The graph of f (0) = -4 cos 0 is shown below. The range of this function is



-4 ≤ f (0) ≤ 0

-π ≤ f (0) ≤ 2π

0 ≤ f (0) ≤ 2π

-4 ≤ f (0) ≤ 4

The Graph Of F (0) = -4 Cos 0 Is Shown Below. The Range Of This Function Is-4 F (0) 0- F (0) 20 F (0)

Answers

Answer 1

Answer:

-4 ≤ f ([tex]\theta[/tex]) ≤ 4

Step-by-step explanation:

The range of a function is the allowed y-values of the function.

We can simply look at the periodic function below and see that the y-value ranges from a negative 4 to a positive 4. It oscillates betwen -4 and 4. That is the range.

We can say -4 ≤ f ([tex]\theta[/tex]) ≤ 4

Last answer choice is right.

*** NOTE: it is a type, not "0", rather "[tex]\theta[/tex]"


Related Questions


Given the similarity statement ΔDEF ∼ ΔXYZ, which side corresponds with ED?



A. EF
B. ZY
C. XZ
D. YX

Answers

YX is corresponding with ED

Hope it helps.

Please mark me brainliest

What kind of geometric transformation is shown in the music?

Will give BRAINLIEST.

Is this glide? I can't really see it. Thank you!

Answers

The geometric transformation shown in the figure is reflection.

What is Reflection?

Reflection is a type of geometric transformation where the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.

here, we have,

Given is a set of lines in the music note.

Three line are drawn separating from a line.

In the first part, when we find the mirror image of the first part, we will get the second part.

Mirror images are found in the transformation of reflection.

So, here, we can say that reflection is the transformation here.

Hence the kind of geometric transformation shown in the line of music is reflection.

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Use the Geometric Mean Theorem to find the value of J if
G=3 and F=12

Answers

Answer:

6

Step-by-step explanation:

The Geometric Mean Theorem states that the altitude (in this case, j) is equal to radical(g*f).

Therefore, j=√(g*f), j=√(3*12), j=6

Answer:

[tex]\boxed{6}[/tex]

Step-by-step explanation:

The Geometric Mean Theorem states that the altitude to the hypotenuse of a right triangle is the geometric mean of the two segments it creates.

Thus, in your triangle,

j = √(fg)

If f = 12 and g = 3,

j = √(12 × 3) = √ 36 = 6

[tex]\boxed{j = 6}[/tex]

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Suppose the dial on the spinner is spun 2 times in a row.

X is the number of times the dial lands on region A.

Which table represents the probability distribution for the variable X?

Answers

Answer:

2nd table

Step-by-step explanation:

Because it’s split into 3 equal sections so each region is one third

Answer:  d) 4/9, 4/9, 1/9

Step-by-step explanation:

Let's look at all of the possible combinations of 1st spin & 2nd spin:

AA        BA         CA

AB        BB         CB

AC        BC         CC

P (X=0): how many times is A not in the combination? 4 out of 9

P (X=1): how many times is A in the combination once? 4 out of 9

P (X=2): how many times is A in the combination twice? 1 out of 9

Which of the following equations is the formula of f(x) = x^1/3 but shifted 4 units to the left and 4 units up?

A. [tex]f(x) = (x-4)^{1/3} +4[/tex]
B. [tex]f(x) = 4x^{1/3} -4[/tex]
C. [tex]f(x)=(x+4)^{1/3} +4[/tex]
D. [tex]f(x) = 4x^{1/3} +4[/tex]

Answers

Answer:

Hence correct chcie is C.

[tex]f\left(x\right)=(x+4)^{\frac{1}{3}}+4[/tex]

Step-by-step explanation:

Given function is [tex]f\left(x\right)=x^{\frac{1}{3}}[/tex]

Now it says that function is shifted 4 units to the left and 4 units up.

We need to find about which of the given choice is correct for the given transformation.

When f(x) is shifted "h" units left then we write f(x+h)

So [tex]f\left(x\right)=x^{\frac{1}{3}}[/tex] will change to

[tex]f\left(x\right)=(x+4)^{\frac{1}{3}}[/tex]

When f(x) is shifted "h" units up then we write f(x)+h

So [tex]f\left(x\right)=(x+4)^{\frac{1}{3}}[/tex] will change to

[tex]f\left(x\right)=(x+4)^{\frac{1}{3}}+4[/tex]

Answer:

C

Step-by-step explanation:

For a function f(x) = [tex]x^{\frac{1}{3}}[/tex], we have:

f(x) = [tex](x-b)^{\frac{1}{3}}[/tex] is original translated b units rightf(x) = [tex](x+b)^{\frac{1}{3}}[/tex] is original translated b units leftf(x) = [tex]x^{\frac{1}{3}}+c[/tex] is original translated c units upf(x) = [tex]x^{\frac{1}{3}}-c[/tex] is original translated c units down

Keeping these translation rules in mind, we can clearly say that 4 units shifted left and 4 units up has the equation  [tex]f(x)=(x+4)^{\frac{1}{3}}+4[/tex]

correct answer is C

Who drove the fastest 363 miles in 6 hours, 435 miles in 7 hours, 500 miles in 8 hours, or 215 miles in 5 hours.

Answers

Answer:

The 3rd person who drove 500 miles in 8 hours drove the fastest.  

Step-by-step explanation:

1st person : 60.5 mph

2nd person : 62.14 mph

3rd person : 62.5 mph

4th person : 43 mph

you simply divide the total miles driven by the amount of time and then you get the miles per hour.

Hope this helps!

Find the domain and range of the function. f(x)=|2x|-sin x

Answers

Answer:

Domain = (-∞,∞)

Range: [0,∞)

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

f(x)=|2x|-sin(x)

From the graph we can see that

- the domain is equal to all real numbers.

- The range goes from [0,∞)

The correct answer is option d, but bear in mind that the range includes zero as well, so it would be Range: [0,∞)

Answer:

Answer is D!!!

Step-by-step explanation:

Use the drop-down menus to complete each equation so the statement about its solution is true.
The drop down menus consist of numbers 0-9

Answers

Answer with explanation:

    A)

No solution--

No solution is obtained when there is a condition such that the equation gives a absurd condition.

Hence we write our equation as:

        2x+9+3x+x=6x+1

 Hence, we have:

          6x+9=6x+1

i.e. we have:   9=1

which is a contradiction.

Hence, we get no solution.

B)

         One solution--

One solution or unique solution is obtained when we obtain a unique value for our given variable.

i.e. if we write our equation as:

             2x+9+3x+x=5x+1

i.e. 6x+9=5x+1

i.e. x= -8

Hence, we get a unique value for x.

C)

            Infinite many solution--

The infinite many solution is where we get a condition such that we could not get a unique value for x but the equation is true.

Hence, we have:

                     2x+9+3x+x=6x+9

i.e.   6x+9=6x+9

as left hand side of equation is equal to right hand side of the equation for every ''x'' Hence, we get infinite many solution.

                 

Answer:

1. 6x+1

2. 5x+1

3. 6x+9

Which ordered pair is a solution of the equation y = 3x?

A. (-8, -18)

B. (-8, -3)

C. (-2, -9)

D. (-10, -30)

Answers

I believe it’s b or c... Hope this helps!

PLS HELP 15 POINTS


Find the missing part.

L=8 W=4 H=2

Find the diagonal (d) of the rectangular solid.

Answers

Answer:

2√21

Step-by-step explanation:

Diagonal =√(L²+W²+H²)

Diagonal =√(8²+4²+2²)=√(64+16+4)=√84=2√21

Select Independent or Not independent for each situation.

A jar contains twenty coins. Two coins are picked randomly without replacement.

A coin is flipped three times.

A bag contains 5 red balls and 3 green balls. A red ball is chosen followed by a green ball without replacement.

A spinner contains 3 equal sectors labeled A, B and C. The spinner is spun twice.

Answers

Answer:

1. Not Independent

2. Independent

3. Not Independent

4. Independent

Step-by-step explanation:

Independent: An event is independent if the outcome of one event doesn't effect the outcome of the other event.

Not independent : An event is Not independent if the outcome of one event effect the outcome of other event.

1. A jar contains twenty coins. Two coins are picked randomly without replacement.

Not Independent because if coins are not replaced the outcome of next event will be effected.

2. A coin is flipped three times.

Independent because when a coin is flipped once its outcome doesn't effect the outcome of the coin flipped again

3. A bag contains 5 red balls and 3 green balls. A red ball is chosen followed by a green ball without replacement.

Not Independent because if balls are not replaced the outcome of next event will be effected.

4. A spinner contains 3 equal sectors labeled A, B and C. The spinner is spun twice.

Independent because when the spinner is spuned once its outcome doesn't effect the outcome of the spinner spun again

The correctcorrect probabilityprobability conditiony for each of the given situation as regards independent or not are;

A) Not Independent

B) Dependent

C) Not Independent

D) Dependent

Independent Events

An independent event is one that doesn't depend on the probability of another one happening while a dependent event is one that depends on the probability of another one happening.

A) A jar contains twenty coins. Two coins are picked randomly without replacement; This is not independent because when we do not replace a selected coin, it affects the outcome of the next choice.

B) A coin is flipped three times; This is dependent because a flip doesn't depend on another flip.

C) A bag contains 5 red balls and 3 green balls. A red ball is chosen followed by a green ball without replacement; This is not independent because when we do not replace a selected ball, it affects the outcome of the next choice.

D) A spinner contains 3 equal sectors labeled A, B and C. The spinner is spun twice; This is independent because spinning doesn't affect the outcome of the next spin.

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Use a calculator to solve for theta in the given interval

Answers

Answer:

d. [tex]1.82\: or\:4.46[/tex]

Step-by-step explanation:

The given trigonometric equation is;

[tex]\sec \theta=-4.0545[/tex]

Recall that;

[tex]\cos \theta=\frac{1}{\sec \theta}[/tex]

[tex]\implies \cos \theta=\frac{1}{-4.0545}[/tex]

[tex]\implies \cos \theta=-0.2466[/tex]

The cosine function is negative in the second and third quadrant.

[tex]\theta=\pi-\cos^{-1}(0.2466)\: or\:\pi+\cos^{-1}(0.2466)[/tex]

[tex]\theta=1.82\: or\:4.46[/tex]

A rectangular prism is 4 meters long, 5 meters wide, and has a height of 7 meters. What is its surface area?

a.140 m2
b.166 m2
c.84 m2
d.70 m2

Answers

Answer:

5 by 4 face = 20 * 2 = 40

5 by 7 face = 35 * 2 = 70

4 by 7 face = 28 * 2 = 56

Total surface area = 166 square meters

Answer is "b"

Step-by-step explanation:

Answer:

your answer will be A

Two number cubes, each with the numbers 1 through 6, are rolled. What is the probability that the sum of the rolled numbers is 2? PLEASE HELP ANYONE IN LIKE @20 min

Answers

Final answer:

The probability of rolling a sum of 2 with two dice is 1/36. This is calculated by determining the independent probabilities of rolling 1 on each die and multiplying these probabilities together.

Explanation:

The subject of this question is probability in mathematics, specifically involving the numbers on two rolled dice. The only way two dice (number cubes) can add up to 2 is if both rolled dice shows 1. Each die has 6 sides, so the probability for each dies rolling 1 is 1/6.

The probability of two independent events both occurring is founding by multiplying the probability of each event. As the two dice is rolled independently, the probability of both are showing 1 (and hence their sum is being 2) is (1/6) x (1/6), which simplifies to 1/36. Therefore, the probability that the sum of the numbers rolled on two dice is 2 1/36.

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According to the general equation for conditional probability, if (image attached)

A. [tex]\frac{40}{49}[/tex]
B. [tex]\frac{24}{49}[/tex]
C. [tex]\frac{32}{49}[/tex]
D. [tex]\frac{16}{49}[/tex]

Answers

Answer: Option A

[tex]P(A|B) = \frac{40}{49}[/tex]

Step-by-step explanation:

In a probabilistic experiment, when two events A and B are dependent on each other, then the probability of occurrence A since B occurs is:

[tex]P(A|B) = \frac{P(A\ and\ B)}{P(B)}[/tex]

Then if [tex]P(A\ and\ B) = \frac{5}{7}[/tex] and [tex]P(B) = \frac{7}{8}[/tex] then:

[tex]P(A|B) = \frac{\frac{5}{7}}{\frac{7}{8}}\\\\P(A|B) = \frac{40}{49}[/tex]

Answer:

Correct choice is A. [tex]P(A|B)=\frac{40}{49}[/tex].

Step-by-step explanation:

Given that [tex]P(A\cap B)=\frac{5}{7}[/tex], [tex]P(B)=\frac{7}{8}[/tex].

Now using those values , we need to find the value of [tex]P(A|B)[/tex].

So apply the formula of conditional probability:

[tex]P(A\cap B)=P(B) \times P(A|B)[/tex]

Plug the given values into above formula,  we get:

[tex]\frac{5}{7}=\frac{7}{8} \times P(A|B)[/tex]

[tex]\frac{7}{8} \times P(A|B)=\frac{5}{7}[/tex]

[tex]P(A|B)=\frac{\frac{5}{7}}{\frac{7}{8}}[/tex]

[tex]P(A|B)=\frac{5}{7}\cdot\frac{8}{7}[/tex]

[tex]P(A|B)=\frac{40}{49}[/tex]

Hence correct choice is A. [tex]P(A|B)=\frac{40}{49}[/tex].

I am in urgent need of some help!! So uh....Please help me A quadrilateral has angles that measure 72 degrees, 98 degrees and 65 degrees what is the measure of the fourth angle??

Answers

So I could be completely wrong, or I could be completely right, but quadrilaterals interior angles equal 360 degrees.

So, if you ad up 98, 72, and 65 you end up with 235 degrees.

In order to find the fourth angle, you would just subtract 235 from 360 and get 125 degrees.

BUT, maybe see if someone else answers too, because I am not 100% sure.

consider the sequence -3,7,17,27...
which function (with domain all integers n>=1) could be used to define and continue the sequence.

A f(n)= 10n-13
B f(n)=-3n+10
C f(n)=10n-3
D f(n)=-3(n-1)+10

Answers

Answer:

The function is f(n) = 10n - 13 ⇒ answer A

Step-by-step explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive

  numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic sequence:

# U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

# Un = a + (n – 1)d, where a is the first term , d is the difference

  between each two consecutive terms, n is the position of the

  term in the sequence

* Now lets solve the problem

- The sequence is -3 , 7 , 17 , 27 , .........

∵ 7 - (-3) = 7 + 3 = 10

∵ 17 - 7 = 10

∵ 27 - 17 = 10

∴ The sequence is arithmetic with constant difference 10

∴ f(n) = a + (n - 1)d

∵ a = -3

∵ d = 10

∴ f(n) = -3 + (n - 1)(10) ⇒ lets simplify it

∴ f(n) = -3 + n(10) + (-1)(10) = -3 + 10n - 10 ⇒ add like terms

∴ f(n) = 10n - 13

* The function is f(n) = 10n - 13

Option A is the correct function to define the sequence. It starts at -3 when n=1 and increases by 10 as n increases, consistently matching the given sequence.

To determine which function could be used to define and continue the given sequence (-3, 7, 17, 27...), we need to analyze the pattern of differences between consecutive terms and see which option best represents this pattern. The sequence increases by 10 each time, as can be seen from the differences (7 - (-3) = 10, 17 - 7 = 10, 27 - 17 = 10).

Looking at the functions provided:

Option A: f(n) = 10n - 13If we put n=1, f(1) = 10*1 - 13 = -3; If we put n=2, f(2) = 10*2 - 13 = 7; and so on. The pattern matches.Option B: f(n) = -3n + 10 If we put n=1, f(1) = -3*1 + 10 = 7, which does not match the first term of our sequence.Option C: f(n) = 10n - 3 If we put n=1, f(1) = 10*1 - 3 = 7, which does not match the first term of our sequence.Option D: f(n) = -3(n - 1) + 10 If we put n=1, f(1) = -3*(1 - 1) + 10 = 10, which does not match the first term of our sequence.

Therefore, Option A is the correct function to define the sequence. It starts at -3 when n=1 and increases by 10 as n increases, consistently matching the given sequence.

A country’s population in 1992 was 50 million. In 2992 it was 53 million. Estimate the population in 2010 using the exponential growth formula. Round your answer to the nearest formula.

Answers

Answer:

P ≈ 56 million

Step-by-step explanation:

Your question is attached in the picture below.

The exponential formula for these cases is

P = Po*e^(kt)

Where,

Po = initial population

k = is a constant used to define the growth rate

t = time transcurred since the time of the initial population

For this exercise,

Po = 50 million

Year 2002

2002 - 1992 = 10

53 million = 50 million *e^(k*10)

(53/50) = e^(k*10)

k*10 = ln(53/50)

k = 0.005827

The equation results

P = 50 million *e^(0.005827*t)

Year 2010

2010-1992 = 18

P = 50 million *e^(0.005827*18)

P = 50 million *(1.11058)

P = 55.53 million

P ≈ 56 million

Answer:

the answer is 56 just got it right

if you need population in 2010

Step-by-step explanation:

Find the solution set.
x^2 – 5x = 0

Answers

Answer:

x=0  and x=5

Step-by-step explanation:

x^2 – 5x = 0

Factor out an x

x(x-5) = 0

Using the zero product property

x=0 and x-5 =0

Solving

x=0 x-5+5 = 0+5

x=0  and x=5

Find the area please

Answers

Answer: 30 square units

=================================================

Explanation:

The base is 10 and the height is 6. So b = 10 and h = 6.

We don't use the 7 at all.

Let's use those b and h values into the formula below

A = b*h/2

A = 10*6/2

A = 60/2

A = 30

Answer:

30 square units

Step-by-step explanation:

Always remember that the equation for the area of a triangle is 1/2 times base times height. With an obtuse triangle, you must always ignore the slant. So, half of the base, which is 10, is equal to 5 and 5 times 6 is 30. Also, remember you can multiply in whichever order and the answer will always be the same because of the commutative property.

Which algebraic expression represents the phrase "two times the quantity of a number minus 12"? A. 2y - 12 B. 2(y -12) C. 2(y + 12) D. 2y + 12

Answers

Answer:

B

Step-by-step explanation:

Two times the quantity of a number minus 12.

Represent the number with the variable y.

The quantity of a number minus 12 is then: (y-12).

Two times this quantity is 2(y-12).

So the answer is 2(y-12), which is B.

For 180° < 0 < 360°, which of the primary trigonometric functions may have positive values?

Answers

Final answer:

For angles between 180° and 360°, only cosine (cos) and cosecant (csc) may yield a positive value. This is because these angles fall in the third and fourth quadrants of the unit circle where only certain functions yield positive results.

Explanation:

In the trigonometric functions, the sign of the function's result can vary depending on the size of the angle. For angles between 180° and 360°, only cosine (cos) and cosecant (csc), which is the reciprocal of sine, may have positive values.

In mathematics circle, these angles are in the third and fourth quadrants. In the third quadrant (180° ≤ θ < 270°), only the function tangent (tan) and its reciprocal cotangent (cot) can be positive. While in the fourth quadrant (270° ≤ θ < 360°), the functions cosine (cos) and its reciprocal secant (sec) can be positive.

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if you were to build a house, one with two-dimensional figures and the other with three-dimensional figures, which one will have a better chance of withstanding a hurricane and why

Answers

Answer:

both

Step-by-step explanation:

Depending on how u look at it, one is comprised of 2d figures and the other is of 3d, but the 2d shapes combine to make the faces of any 3d shape, so its basically the same.

The measurement from the base of a tree to the tip of its shadow is 100ft.

Answers

the answer is200ftbecause cos(60)=100/the hight of the treethe hight of the tree=100/cos(60)=200ft

Answer: it’s 200ft

Step-by-step explanation:

How are possibilities observed in a game of poker?

Answers

Answer:

the number if different possible poker hands is found by counting the number of ways that 5 cards can be selected from 52 cards.

Step-by-step explanation:

this is a valid answer for e2020

Final answer:

In poker, the number of microstates when dealing with five cards from separate decks is 52^5, and the probability of getting 5 queens of hearts is (1/52)^5. The probability of drawing any specific hand is also 1 in 380,204,032. Poker hand values are inversely proportional to their entropy, with rarer hands having greater value.

Explanation:

Calculations Involved in Poker Probabilities

The game of poker involves a combination of skill and luck, with probabilities playing a significant role in the strategy. To answer the student's questions regarding probabilities in poker, we need to delve into some detailed calculations.

Microstates in Poker: A microstate refers to a specific arrangement of cards. When dealing five random cards from five separate decks, we consider each deck to have 52 unique cards. The number of microstates would be 52^5 (or 380,204,032) because for each card drawn there are 52 possibilities, and each draw is independent from the others.Probability of getting 5 queens of hearts: Given that each deck has one queen of hearts, the probability of drawing the queen of hearts from each deck in one try is (1/52)^5, which is 1 in 380,204,032.Probability of a specific hand: Since there are 52 possible cards for each of the five draws, the probability of getting any specific hand of five cards, regardless of suit or rank, is also 1 in 380,204,032.

In analyzing poker hands and their respective values, we find that the value of a hand is typically inversely proportional to its entropy, meaning a less likely hand equates to a higher value.

Pascal's Wager as applied to gambling is not directly related to poker probabilities, but it is an interesting philosophical approach to decision-making under uncertainty. Rather than calculating monetary risk, it assesses the existential gamble of believing in a deity.

Understanding probabilities like these allows gamblers, politicians, teachers, doctors, and individuals in many other fields to make more informed decisions about probable outcomes.

Find the area of the composite figure. Round to the nearest hundredth.

Answers

**Cracks knuckles** let's do this.

Area of triangle = 31.25 yd^2

10 x 6.25 = 62.5

62.5 / 2 = 31.25

Area of rectangle A = 50 yd^2

10 (length) x 5 (7.5 - 2.5) (width) = 50

Area of rectangle B = 48.75 yd^2

7.5 x 6.5 = 48.75

Total area of composite = 130 yd^2

31.25 + 50 + 48.75 = 130

Eric practiced the piano and guitar for a total of 8 hours this week he practiced the piano for 1/4 of that time how many hours did he practice piano this week

Answers

Answer: 2

Step-by-step explanation:

If 8 hours are spent the week, and there is only 1/4 used to play piano then you have to know how much 1/4 is of 8.

To get 1/4 of 8 you need to multiply 8 by 1/4.

The answer is 2.

What is the surface area of the cube below?


A. 150 units^2

B. 75 units^2

C. 300 units^2

D. 50 units^2

Answers

ANSWER

A. 150 units^2

EXPLANATION

The surface area of a cube is calculated using the formula:

[tex]SA=6 {l}^{2} [/tex]

where

[tex]l = 5[/tex]

We substitute the length to obtain:

[tex]SA=6 {l}^{2} [/tex]

[tex]SA=6 \times {5}^{2} [/tex]

[tex]SA=150 \: {units}^{2} [/tex]

What is the lateral area of the cylinder?

Answers

Answer: second option.

Step-by-step explanation:

The formula used for calculate the lateral area of a cylinder is this one:

[tex]LA=2\pi rh[/tex]

Where "r" is the radius and "h" is the height

The formula for calculate the area of a circle (which is the base of a cylinder) is:

[tex]A=\pi r^2[/tex]

Knowing the area of the base, you can solve for the radius:

[tex]36\pi=\pi r^2\\\\r=\sqrt{\frac{36\pi units^2}{\pi}} \\\\r=6units[/tex]

Substitute the radius and the height into the formula [tex]LA=2\pi rh[/tex]:

[tex]LA=2\pi (6units)(2units)[/tex]

[tex]LA=24\pi\ units^2[/tex]

The area of a rectangle is (81x^2 − 4y^2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work.

Answers

Answer 81x^2 - 4y^2     Note this is the difference of 2 perfect squares

a^2 - b^2 = (a + b)(a - b)

so here we have a = 9x and b = 2y

and our factors are

(9x + 2y)(9x - 2y)

the dimensions are 9x + 2y and 9x - 2y

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Show Work

81x^2 - 4y^2     Note this is the difference of 2 perfect squares

a^2 - b^2 = (a + b)(a - b)

so here we have a = 9x and b = 2y

and our factors are

(9x + 2y)(9x - 2y)

The dimensions of the rectangle with an area of (81x² - 4y²) square units are (9x + 2y) and (9x - 2y) units, as the area expression is a difference of squares that has been factored accordingly.

The area of a rectangle is given by the expression (81x² − 4y²) square units. To determine the dimensions of the rectangle, we need to factor this expression completely.

This expression is a difference of squares and can be factored as follows:Use the difference of squares formula, which is a²- b² = (a - b)(a + b).Apply the formula: (81x² − 4y²) = (9x)² - (2y)² = (9x + 2y)(9x - 2y).

Therefore, the dimensions of the rectangle can be 9x + 2y and 9x - 2y units.

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