Find all vertical asymptotes of the rational function. (Enter your answers as a comma-separated list of equations.)
F(x) =
x2 + 11
6x2 − 19x − 36

The expression that represents the amount of canned food collected so far by the three friends is [tex]$4x^2 + 2xy - 3$[/tex] and the expression that represents the number of cans the friends still need to collect to meet their goal is [tex]7x^2 + 9$.[/tex]

What is an expression?

In mathematics, an expression is a combination of numbers, variables, operators, and/or functions, which when arranged in a meaningful way, represents a mathematical relationship or a quantity.

Part A:

To find the amount of canned food collected so far by the three friends, we need to add up the number of cans collected by each friend. So, we can write:

Amount collected [tex]$= \text{Jessa's collection} + \text{Tyree's collection} + \text{Ben's collection}$[/tex]

Substituting the given expressions, we get:

Amount collected [tex]$= (2xy + 4) + x^2 + (3x^2 - 7)$[/tex]

Simplifying the expression, we get:

Amount collected [tex]$= 4x^2 + 2xy - 3$[/tex]

Therefore, the expression that represents the amount of canned food collected so far by the three friends is [tex]$4x^2 + 2xy - 3$[/tex].

Part B:

To find the number of cans the friends still need to collect to meet their goal, we need to subtract the amount collected by the three friends from the goal expression. So, we can write:

Number of cans needed [tex]$= \text{Goal} - \text{Amount collected}$[/tex]

Substituting the given expressions, we get:

Number of cans needed [tex]$= (11x^2 - 2xy + 6) - (4x^2 + 2xy - 3)$[/tex]

Simplifying the expression, we get:

Number of cans needed [tex]$= 7x^2 + 9$[/tex]

Therefore, the expression that represents the number of cans the friends still need to collect to meet their goal is [tex]7x^2 + 9$.[/tex]

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Answer:

120 ft

Step-by-step explanation:

Let's assume that the length of the field is x feet. Then, according to the problem statement, the width of the field is (x - 20) feet.

The area of a rectangle is given by the formula A = length x width. So, we can write:

x(x - 20) = 12,000

Expanding the left-hand side, we get:

x^2 - 20x = 12,000

Bringing all the terms to one side, we have:

x^2 - 20x - 12,000 = 0

Now, we can solve this quadratic equation using the quadratic formula:

x = (-(-20) ± sqrt((-20)^2 - 4(1)(-12,000))) / (2(1))

x = (20 ± sqrt(20^2 + 48,000)) / 2

x = (20 ± 220) / 2

We discard the negative root, since a length cannot be negative, and we get:

x = 120

Therefore, the length of the field is 120 feet.

Answer:

-116u

Step-by-step explanation:

-69-47 is 116. The varblie stays making it -116u

Answer:

Let x be the number of shakes you can buy.

The cost of 5 meals is:

5 * $4 = $20

The total cost of the meals and shakes is:

$20 + $3x = $30

Subtracting $20 from both sides of the equation:

$3x = $10

Dividing both sides of the equation by $3:

x = 3.33

Rounding down to the nearest whole number, you can buy 3 shakes.

I hope this helps!

The direction angle of the vector Ū is approximately 16.26°.

A vector's direction angle is the angle, measured anticlockwise, between the positive x-axis and the vector in standard position.

Trigonometry can be used to determine the direction angle of the vector = (-7, 2).

The direction angle is determined by:

θ = tan^-1(y/x)

where y is the vector's vertical component and x is its horizontal component (in this example, -7). (in this case, 2).

θ = tan^-1(2/-7)

We can determine: Using a trigonometric table or a calculator

θ ≈ 16.26°

As a result, the vector's direction angle is roughly 16.26°.

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In reality, [tex]96[/tex] miles distance separate the two cities.

We kept an eye on them from afar. Compared to earlier, she perceives a gap between her and her brother. They had been close friends earlier, but now there was a great distance between them. He desires to disassociate himself from his old employer.

Mileage is a vector variable that quantifies "how much space an object has travelled through" while in motion. An object's dependent and independent variables in position is referred to as displaced, a vector variable that measures "the extent to which place an item is."

Using the scale provided, we can establish the proportion:

[tex]2 cm / 40 miles = 4.8 cm / x[/tex]

where [tex]x[/tex] is the actual distance between the two cities in miles.

To solve for [tex]x[/tex], we can cross-multiply:

[tex]2 cm * x = 40 miles * 4.8 cm[/tex]

Simplifying:

[tex]2x = 192[/tex]

[tex]x = 96[/tex]

Therefore, the actual distance between the two cities is [tex]96[/tex] miles.

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We find the following conclusions concerning the telegraph wire:

Case 1: The perimeter of the circle is equal to 20π centimeters.

Case 2: The extra length for the telegraph wire is equal to 10π meters.

In this problem we find two cases where the perimeter of a circle must be computed for a telegraph wire, this can be done by using the following formula:

s = 2π · r

Where:

Now we proceed to determine the perimeter for each case.

Case 1: (Please notice that diameter is twice the radius)

s = 2π · (20 / 2)

s = 20π cm

The circle has a perimeter of 20π centimeters.

Case 2: (The Earth has a radius of 6371000 meters)

Δs = 2π · (6371005 - 6371000)

Δs = 2π · 5

Δs = 10π m

An extra length of 10π meters is required for the telegraph wire.

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To convert the total time from seconds to minutes, we need to divide by 60. So, the total time in minutes would be: (720 + 420) / 60 = 1140 / 60 = 19 minutes.

To find the total time it takes Andrew to take a shower and eat breakfast, we need to add the time it takes for each activity. Andrew takes 720 seconds to take a shower and 420 seconds to eat breakfast. To convert seconds to minutes, we divide the total time in seconds by 60. So the total time it takes Andrew to take a shower and eat breakfast is (720 + 420) / 60 = 19 minutes. Therefore, it takes Andrew 19 minutes to take a shower and eat breakfast.

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Complete question:

It takes Andrew 720 seconds to take a shower. He spends an additional 420 seconds eating breakfast. How many minutes does it take Andrew to take a shower and eat breakfast?

Answer:

Let's use variables to represent the number of kittens each person has fostered.

Let x be the number of kittens Kim has fostered.

Then, according to the problem, Preston has fostered one less than one third as many kittens as Kim, so Preston has fostered:

(1/3)x - 1

We know that the total number of kittens fostered is 47. Therefore, we can write an equation:

x + (1/3)x - 1 = 47

Simplifying and solving for x:

(4/3)x = 48

x = 36

So Kim has fostered 36 kittens.

To find out how many kittens Preston has fostered, we can substitute x = 36 into the expression we found earlier:

(1/3)x - 1 = (1/3)(36) - 1 = 11

Therefore, Preston has fostered 11 kittens.

In summary, Kim has fostered 36 kittens and Preston has fostered 11 kittens.

Answer:

36, 11

Step-by-step explanation:

Preston and Kim 47 kittens

Kim has fostered X number of kittens

Preston has fostered X/3 - 1 ( 1/3 of Kim - 1)

Total number of kitten will be Preston +Kim

X +1/3X - 1 = 47

Add 1 to both sides

X + 1/3X = 48

If 4/3X is 48, X is 36

If Kim has 36kittens, Preston fostered 47- 36 =11

To check

1/3 of 36 = 12

Subract 1 = 11

Answer:

To find the extreme value of the function f(x) = 6x^2 - 180x + 1000, we can first take the derivative of the function and set it equal to zero:

f'(x) = 12x - 180 = 0

Solving for x, we get x = 15. Substituting this value back into the original function, we get:

f(15) = 6(15)^2 - 180(15) + 1000 = 1250

So the extreme value of the function is 1250, which represents the maximum profit in thousands of dollars that can be earned by selling a certain number of items.

More specifically, the value x = 15 is the value of x that maximizes the profit, and the maximum profit is $1,250,000. This means that if the company sells 15 items, they will make the most profit possible.

Step-by-step explanation:

The probability of drawing 6 cards of the same suit is 0.002% while the probability of drawing a hand containing only one pair is 42.3%.

(a) The probability of drawing 6 cards of the same suit can be calculated as follows:

First, choose one of the four suits. There are 4 ways to do this.

Next, choose 6 cards from the chosen suit. There are 13 cards in each suit, so there are C(13,6) ways to do this.

Finally, choose any 6 cards from the deck. There are C(52,6) ways to do this.

Therefore, the probability of drawing 6 cards of the same suit is:

P(6 cards of the same suit) = (4 * C(13,6)) / C(52,6) ≈ 0.002%

(b) The probability of drawing a hand containing only one pair can be calculated as follows:

First, choose a rank for the pair. There are 13 ranks to choose from.

Next, choose 2 cards of the chosen rank. There are C(4,2) ways to do this.

Then, choose 4 cards from the remaining 48 cards. There are C(48,4) ways to do this.

Therefore, the probability of drawing a hand containing only one pair is:

P(only one pair) = (13 * C(4,2) * C(48,4)) / C(52,6) ≈ 42.3%

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Answer:

Step-by-step explanation:

(D)

A sample size οf 805 Flοrida panthers will give a standard deviatiοn οf 0.8 years.

It displays the average deviatiοn οf each scοre frοm the mean. In a nοrmal distributiοn, a high standard deviatiοn indicates that values are spread οut frοm the mean, whereas a lοw standard deviatiοn indicates that values are clustered clοse tο the mean.

We can use the fοllοwing fοrmula tο calculate the sample size that will result in a standard deviatiοn οf 0.8 years:

n = (z * σ / E)²

Where:

The sample size is denοted by n.

z is the desired cοnfidence level's z-scοre (we'll assume 95% cοnfidence, sο z = 1.96)

is the standard deviatiοn οf the pοpulatiοn (given as 14.3 years)

E represents the margin οf errοr (given as 0.8 years)

The fοllοwing results are οbtained when the given values are substituted:

[tex]n = (1.96 * 14.3 / 0.8)^2 \sn = 804.57[/tex]

We get the fοllοwing when we rοund up tο the nearest whοle number:

n = 805

A sample size οf 805 Flοrida panthers results in a standard deviatiοn οf 0.8 years.

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The required length of AD is equal to the length of BC.

A polygon with four edges, four angles, and four vertices is called a quadrilateral. The Latin terms quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral. A quadrilateral is shown in the above picture as an example.

First, we draw the quadrilateral ABCD and label the given angles:

[tex]$\begin{align*}\angle ABD &= 35^\circ \\angle BDC &= 25^\circ\end{align*}[/tex]

Since opposite sides of quadrilateral ABCD are equal, we have:

[tex]$\begin{align*}AB &= DC\end{align*}[/tex]

We can use this fact to draw diagonal BD and label its length as x:

[tex]$\begin{align*}AB &= DC \AD + DB &= BC + DB \AD &= BC\end{align*}[/tex]

Therefore, we can conclude that:

[tex]$\begin{align*}AD &= BC\end{align*}[/tex]

Thus, the length of AD is equal to the length of BC.

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The simplest form οf the expression (-5/2)+(4/5)x - 17x is (-5/2)-(81/5)x.

Mathematical expressions cοnsist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical οperation.

The term "like terms" in algebra refers tο terms that have the same variable raised tο the same power. Only the numerical coefficients can change in terms similar tο those of algebra. The algebraic expressions can be made simpler by cοmbining like terms, making it much simpler to determine the expressiοn's outcome.

The given expressiοn is

(-5/2)+(4/5)x - 17x

The like terms are (4/5)x and - 17x

Combine like terms:

= (-5/2)+(4 - 85/5)x

= (-5/2)+(- 81/5)x

=  (-5/2) - (81/5)x

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Answer: The function y = 7(2/3)^x is an example of exponential decay.

This is because the base of the exponential function, 2/3, is between 0 and 1, which means that the function is decreasing as x increases. As x increases, the value of (2/3)^x becomes smaller and smaller, which causes the overall value of the function y to decrease over time.

Exponential decay is a type of exponential function where the value of the function decreases over time. In contrast, exponential growth is a type of exponential function where the value of the function increases over time, and the base of the function is greater than 1.

Step-by-step explanation:

Since, that the total interest that will be paid on a 40-year mortgage from a home loan of $100,000 is going to be $480,000. Then,  the payments each month if the payments are to pay off both the loan and the interest will be $1,504.

The 40-year loan has the lowest monthly payment at $1,504. But that only means "saving" $183 per month on the 30-year loan. When considering the total price of the house in this example, adding an additional 10 years to the term of the loan seems overkill, reducing the monthly payment by less than $200.

A 40-year loan doesn't sound like a good deal. But for homeowners struggling to meet their monthly payments and get a 40-year loan modification, the lower payments could have a big impact.

Comparing the 30-year and 15-year numbers is even more extreme. The monthly payment on the 15-year loan is an additional $700. Some buyers can afford higher payments. The advantage of the 15-year loan is that the total interest paid on the loan is $103,218, compared to $289,970 for the 30-year loan. Fifteen years seems to pass so quickly, and it's an exciting feeling to stop paying.

Objections to the 15-year loan could include a missed opportunity. With an interest rate of 4.67% on the 30-year loan, one can expect a higher rate of return in the long run by investing heavily in the stock market. But that raises the question of whether the $700 a month in cash freed up by the 30-year loan will be invested. It might be tempting to spend that money on a more expensive car than the one you would otherwise have purchased.

A family's needs, including space, savings and investment for retirement and education, as well as many household expenses should be considered when deciding which home to buy and the term of the loan. At a minimum, homebuyers need to understand how the different types of loans work.

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Answer:Park rangers released 4 fish into a pond in year 0. Each year, there were three times as many fish as the year before. How many fish were there after x years? Write a function to represent this scenario.

Step-by-step explanation:

An function which best represent the given scenario is,  4 x 3ˣ. So option B is correct.

What is geometric progression?

In algebra, in sequence we study various progressions, one of the progression is geometric, in this progression for every two consecutive terms, the common ratio is the same.

Formula for nth term of G.P.,

Tₙ = a×rⁿ

where a is first term and r is common ratio

Given that,

Park rangers released 4 fish into a pond in year 0.

Each year, there were three times as many fish as the year before.

The number of fish after x years = ?

After 1 year,

the number of fish  =  4 x 3

After 2 year,

the number of fish  = 4 x 3 x 3

                               = 4 x 3²

After 3 year,

the number of fish = 4 x 3² x3

                              = 4 x 3³

Similarly, after x years

the number of fish =  4 x 3ˣ

Hence, the expression is  4 x 3ˣ

Answer:

4/7

Step-by-step explanation:

16/28= 8/14= 4/7

The common attributes of a right pyramid and a sphere are that they both have an apex and a curved surface.

What is a shape?

Shape can be defined as the external physical outline, structure or form of an object or entity. It refers to the appearance or visual characteristic of an object or entity, and is often determined by its edges, contours, curves, angles, or other physical attributes.

A right pyramid and a sphere have some similarities and differences in their attributes.

Similarities:

Both shapes have a single point at the top which is called the apex.

Both shapes have a curved surface. In the case of the right pyramid, the curved surface is a set of triangles that converge to the apex. In the case of the sphere, the curved surface is a continuous, smooth surface.

Both shapes are three-dimensional objects that occupy space.

Differences:

The base of a right pyramid is a polygon, whereas a sphere has no edges or vertices.

The curved surface of a right pyramid is made up of flat triangles, whereas a sphere's curved surface is continuous and has no flat faces.

A right pyramid has edges where the flat faces meet, whereas a sphere has no edges or corners.

A right pyramid has a finite number of vertices and edges, whereas a sphere has an infinite number of points on its curved surface.

A right pyramid can have different base shapes and sizes, whereas a sphere has only one size and shape.

Therefore, the common attributes of a right pyramid and a sphere are that they both have an apex and a curved surface.

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If the total amount given the original price and tax or tip are 123.28,7. 5%, the total amount including tax is $132.52.

To find the total amount given the original price and tax or tip, we need to add the amount of tax or tip to the original price.

In this case, the original price is $123.28 and the tax is 7.5%. To find the amount of tax, we can multiply the original price by the tax rate expressed as a decimal.

Tax = 0.075 x $123.28 = $9.24

Therefore, the amount of tax is $9.24. To find the total amount, we simply add the original price and the amount of tax:

Total amount = $123.28 + $9.24 = $132.52

Note that if the 7.5% was a tip instead of a tax, we would calculate it in the same way by multiplying the original price by the tip rate expressed as a decimal.

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1. For your 24 cans of juice, the possibilities of organizing them in arrays can be:

2. For Teyo's 25 cans of juice, the possible arrays are:

You must first consider the factors of the total number of juice cans you own. For activity 1, you must consider the factors of the 24 cans of juice, that is, the factors of 24, which are 1,2,3,4,6,8,12 and 24, and then find the combinations of these factors to sort them into arrays.

Using the information above, you can effectively draw the arrays on a separate sheet of paper.

Therefore, matrices are meant to represent a set of objects or values in a rectangular shape, arranged in rows and columns and are intended to represent a variety of numerical data, text and images.

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One bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.

William uses 40 milliliters of liquid plant food per week, so to find out how much plant food he needs for 12 weeks, we can simply multiply the weekly usage by the number of weeks:

Amount of plant food needed for 12 weeks = 40 milliliters/week x 12 weeks = 480 milliliters

So, William needs 480 milliliters of liquid plant food for 12 weeks.

Since the bottle of liquid plant food, William purchased contains 0.5 liters or 500 milliliters of liquid plant food, we can see that one bottle is enough for 12 weeks since 480 milliliters is less than the total amount of liquid plant food in the bottle.

In fact, we can calculate how many weeks one bottle of liquid plant food will last William by dividing the total amount of liquid plant food in the bottle by the amount used per week:

Time to use up the liquid plant food = (Total amount of liquid plant food) / (Amount used per week) = 500 ml / 40 ml/week ≈ 12.5 weeks

So, we can say that one bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.

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The correct question should be:

William bought a 0.5 -liter bottle of liquid plant food. He uses 40 milliliters each week? How much plant food does William need for 12 weeks? Is one bottle enough for 12 weeks?

The equation represents the amount of money, in dollars, Kenny will save in x weeks is y = $10*x

We know that Kenny saved 10 dollars every week.

Then, if we define the variable y as the savings, after one week we know that:

y = 10

After another week:

y = 20

And so on.

We can define x as the number of weeks, and now we know that after x weeks, the amount of money that Kenny has saved is x times $10, this gives the linear equation.

y = $10*x

That is the equation we wanted.

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Answer:

To solve this problem, we can use the formula for exponential growth:

N = N0 * (1 + r)^t

Where:

N0 = the initial population size

N = the population size after t time periods

r = the growth rate per time period

t = the number of time periods

In this case, we know that the initial population (N0) is 6000, the growth rate (r) is 15% per day, and we want to find the population size (N) after 10 days (t = 10).

First, we need to convert the growth rate from a percentage to a decimal:

r = 15% / 100% = 0.15

Now we can plug in the values and solve for N:

N = 6000 * (1 + 0.15)^10

N = 6000 * 3.439

N ≈ 20,634

Therefore, the population of bacteria after 10 days would be approximately 20,634.

Answer:

(8x + 1) (8x - 1)

Step-by-step explanation:

64x² - 1

Rewrite 64x² as (8x)²

(8x)² - 1

Rewrite 1 as 1²

(8x)² - 1²

Since both terms are perfect squares, factor using the difference of squares formula, a² - b² = (a + b) (a - b) where a = 8x and b = 1

So, our answer is (8x + 1) (8x - 1)

To solve this equation, we need to consider two cases, one where 2x + 1 is positive and another where it is negative. We will then solve for x in each case and check our solutions to make sure they satisfy the original equation.

Case 1: 2x + 1 ≥ 0

In this case, we have:

|2x + 1| = 2x + 1

and

|3x - 11| = 3x - 11

Substituting these expressions into the original equation, we get:

2x + 1 = 3x - 11

Solving for x, we get:

x = 12

Checking our solution, we have:

|2x + 1| = |2(12) + 1| = 25

and

|3x - 11| = |3(12) - 11| = 25

Therefore, x = 12 is a valid solution to the equation.

Case 2: 2x + 1 < 0

In this case, we have:

|2x + 1| = -(2x + 1) = -2x - 1

and

|3x - 11| = -(3x - 11) = -3x + 11

Substituting these expressions into the original equation, we get:

-2x - 1 = -3x + 11

Solving for x, we get:

x = -10

Checking our solution, we have:

|2x + 1| = |2(-10) + 1| = 21

and

|3x - 11| = |3(-10) - 11| = 41

Therefore, x = -10 is not a valid solution to the equation.

Therefore, the only solution to the equation |2x + 1| = |3x - 11| is x = 12.

Answer:

A kite

Step-by-step explanation:

A kite shape is a quadrilateral in which two pairs of adjacent sides are of equal length. No pair of sides in a kite are parallel but one pair of opposite angles are equal

The diagonals bisect at right angles but all four sides are not equal, the sides are not parallel and there is only one line of symmetry

Answer:

D is (3, -2)
Option D

Step-by-step explanation:

If E is the midpoint of DF then the x-distance between D and E must be the same as that between E and F and similarly for the y-distance

In addition, the x, y coordinates of D must be less than the x, y coordinates for E

x-distance from E to F = 5- 4 = 1

x-distance from D to E = 1 so x-coordinate of D = 4 - 1 = 3

y-distance from E to F = 8 - 3 =  5

y-distance from D to E = 3 - 5 = -2

So coordinate of D is(3, -2)