards ms johnson folded to the number of report cards ms smith folded is 2:3. At the end of the day , ms Johnson and ms smith folded at total of 300 report cards. How many did each person fold?

Answers

First you would divide 300 by 5, you would add 2 and 3 together, to get 60. Then multiply 2 and 3 by 60 and you would get 120 and 180. Add those two together and you will get 300. So Ms. Johnson folded 120 report cards while Ms. Smith folded 180 report cards.

If you put down 20% on a $7000 car and pay monthly payments of $109.40 for 60 months, what is the total price of the car?

Answers

$7000 x 20% = $1400
$109.40 x 60 = $6564
$1400 + $6564 = $7964

Answer:

7964

Step-by-step explanation:

The measure of ______________ in a circle is half the measure of the intercepted arc.

A. a central angle
B. an interior angle
C. an inscribed angle

Answers

YES slay5 is correct the answer is : C. an inscribed angle

Answer: C. An inscribed angle

Step-by-step explanation:

Central angle is an angle that is subtended by an arc in a circle, it is also known as the arc's angular distance.

Interior angle is an angle between two sides inside a polygon or a shape.

Inscribed angle is an angle formed by two chords in a circle which have a common endpoint, and by the inscribed angle theorem, the measurement of inscribed angle is half the measure of the intercepted arc.

THIS IS TIMED AND I NEED HELP!!!
Which represents the solution(s) of the graphed system of equations, y = x2 + 2x – 3 and y = x – 1? (1, 0) and (0, –1) (–2, –3) and (1, 0) (0, –3) and (1, 0) (–3, –2) and (0, 1)

Answers

y = x^2 + 2x - 3
y = x - 1

x^2 + 2x - 3 = x - 1
x^2 + 2x - x - 3 + 1 = 0
x^2 + x - 2 = 0
(x + 2)(x - 1) = 0

x + 2 = 0 y = x - 1
x = -2 y = -2 - 1
y = -3

x - 1 = 0 y = x - 1
x = 1 y = 1 - 1
y = 0

ur solutions are : (-2,-3) and (1,0)

Suppose that a colony of bacteria starts with 1 bacterium and doubles in number every half hour. how many bacteria will the colony contain at the end of 24

Answers

let [tex]a_n[/tex] represent the number of bacteria after [tex] \frac{n}{2} [/tex] hours.

so

[tex]a_0[/tex] is the number of bacteria after 0/2 = 0 hours

[tex]a_1[/tex] is the number of bacteria after 1/2 hours

[tex]a_2[/tex] is the number of bacteria after 2/2 = 1 hours and so on

so if we list a few terms of this sequence, we have:

[tex]a_0=1[/tex]

[tex]a_1=1*2[/tex]

[tex]a_2=1*2*2[/tex]

[tex]a_3=1*2*2*2[/tex]

[tex]a_4=1*2*2*2*2[/tex]

so clearly, [tex]a_n[/tex], the number of bacteria after [tex] \frac{n}{2} [/tex] hours, is equal to [tex] 2^{n} [/tex].

[tex]a_4_8[/tex] is the number of bacteria after

[tex]\frac{n}{2}=\frac{48}{2}= 24[/tex] hours.

Thus, we calculate [tex]a_4_8[/tex], which is [tex] 2^{48} [/tex].

Answer: the number of bacteria after 24 hours is [tex] 2^{48} [/tex].

Final answer:

A colony of bacteria that starts with 1 bacterium and doubles in number every half hour will contain approximately 281,474,976,710,656 bacteria at the end of 24 hours.

Explanation:

The number of bacteria in a colony that starts with 1 bacterium and doubles in number every half hour can be calculated using the formula 2ⁿ, where n is the number of generations. Since each generation is half an hour, there are 48 generations in 24 hours. Plugging in n=48 into the formula, we get 2⁴⁸, which is approximately 281,474,976,710,656 bacteria.

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If a triangle has legs measuring 8 inches and 15 inches and has a hypotenuse measuring 17 inches, what is the ratio, in simplest form, of the shorter leg to the hypotenuse?

Answers

ratio of shorter leg to the hypotenuse = 8/17

hope that helps

Express -2 in triganomic form

Answers

[tex]\bf -2\implies -2+0i\implies \stackrel{a}{-2}+\stackrel{b}{0}i\quad \begin{cases} r=\sqrt{a^2+b^2}\\ r=\sqrt{(-2)^2+0^2}\\ r=2\\ ----------\\ \theta =tan^{-1}\left( \frac{b}{a} \right)\\ \theta =tan^{-1}\left( \frac{0}{-2} \right)\\ \theta =tan^{-1}(0)\\ \measuredangle \theta =0~,~\pi \end{cases}[/tex]

now, there are two possible angles for that tangent... however, let's look at our a,b components.

"a" is negative whilst "b" is positive, so is not 0 then, thus

[tex]\bf -2+0i\implies r[cos(\theta )+i~sin(\theta )]\implies 2[cos(\pi )+i~sin(\pi )][/tex]

Final answer:

To express -2 in trigonometric form, we find the magnitude (absolute value) and the argument (angle) of the complex number.

Explanation:

The trigonometric form of a complex number is expressed in the form r(cosθ + isinθ), where r is the magnitude of the complex number and θ is the argument or angle.

In this case, to express -2 in trigonometric form, we first find the magnitude, which is the absolute value of -2, so |-2| = 2. The argument can be found using the arctan function, which is θ = arctan(b/a), where a is the real part and b is the imaginary part.

For -2, the real part is -2 and the imaginary part is 0. Thus, the argument is θ = arctan(0/(-2)) = arctan(0) = 0. Therefore, -2 in trigonometric form is 2(cos0 + isin0), which simplifies to just 2.

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