Can a non-complex equation have 2 horizontal asymptotes? Excluding piecewise equations, o course. Also, what about 2 vertical asymptotes? And using a complex number as x could an equation pass the vertical asymptote? What about the horizontal one?

Answer:

Step-by-step explanation:

To find:-

Answer:-

The given coordinates of the triangle are , A(3,-4) ; B(-2,1) and C(5,0) .

To find out the coordinate of the centroid we can use the below formula ,

[tex]\longrightarrow \boxed{\rm{Centroid\ (G)}= \bigg(\dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3}\bigg)} \\[/tex]

where ,

On substituting the respective values, we have;

[tex]\longrightarrow G =\bigg(\dfrac{3-2+5}{3},\dfrac{-4+1+0}{3}\bigg) \\[/tex]

[tex]\longrightarrow G =\bigg(\dfrac{ 6}{3},\dfrac{-3}{3}\bigg) \\[/tex]

[tex]\longrightarrow \boldsymbol{ G = (2,-1) }\\[/tex]

Hence the centroid of the given triangle is (2,-1) .

Now the given equation of the line is,

[tex]\longrightarrow x - 3y = 4 \\[/tex]

Convert this into slope intercept form of the line, which is,

Slope intercept form:-

[tex]\longrightarrow y = mx + c\\[/tex]

where, m is the slope of the line and c is the y-intercept .

So , we have;

[tex]\longrightarrow -3y = 4-x\\[/tex]

[tex]\longrightarrow 3y = x - 4 \\[/tex]

[tex]\longrightarrow y =\dfrac{x-4}{3} \\[/tex]

[tex]\longrightarrow y =\dfrac{1}{3}x-\dfrac{4}{3} \\[/tex]

On comparing it with the slope intercept form, we have;

[tex]\longrightarrow m =\dfrac{1}{3}\\[/tex]

Secondly we know that the slopes of parallel lines are equal . So the slope of the line parallel to the given line would also be ⅓ .

Now we may use point slope form of the line to find out the equation of the required line. The point slope form of the line is,

Point slope form:-

[tex]\longrightarrow y - y_1 = m(x-x_1) \\[/tex]

where the symbols have their usual meaning.

Here the line will pass through the centroid of the triangle which is (2,-1) .

On substituting the respective values, we have;

[tex]\longrightarrow y - (-1) =\dfrac{1}{3}(x-2) \\[/tex]

[tex]\longrightarrow 3( y +1) = x - 2 \\[/tex]

[tex]\longrightarrow 3y + 3 = x -2\\[/tex]

[tex]\longrightarrow x - 2 - 3 - 3y = 0 \\[/tex]

[tex]\longrightarrow\boxed{\boldsymbol{ x - 3y - 5 =0}} \\[/tex]

This is the required equation of the line.

Answer: C and D

Step-by-step explanation:

The correct centre measure, with a mean value of approximately 5 gallons, will be C. Coffee Ground, with a mean value of about 5 gallons, which will show which shop usually sells the most coffee per hour.

By summing up all the data points and dividing by the total number of data points, the mean is determined.

To determine which coffee shop typically sells the most amount of coffee per hour, we can compare the measures of center, specifically the mean and median, of the two datasets.

Calculating the mean for each dataset, we get:

Coffee Ground: (1.5+20+3.5+12+2+5+11+7+2.5+9.5+3+5)/12 = 6.125 gallons

Wide Awake: (2.5+10+4+18+4+3+6+5+2.5)/9 = 6.0556 gallons

Therefore, Coffee Ground has a higher mean than Wide Awake, suggesting that Coffee Ground typically sells more coffee per hour.

Calculating the median for each dataset, we get:

Coffee Ground: 5 gallons

Wide Awake: 4.5 gallons

Therefore, the median for Wide Awake is lower than that of Coffee Ground, suggesting that Wide Awake typically sells less coffee per hour.

Based on these measures of center, we can conclude that the answer is: C. Coffee Ground, with a mean value of about 5 gallons.

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54 inches = 1 1

2

yards

Formula: divide the value in inches by 36 because 1 yard equals 36 inches.

So, 54 inches = 54

36

= 1 1

2

or 1.5 yards.

Conversion of 54 inches to other length, height & distance units

54 inches = 0.00137 kilometer

54 inches = 1.37 meters

54 inches = 137 centimeters

54 inches = 13.7 decimeters

54 inches = 1370 millimeters

54 inches = 1.372 × 1010 angstroms

54 inches = 0.000852 mile

54 inches = 3

4

fathom

54 inches = 4 1

2

feet

54 inches = 13 1

2

hands

54 inches = 12 fingers

54 inches = 0.429 bamboo

54 inches = 161 barleycorns

Answer: 122 cm²

Step-by-step explanation:

Answer:

a. The scale factor of the smaller cylinder to the larger cylinder is the ratio of their radii, which is 4/6 or 2/3.

b. The circumference of the base of a cylinder is given by 2πr, where r is the radius of the base. Thus, the ratio of the circumferences of the bases of the two cylinders is:

(2π)(4)/(2π)(6) = 4/6 = 2/3

c. The lateral area of a cylinder is given by the formula 2πrh, where r is the radius of the base and h is the height. The ratio of the lateral areas of the two cylinders is:

(2π)(4)(9)/(2π)(6)(9) = 4/6 = 2/3

d. The volume of a cylinder is given by the formula πr²h. Thus, the ratio of the volumes of the two cylinders is:

(π)(4²)(9)/ (π)(6²)(9) = 16/36 = 4/9

e. If the volume of the smaller cylinder is 144π cm³, then we can use the formula for the volume of a cylinder to solve for the height of the smaller cylinder:

144π = π(4²)h

h = 9 cm

Since the two cylinders are similar, we know that the ratio of their heights is the same as the ratio of their radii, which is 2/3. Thus, the height of the larger cylinder is:

(2/3)(9) = 6 cm

Using the formula for the volume of a cylinder, we can now calculate the volume of the larger cylinder:

V = π(6²)(6) = 216π cm³

Step-by-step explanation:

pa brainliest po.

Answer:

d.

Step-by-step explanation:

To find the weight of the puppy when it is 15 weeks old, we need to substitute 15 for x in the equation of the line of best fit:

y = 2x + 1.5

y = 2(15) + 1.5

y = 31.5

Therefore, the weight of the puppy when it is 15 weeks old is 31.5 units, where the units depend on the units used to measure weight (e.g. pounds, kilograms, etc.).

Therefore , the solution of the given problem of volume comes out to be  roughly 1,814.4 cubic feet.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. These symbols for cubic dimensions are liter and in3. However, you must be aware of an object's volume in order to calculate its dimensions. It is standard practice to translate an object's weight to mass units like grams and kilograms.

Here,

V = r2h, where r is the radius and h is the height, is the expression for a cylinder's volume.

We are informed that the cylindrical has a 9-foot height and an 8-foot radius. (since the diameter is 16 ft).

When the formula's numbers are substituted, we obtain:

=> V = π(8 ft)²(9 ft)

=> V = π(64 ft²)(9 ft)

=> V = 1,814.37 ft³

We can calculate this result as V = 1,814.4 ft³ by rounding to the nearest tenth.

The cylinder's capacity is therefore roughly 1,814.4 cubic feet.

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The probability that an individual has a total cholesterol level between 200 and 250 is calculated to be approximately 0.5020 or 50.2%.

To solve this problem, we need to find the z-scores corresponding to the lower and upper bounds of the cholesterol range, and then find the area under the normal distribution curve between these z-scores.

First, we calculate the z-score for 200:

z1 = (200 - 219) / 41.6 = -0.455

Next, we calculate the z-score for 250:

z2 = (250 - 219) / 41.6 = 0.746

Now we can use a standard normal distribution table or calculator to find the area between these two z-scores:

P(-0.455 < Z < 0.746) ≈ 0.5020

This means that the probability that an individual has a total cholesterol level between 200 and 250 is approximately 0.5020 or 50.2% (rounded to one decimal place).

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Port C is approximately 148.96 kilometers to the east of Port A, at a bearing of 013.93 degrees from the positive x-axis.

How to find distance and direction?

To find the distance and direction of Port C from Port A, we can use basic trigonometry and vector analysis.

First, we need to draw a diagram of the situation. We can assume that Port A is located at the origin (0,0) of a two-dimensional coordinate system, and that the ship sails in a straight line from A to B on a bearing of 050 degrees, which means that its direction is 40 degrees clockwise from the positive x-axis. Since Port B is 80 kilometers to the east of A, we can represent it as the point (80,0) in the coordinate system.

Next, the ship sails from B to C on a bearing of 062 degrees, which is 22 degrees clockwise from its previous direction. To calculate the distance and direction of C from A, we need to find the vector that represents the displacement of the ship from B to C, and add it to the vector that represents the displacement from A to B.

To find the vector that represents the displacement from B to C, we can use basic trigonometry. Let d be the distance from B to C, and let θ be the angle between the displacement vector and the positive x-axis. Then, we have:

cos(θ) = adjacent/hypotenuse = 80/d

sin(θ) = opposite/hypotenuse = (d*sin(22))/d = sin(22)

Solving for d, we get:

d = 80/cos(θ) = 80/cos(arctan(sin(22)/cos(22))) ≈ 92.56 km

Therefore, the vector that represents the displacement from B to C is (dcos(θ), dsin(θ)) ≈ (64.39 km, 35.77 km) in the coordinate system.

To find the vector that represents the displacement from A to C, we can add the two vectors:

(80,0) + (64.39,35.77) ≈ (144.39,35.77)

Therefore, the distance from A to C is the magnitude of this vector:

|AC| = sqrt((144.39)² + (35.77)²) ≈ 148.96 km

To find the direction of C from A, we can use the inverse tangent function:

tan⁻¹(35.77/144.39) ≈ 13.93 degrees

Therefore, Port C is approximately 148.96 kilometers to the east of Port A, at a bearing of 013.93 degrees from the positive x-axis.

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The actual population mean is between 1.5 and 2.1 vehicles per household.

The median is a statistical measure that represents the middle value of a dataset. It is the value that separates the lower half of the dataset from the upper half. To find the median, the data must be arranged in order from smallest to largest, and then the middle value is identified.

If the dataset contains an odd number of values, then the median is the middle value. For example, if the dataset is {2, 4, 6, 7, 9}, then the median is 6, which is the middle value.

If the dataset contains an even number of values, then the median is the average of the two middle values. For example, if the dataset is {2, 4, 6, 7, 9, 10}, then the median is (6+7)/2 = 6.5, which is the average of the two middle values, 6 and 7.

The actual population mean is between 1.5 and 2.1 vehicles per household.

The margin of error represents the possible distance between the sample mean and the true population mean.

The lower bound is found by subtracting the margin of error from the sample mean:

1.8 - 0.3 = 1.5

The upper bound is found by adding the margin of error to the sample mean:

1.8 + 0.3 = 2.1

Therefore, we can be 95% confident that the true population mean falls between 1.5 and 2.1 vehicles per household.

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Answer:

look below its the answer i promise

Step-by-step explanation:

This is challenging to visualize but similar to your other problem. You want to maximize x and y to maximize c.

The problem just boils down to solving the linear system.

2x + 2y = 10

3x + y = 9

I changed the less than or equal signs to equal signs because we want the largest values not the ones less than the max. I think you know how to solve this system based on the difficulty of the problem but I can give a solution. Let's use elimination. Multiplying the second equation by two and adding it to the first we have...

   -2(3x + y = 9)

+ (2x + 2y = 10)

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

-4x = -8

x = 2

Then y = 9 - 3x (from eq 2) = 9 - 3(2) = 3

Then the max value of c = 4(2) + 2(3) = 14

Answer:x+y=c

Step-by-step explanation:

Answer: 247in

Step-by-step explanation:

Area of a circle is pi radius squared.

So that'll be 3.14 times 9 (because radius is halve if a diameter) squared.

First using Order of Operations squaring the 9, so that'll be 81.

Lastly you multiply π or 3.14.

So 81 x 3.14 is 247.  Which is rounded down to the nearest whole number.

Happy Solving.

Answer:

[tex]728 \: {m}^{2} [/tex]

Step-by-step explanation:

Given:

l = 15 m (length)

w = 16 m (width)

h = 4 m (height)

Find: a (surface) - ?

First, let's find the area of the base:

a (base) = l × w

a (base) = 15 × 16 = 240 m^2

Since the rectangular prism has 2 bases, we multiply this number by 2:

240 × 2 = 480 m^2 (area of both bases)

Now, let's find the lateral surface area:

a (lateral) = 2(4 × 15) + 2(4×16) = 2 × 60 + 2 × 64 = 120 + 128 = 248 m^2

Finally, in order to find the whole surface area, we have to add the lateral surface area and both bases area together:

a (surface) = a (lateral) + a (base)

a (surface) = 248 + 480 = 728 m^2

The solutions to the equation log4(x² - 2x) = log4(3x + 8) are x = 8 and x = -1.

To solve the equation log4(x² - 2x) = log4(3x + 8), we can use the property of logarithms that says if logb(a) = logb(c), then a = c.

Using this property, we can set the expressions inside the logarithms equal to each other:

x² - 2x = 3x + 8

Now we have a quadratic equation that we can solve:

x² - 2x - 3x - 8 = 0 x² - 5x - 8 = 0

We can factor this equation using the product-sum method:

x² - 5x - 8 = (x - 8)(x + 1)

Setting each factor equal to zero gives us the possible solutions:

x - 8 = 0 or x + 1 = 0

Solving for x in each case gives us:

x = 8 or x = -1

However, we need to check if either of these solutions make the argument of the logarithm negative or zero. If the argument is negative or zero, then the logarithm is undefined.

For the first solution, x = 8, we have:

log4(8² - 2(8)) = log4(3(8) + 8) log4(48) = log4(32)

Both arguments are positive, so x = 8 is a valid solution.

For the second solution, x = -1, we have:

log4((-1)² - 2(-1)) = log4(3(-1) + 8) log4(3) = log4(5)

Again, both arguments are positive, so x = -1 is also a valid solution.

Therefore, the solutions to the equation log4(x² - 2x) = log4(3x + 8) are x = 8 and x = -1.

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Therefore, according to Paul's model, a student who spends 3 hours on homework is predicted to get a test score of 64.

In mathematics, a function is a rule or relationship that maps each input value (also known as the "argument" or "independent variable") to a corresponding output value (also known as the "value" or "dependent variable").

In other words, a function is a way to describe how one set of values (the inputs) are transformed into another set of values (the outputs). Functions are often represented using algebraic equations or graphical representations, such as graphs or charts.

For example, the function f(x) = 2x + 1 maps each input value x to the output value 2x + 1. So, if we input x=2, the output value would be f(2) = 2(2) + 1 = 5. Similarly, if we input x=3, the output value would be f (3) = 2(3) + 1 = 7.

(a) Based on the scatter plot, we can see a positive linear relationship between the hours spent on homework and the test scores. As the number of hours spent on homework increases, the test scores also tend to increase.

(b) To use Paul's function to predict the test score for 3 hours of homework, we can substitute x = 3 into the equation:

[tex]y = 8x + 40[/tex]

[tex]y = 8(3) + 40[/tex]

[tex]y = 24 + 40[/tex]

[tex]y = 64[/tex]

Therefore, according to Paul's model, a student who spends 3 hours on homework is predicted to get a test score of 64.

(c) In the context of the situation, the number 40 in Paul's model represents the baseline or minimum test score that a student would get if they didn't study at all. This is the y-intercept of the line and indicates that a student who does not spend any time on homework is predicted to get a score of 40.

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To factorize the expression 2x3 + 5x2 + 6x + 15, we can look for common factors: 2x3 + 5x2 + 6x + 15 = x2(2x + 5) + 3(2x + 5) = (x2 + 3)(2x + 5)

Therefore, option C (x2 + 3)(2x + 5) is equivalent to the given expression.

To solve the problem, we need to factorize the given expression and compare it with the given options to find the equivalent expression.

The given expression is:

2x3 + 5x2 + 6x + 15

To factorize it, we can look for common factors:

2x3 + 5x2 + 6x + 15 = x2(2x + 5) + 3(2x + 5)

Now we can see that (2x + 5) is a common factor. Factoring it out, we get:

2x3 + 5x2 + 6x + 15 = (2x + 5)(x2 + 3)

Complete Question Below:

2x3 + 5x2 + 6x + 15

Which of the following is equivalent to the expression above?

A. (x + 3)(2x2 + 5)

B. (x + 5)(2x2 + 3)

C. (x2 + 3)(2x + 5)

D. (x2 + 5)(2x + 3)

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The amount of money in an account at the end of 5 years will be $14,014.40.

To calculate this, we can use the continuous compounding formula: [tex]A = Pe^(rt)[/tex] where P = 10,000, r = 6.75% (0.0675), t = 5.

Now, the amount of money in an account at the end of 5 years will be:

A = 10,000*e^(0.0675*5)

A = 10,000*e^0.3375

A = 10,000*1.40143960839

A = 14014.3960839

A = $14,014.40

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The school begin with 25 cookies based on remaining 24 cookies and first selling of 4% cookies.

Let us assume the initial number of cookies be x. So, the remaining cookies percentage = 96%

Now, we are given the remaining cookies number. So, the equation will be -

96% × x = 24

Solving the equation by firstly converting the percentage into decimal

0.96x = 24

Rewriting the equation to further calculate the value of x

x = 24/0.96

Performing division on Right Hand Side of the equation

x = 25

Thus, there were total 25 cookies.

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The probability that a randomly selected user is online less than 15 hours a week is 0.1056 (approx).

As per the given statement, u.s. internet users spend an average of 18.3 hours a week online. If 95% of users spend between 13.1 and 23.5 hours a week, we need to determine the probability that a randomly selected user is online less than 15 hours a week.

To find the probability that a randomly selected user is online less than 15 hours a week, we need to use the Z-score formula, which is defined as:

Z = (X - μ) / σ

Where Z is the z-score, X is the value of the element, μ is the mean of the population, and σ is the standard deviation. Therefore, the probability of a randomly selected user being online less than 15 hours per week can be calculated as follows:Z = (15 - 18.3) / σ

We know that 95% of users spend between 13.1 and 23.5 hours per week, which means that the standard deviation is given by:

13.1 - 18.3 = 5.4 hours (lower bound)

23.5 - 18.3 = 5.2 hours (upper bound)

Therefore, σ = (5.4 + 5.2) / 4 = 2.65 hours

Hence, the z-score can be calculated as follows:Z = (15 - 18.3) / 2.65 = -1.25

Thus, the probability that a randomly selected user is online less than 15 hours a week is P(Z < -1.25). Using a standard normal distribution table, we can find that P(Z < -1.25) = 0.1056 (approx).

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The answer to the given question about IQR is option b Bus 14, with an IQR of 6.

To determine which bus is the most consistent, we need to look at the measure of variability for each data set. In this case, we are given the interquartile range (IQR) and the range for each bus. The IQR is a better measure of variability than the range because it is less affected by outliers.

Bus 47 has an IQR of 8, which means that the middle 50% of the data falls within a range of 8 minutes. Bus 14 has an IQR of 6, which means that the middle 50% of the data falls within a range of 6 minutes.

Since Bus 14 has a smaller IQR, it is more consistent than Bus 47. This means that the travel times for Bus 14 are more similar to each other than the travel times for Bus 47. Therefore, we can conclude that Bus 14 is the most consistent of the two buses.

Therefore, the correct answer is:

Bus 14, with an IQR of 6.

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To determine the rows where the expression (p ∧ q) ∨ (p ∧ r) is true, we can construct a truth table with columns for p, q, r, p ∧ q, p ∧ r, (p ∧ q) ∨ (p ∧ r), as shown below:

```

p | q | r | p ∧ q | p ∧ r | (p ∧ q) ∨ (p ∧ r)

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

T | T | T | T | T | T

T | T | F | T | T | T

T | F | T | F | T | T

T | F | F | F | F | F

F | T | T | F | F | F

F | T | F | F | F | F

F | F | T | F | F | F

F | F | F | F | F | F

```

The rows where the expression (p ∧ q) ∨ (p ∧ r) is true are the first, second, and third rows, where the last column is true. Therefore, the rows where the expression is true are:

```

p | q | r

--------

T | T | T

T | T | F

T | F | T

```

the simplified form of the given expression is 2cd³(12c + 5d²).just by using simple mathematics we are able to solve to get answer.

what is simplified form ?

Simplified form refers to the expression of a mathematical expression or equation in a way that is easier to read, understand, and manipulate. Simplification involves combining like terms, factoring out common factors, reducing fractions, or using identities to transform the original expression to an equivalent but simpler form. The simplified form of an expression should have no unnecessary or redundant terms or factors and should be as concise and clear as possible.

In the given question,

Simplified form refers to the expression of a mathematical expression or equation in a way that is easier to read, understand, and manipulate.

Simplification involves combining like terms, factoring out common factors, reducing fractions, or using identities to transform the original expression to an equivalent but simpler form.

The simplified form of an expression should have no unnecessary or redundant terms or factors and should be as concise and clear as possible.

The given expression is a polynomial in two variables c and d. We can simplify it by factoring out the common factors from each term:

24c² d³ + 10cd⁵ =2cd³(12c + 5d²)

Therefore, the simplified form of the given expression is 2cd³(12c + 5d²)

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what is simplified form of 24c² d³+10cd⁵ ?

...where h = -8 and k = -3.

The graph for y = 4(1/4)ˣ is B)

Explain graphs.

A graph is a visual representation of a set of data, typically in the form of a diagram or a chart. A graph is made up of points, called vertices or nodes, that are connected by lines or curves, called edges. Graphs can be used to display various types of information, including mathematical functions, relationships between variables, and patterns in data. They are commonly used in fields such as science, engineering, economics, and social sciences to convey complex information in a simple and easy-to-understand manner.

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The equivalent expression to the given equation is (2 x 10⁸)(2 x 10⁻²) and  40 x 10⁵.

What is an equivalent expression?

Equivalent expressions do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two equivalent algebraic expressions have the same value (s).

Here, we have

Given: 4 x 10⁶

We have to find the equivalent expression to the given equation.

A. (2 x 10⁸)(2 x 10⁻²)

= (2 × 2)(10⁸× 10⁻²)

= 4×10⁶

B. 40 x 10⁵

= 4×10×10⁵

= 40×10⁵

Hence,  the equivalent expression to the given equation is (2 x 10⁸)(2 x 10⁻²) and  40 x 10⁵.

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