Find an equation of the tangent line to the curve
xey + yex = 5

Since f(x) is an even function, the statement which is true is the graph of f(x) has a line of symmetry about the y-axis.

To answer the question, we need to know what an even function is.

An even function is a function f(x) such that f(x) = f(-x). That is f(x) is single valued for both positive and negative values of x.

Now, for an even function, since f(x) = f(-x), both positive and negative values of x give a single value of f(x).

For this to be true, the graph of f(x) is symmetric about the y-axis.

So, since f(x) is an even function, the statement which must be true is graph of f(x) has a line of symmetry about the y-axis.

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Answer:

16.00

Step-by-step explanation:

80% of 20.00 is 16.00

To solve for x in the equation 6(x – 1) = 9(x + 2), expand and simplify the equation, combine like terms, isolate the variable x, and solve for x by dividing both sides by 3.

To solve for x in the equation 6(x – 1) = 9(x + 2), we can begin by expanding the equation:

6x - 6 = 9x + 18

Next, we can combine like terms by subtracting 6x from both sides:

-6 = 3x + 18

Then, we can isolate the variable x by subtracting 18 from both sides:

-24 = 3x

Finally, we can solve for x by dividing both sides by 3:

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Answer:

the answer is actually 3x - 0.03 = 0.75

Step-by-step explanation:

To find the total length of lights needed, we find the perimeter of one window and multiply that by the number of windows. Mr. Green needs 56 meters of lights for all 8 windows.

To solve the problem, we need to find the total length of lights Mr. Green needs for all the windows. First, we need to compute the perimeter for one window, which is two times the sum of the length and the width. Therefore, for one window, that would be 2×(1.5m + 2m) = 7m. Since there are 8 windows, Mr. Green would need a total of 8×7m = 56m of lights.

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Answer:

Equation of Pedro's   rocket  

[tex]h= -16t^2+120t+2[/tex]

Equation of Pedro's   rocket  [tex]h= -16t^2+120t+2[/tex]

Step-by-step explanation:

[tex]h= -16t^2+60t+2[/tex]

on comparing the given equation with general equation

[tex]h= -gt^2+vt+h_{0}[/tex]

           we get v = 60 feet /second which is the speed of Justin's rocket.

          Speed of  Pedro's rocket = double of Justin's rocket

                                                     = 2(60 ) = 120 feet second

therefore equation for Pedro will be given by

[tex]h= -16t^2+120t+2[/tex]

Daniel can go on 14 rides at the fair.

To find out the greatest number of rides Daniel can go on, we need to calculate the cost of admission and the cost of the rides. The admission to the fair is $4 and each ride costs $1.50. To determine the number of rides, we subtract the cost of the admission from the total amount Daniel has to spend and then divide that by the cost of each ride. So, Daniel can go on (25 - 4) / 1.50 = 14 rides. Therefore, the greatest number of rides Daniel can go on is 14.

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Answer:

Surface area is, 478 square centimeter

Step-by-step explanation:

Surface area (S)of rectangle is given by:

[tex]S = 2(lw+wh+hl)[/tex]                 .....[1]

where,

l is the length

w is the width

h is the height of the rectangle respectively.

As per the statement:

A rectangular solid has sides of 7 cm, 9 cm, and 11 cm

⇒ l = 7 cm , w = 9 cm and h = 11 cm

Substitute in [1] we have;

[tex]S = 2(7 \cdot 9+9 \cdot 11+11 \cdot 7)[/tex]

⇒[tex]S = 2(63+99+77) = 2 \cdot 239 = 478 cm^2[/tex]

Therefore, the surface area is, 478 square centimeter

Answer:

The square root of -64 is 8i

Step-by-step explanation:

Given the number -64

we have to find the square root of the above number i.e [tex]\sqrt{-64}[/tex]

As

[tex]\sqrt{-64}=\sqrt{-8\times 8}[/tex]

[tex]=\sqrt{-(8)^2}[/tex]

[tex]=\sqrt{(-1)(8)^2}[/tex]

[tex]=\sqrt{-1}\sqrt{8^2}=8i[/tex]

Hence, the square root of -64 is 8i

Various factors cause the disappearance of animals in the wild, including habitat destruction, hunting, disease, and changes in predator-prey relationships.

The disappearance of animals in the wild can be caused by various factors, including habitat destruction, hunting, disease, and changes in predator-prey relationships. One of the main factors is habitat destruction, which occurs when natural habitats are altered or destroyed by human activities such as farming, logging, and construction. This leads to a loss of biodiversity as plant and animal populations are destroyed or displaced.

Hunting is another major cause of animal disappearance. Animals are hunted for various purposes including meat, hides, and horns. Large mammals are particularly vulnerable as they are often targeted for their valuable resources. In addition, diseases can spread among animals due to human activities, such as the introduction of domestic animals, leading to population declines and even extinctions.

Changes in predator-prey relationships can also affect animal populations. For example, the decline of predators like cougars, lions, and leopards can result in an increase in the prey population. This can lead to changes in vegetation, stream paths, and overall biodiversity.

After analyzing each option and testing them in the equation UW = 9x - 9, none of the provided options (5 units, 6 units, 30 units, 36 units) result in a consistent solution for the length of UW in units. Without additional information or a correct option, it is impossible to determine the length of UW in units.

The student's question asks us to find the length of segment UW in units given that the formula for its length is UW = 9x - 9. To ascertain the correct length, we need a value for 'x'. Since the options provided are measured in units and do not contain variables, we have to assume that 'x' represents a specific value that, when substituted into the equation, will yield one of the given numerical options for UW.

Going through the provided options, we can test each number to see which, when substituted into 'x', will make UW a whole number. Starting with the smallest '5 units' and '6 units', we quickly find that none of these values, when multiplied by 9 and then decreased by 9, will yield themselves as a result. Thus, they can be dismissed as possible lengths of UW.

Moving on to '30 units' and trying x = 30 in the equation UW = 9x - 9, we get UW = 9(30) - 9 = 270 - 9 = 261, which does not match. Lastly, checking x = 36 in the equation gives us UW = 9(36) - 9 = 324 - 9 = 315, which is also not an option. None of the provided options are valid when 'x' is placed into the equation UW = 9x - 9.

Therefore, without additional information or a correct choice in the options, we cannot determine the length of UW in units.

Answer:

Two variables which have a constant ratio between them are said to be proportional.

Step-by-step explanation:

We have been given an incomplete sentence. We are supposed to complete our given sentence.

We know that two quantities are proportional, when they share a common ratio between them.

Therefore, the missing word from our given sentence is 'proportional'.

Answer is 483,542

Compound Interest:

The formula for compound interest is   [tex]A = p(1 + \frac{r}{n} )^{nt}[/tex]

where P is the principal balance

r is the interest rate

n is the number of times interest is compounded per time period.

t is the number of time periods.

(Given),

P = 320,000

n = 1

t = 12

r = 3.5% = 3.5 / 100 = 0.035

[tex]A = 320,000 (1 + 0.035)^{12}[/tex]

[tex]A = 320000(1.035)^{12}[/tex]

A = 483,541.970 (approx)

A = 483,542 (Rounded to the nearest whole number).

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The length of the escalator is approximately 180 feet.

To find the length of the escalator, we can use trigonometry. The vertical distance traveled by the escalator is given as 90 feet and the angle it makes with the ground is 30°.

Using the sine function, we can determine the length of the escalator:

Length of escalator = Vertical distance traveled / sin(angle)

Therefore, the length of the escalator is:

Length of escalator = 90 feet / sin(30°)

Calculating the above expression, the length of the escalator is approximately 180 feet.

Final answer:

The length of the escalator is found using the cosine function for a 30° angle and a vertical height of 90 feet. The calculated length is approximately 77.94 feet.

Explanation:

The question asks how long an escalator is if it covers a vertical distance of 90 feet at a 30° angle with the ground. To find the length of the escalator, we can use trigonometric functions, specifically the cosine function, which relates the adjacent side (the length of the escalator) to the hypotenuse (the vertical height) in a right-angled triangle.

Using the formula:

cos(θ) = adjacent/hypotenuse

Where:

θ is the angle

'Adjacent' is the length of the escalator

'Hypotenuse' is the vertical height, which is 90 feet

To solve for the length (L) of the escalator:

cos(30°) = L / 90 feet

L = 90 feet * cos(30°)

L = 90 feet * (√3/2)

L = 45√3 feet

Or approximately L = 45 * 1.732 = 77.94 feet

Therefore, the length of the escalator is approximately 77.94 feet.

Answer:

A. 50 − 2.5x = y

 40 − 2x = y

Step-by-step explanation:

We know that x represents the number of trips and y represents the amount remaining in each account, then, let's think in an example; after the first trip x = 1, therefore, Kaisorn's account must decrease from $50 to $50 - $2.5 = $47.5 = y, and Thom's account must decrease from $40 to $40 - $2 = $38 = y. Replacing x = 1 in each case gives:

A

50 − 2.5(1) = y

47.5 = y

   40 − 2(1) = y

   38 = y

B

50 + 2.5(1) = y

52.5 = y

 40 + 2(1) = y

 42 = y

C

50 − 2.5y = (1)

y = (1 - 50)/(-2.5)

y = 19.6

 40 − 2y = (1)

  y = (1 - 40)/(-2)

  y = 19.5

D

50 + 2.5y = (1)

y = (1 -50)/2.5

y = -19.6

 40 + 2y = (1)

 y = (1 - 40)/(2)

 y = -19.5

As it can be seen, option A is the correct one.

The more boys than girls are signed up for camp are 22.

We have given that

Summer day camp is about to begin. Today there are 132 boys signed up and 219 total children signed up.

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign

Therefore for the girl

219-132 is the equation because the rest of the 219 comes from the girls who signed up.

219-132= 77.

To find how many more boys than girls signed up you need to subtract 77 from 132.

132-77= 55

Therefore the more boys than girls are signed up for camp are 22.

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The inverse function of f(x) = x^2 - 81 is found by swapping x and y in the original equation and solving for y, resulting in f^-1(x) = ±√(x + 81).

To find the inverse function f-1(x) of the function f(x) = x2 - 81, we need to swap the roles of x and y in the original function and solve for y, which represents f-1(x). Here are the steps:

The correct answer is option 1, ±√(x + 81).