Find the vertical asymptotes of the rational function: g(x) x3 - x2 + 5x - 3 4x2 - 1

WE WILL USE THE FORMULA OF CALCULATING GRADIENT

\(m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{j - 1}{9 - 6} \\ \frac{1}{3} = \frac{j - 1}{3} \)

I WILL USE CROSS MULTIPLICATION

\(3(j - 1) = 3 \\ \frac{3(j - 1)}{3} = \frac{3}{3} \\ j - 1 = 1 \\ j = 1 + 1 \\ j = 2\)

ATTACHED IS THE SOLUTION

BE ALERT I INSERTED THE KNOWN VALUES IN THE FORMULA OF FINDING THE GRADIENT.

Answer:

A≈28.27

Step-by-step explanation:

Solved for area

Shape: circle

Radius: 3cm

Formula: A=πr2

Answer: A≈28.27

Hope this helps.

The equatiion where C is the constant of integration.To evaluate the indefinite integral ∫(3e^x + 4x^5 - x^3/4 + 1)dx, we can integrate each term separately.

∫3e^x dx = 3∫e^x dx = 3e^x + C₁

∫4x^5 dx = 4∫x^5 dx = 4 * (1/6)x^6 + C₂ = (2/3)x^6 + C₂

∫-x^3/4 dx = (-1/4)∫x^3 dx = (-1/4) * (1/4)x^4 + C₃ = (-1/16)x^4 + C₃

∫1 dx = x + C₄

Now, we can combine these results to obtain the final answer:

∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C

Therefore, the indefinite integral of (3e^x + 4x^5 - x^3/4 + 1)dx is:

∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C

where C is the constant of integration.

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Answer:answer is D relative house

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

To find the parametric equations of the intersection of the planes, we can set up a system of equations by equating the two given plane equations:

x + (y - 8) + z = 0

-x + (y + 8) - z = 0

Let's isolate the variables:

From the first equation, we have:

x = -y + 8 - z

Substituting this into the second equation, we get:

-(-y + 8 - z) + (y + 8) - z = 0

Simplifying, we have:

y - 8 + z + y + 8 - z = 0

2y = 0

y = 0

Substituting y = 0 back into the first equation, we get:

x = -0 + 8 - z

x = 8 - z

Now, we can express the variables x, y, and z in terms of a parameter t:

x = 8 - t

y = 0

z = t

Therefore, the parametric equations of the intersection of the planes are:

x = 8 - t

y = 0

z = t

In vector form, the parametric equations can be written as:

(r(t) = (8 - t) i + 0 j + t k

where i, j, and k represent the unit vectors along the x, y, and z axes, respectively.

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Answer:

4 hours.

Step-by-step explanation:

According to the statement, you know that the amount she earns per week is equal to the first 30 hours for the price per hour that is $4 plus the number of hours over 30 hours multiply for its price that is $6. According to this, you can write the following equation where x is the hours of overtime per week:

4(30)+6x=144

120+6x=144

Now, you can solve for x:

6x=144-120

6x=24

x=24/6

x= 4

According to this, the answer is that Kate will need 4 hours of ovetime per week to achieve her goal.

Answer: C: y=1.15x + 10.95

Step-by-step explanation:

look it up

Answer:

X=12,-4

Step-by-step explanation:

Set them equal to each other to get x^2=8x+48. Then move them both to the other side to get x^2-8x-48. Then factor the expression to get (x-12)(x+4). Set that to 0 to get x=12 and x=-4

Given vector u, the magnitude |u| is 10 and the directional angle θ in the standard position is 143.1°.

To determine the magnitude |u| and directional angle θ of a vector, we need the x-component and y-component of the vector. However, the given options only provide the magnitude and directional angle. Therefore, we need to use trigonometry to calculate the x and y components.

Let's assume the vector u is represented as (x, y) in the standard position. We can use the magnitude |u| and the directional angle θ to find the x and y components. The x component is given by |u| * cos(θ) and the y component is given by |u| * sin(θ).

Comparing the given options, we find that option d) |u| = 10 and θ = 143.1° matches our calculated values for the magnitude and directional angle.

Therefore, the correct answer is d) |u| = 10, θ = 143.1°.

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Answer:

3/5

Step-by-step explanation:

\( \frac{27}{45} = \frac{27 \div 9}{45 \div 9} = \frac{3}{5} \\ \)

The distance between the base of the 11-foot ladder and the base of the wall, rounded to the nearest hundredth, is approximately 4.28 feet.

We can use the idea of right triangles that are similar to each other to solve this issue. In similar triangles, the lengths of the sides that are corresponding to each other are equal.

Let's say that there is a distance of "x" feet between the base of the wall and the base of the 11-foot ladder.

Regarding the 9-foot ladder:

The hypotenuse measurement of the ladder is 9 feet, and the adjacent side measurement of the distance is 3.5 feet. For the 11-foot ladder:

The length of the stepping stool (hypotenuse) = 11 feet

The separation from the foundation of the stepping stool to the foundation of the wall (neighboring side) = 'x' feet

Utilizing the proportion of comparing sides of comparative triangles, we can set up the accompanying extent:

9 / 3.5 = 11 / x We can cross-multiply to solve for "x":

9x = 3.5 * 11 9x = 38.5 Now divide by 9 on both sides:

x = 38.5 / 9 x  4.28 indicates that the 11-foot ladder's base is approximately 4.28 feet away from the wall's base, rounded to the nearest hundredth.

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Answer:

Step-by-step explanation:

Given:

Isolate b:

Find b:

\(\\ \sf\longmapsto t+\dfrac{1}{2}b=Y\)

\(\\ \sf\longmapsto \dfrac{1}{2}b=Y-t\)

\(\\ \sf\longmapsto \dfrac{b}{2}=Y-t\)

\(\\ \sf\longmapsto b=2(Y-t)\)

\(\\ \sf\longmapsto b=2Y-2t\)

Answer:

A = £1102.50

Step-by-step explanation:

Use the compound amount formula:

A = P(1 + r)^t, where P is the principal, r is the interest rate as a decimal fraction, and t is the number of years.

Here A = £1000·(1 + 0.05)^2, which evaluates to  A = £1102.50

If the confidence level were increased to 99%, the width of the confidence interval increases, when decreased to 80%, the width of the confidence interval decreases.

A confidence interval provides a range of estimated values for a population parameter's real value. A confidence level is connected to confidence intervals. The width of the confidence interval grows as the confidence level increases. The width of the confidence interval reduces as the confidence level goes down.

Since the margin of error grows as the confidence level does as well, the confidence interval will be bigger. Hence it increases for 99% and decreases for 80%.

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Answer:

It's the 1st one:

\( \frac{2x + 1}{x - 1} \)

Step-by-step explanation:

There is a correct way to do this, but because it's multiple choice you can plug any value, preferably not any negatives, 0 or 1, into the x and then calculate. I plug 2 in for x and got 5 as my answer then I went to the answers and the 1st equaled 5

Answer:

Step-by-step explanation:

Number of side = n = 7

Sum of interior angles of 'n' sided polygon = (n - 2) *180

    = (7 - 2)* 180

    = 5 * 180

     = 900

x + 150 + x -20 + 140 + 120 + x + 20 + 130 = 900

Combine like terms

x +x +x + 150 - 20 + 140 + 120 + 20 +130 = 900

3x + 540 = 900    {Subtract 540 from both sides}

           3x  = 900 - 540

           3x = 360       {Divide both sides by 3}

             x = 360/3

x = 120

  Interior angle                    Exterior angle

∠A = 120                                  180 - 120 = 60

∠B = 130                                   180 - 130 = 50

∠C = 120 + 20 = 140                180 - 140 = 40

∠D = 120                                   180 - 120 = 60

∠E =  140                                   180 - 140 = 40

∠F = 120 - 20 = 100                  180 -100  = 80

∠G = 150                                    180 - 150 = 30

The alternative hypothesis will be French people differ from English people in height.

A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables.

In statistical hypothesis testing, null and alternate hypotheses are applied. The null hypothesis of a test always predicts no effect or no association between variables, but the alternative hypothesis reflects the effect or relationship that your research predicts.

Given

Null hypothesis- French people do not differ from English people in height.

Therefore, the Alternative hypothesis for the given statement is - French people differ from English people in height.

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The graph of the transformation by of horizontally compressing g(x) by a factor of 1/2 and then reflecting across the x-axis is graph Y

The function is given as:

\(g(x) = 2^x\)

When compressed horizontally by a factor of 1/2, the transformation rule is:

g'(x) = g(2x)

So, we have:

\(g(2x) = 2^{2x}\)

\(g(2x) = 4^x\)

When reflected across the x-axis, the transformation rule is:

\((x,y) \to (x,-y)\)

So, we have:

\(f(x) = -4^x\)

The graph represented by this is graph Y.

Hence, the graph of the transformation is graph Y

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Answer:

It will take 2 snacks for Benjamin and Landon to spend the same amount

Step-by-step explanation:

Assume they bought x snacks

∵ Benjamin spends $9.50 for a movie ticket at Emagine and $4.50

  for each snack

∵ He bought x snacks

→ Multiply the number of snacks by 4.50 and add it to 9.50

∴ The amount he spent = 4.50x + 9.50

∵ Landon spends $8 for a movie ticket at AMC and $5.25 for each snack

∵ He bought x snacks

→ Multiply the number of snacks by 5.25 and add it to 8

∴ The amount he spent = 5.25x + 8

∵ They spent the same amount of money

→ Equate the right sides of their amount spent

∴ 5.25x + 8 = 4.50x + 9.50

→ Subtract 4.50x from both sides

∵ 5.25x - 4.50x + 8 = 4.50x - 4.50x + 9.50

∴ 0.75x + 8 = 9.50

→ Subtract 8 from both sides

∵ 0.75x + 8 - 8 = 9.50 - 8

∴ 0.75x = 1.50

→ Divide both sides by 0.75

∴ x = 2

∵ x represents the number of snacks they bought

∴ It will take 2 snacks for Benjamin and Landon to spend the same amount

Answer:

c = 3.6

Step-by-step explanation:

  x - 4y = 4

-3x - 4y = 12

Subtract the first equation from the second

  x - 4y = 4

-4x      = 12

Divide the second equation by (-4)

  x - 4y = 4

  x      =  -3

Subtract the second equation from the first

   - 4y  =  7

  x      =  -3          

Divide the first equation by (-4)    

       y  =  -7/4

  x      =  -3        

After answering the given query, we can state that  where w is the graphs amount of service weeks and c is the cost in dollars. Solution: c = 7w plus 35

Mathematicians use graphs to visually depict or chart facts or values in a logical way. Usually, a graph point will show the connection between two or more objects. A graph is a non-linear data structure made up of nodes, also known as vertices, and lines. The nodes, also referred to as edges, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, while edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical representations of exponential development in statistical charts, such as bar charts, pie charts, and line graphs. a triangle-shaped exponential graph.

Y = mx + b, where y is the expense (in dollars), x is the number of weeks, m is the slope, and b is the y-intercept, can be used as the slope-intercept form of a linear equation.

As we can see from the histogram, when w = 1, the price is $35, so the y-intercept is set to b = 35. Additionally, we can see that the price rises by $7 for each extra week of service, resulting in a slope of m = 7.

Consequently, the following equation depicts the price of the food delivery service:

c = 7w + 35

where w is the amount of service weeks and c is the cost in dollars.

Solution: c = 7w plus 35

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The expression should be substituted into the first equation is "x = 8 -2y"  and also the value of x = 3 and y = 2.5

What do you mean by substitution?

The substitution method is an algebraic strategy for resolving simultaneous linear equations. This approach, as the name suggests, involves substituting the value of one variable from one equation into the second equation. This makes it easier to answer a pair of linear equations by combining them into a single equation with a single variable.

The equations given in the question,

2x - 4y = -4

x + 2y = 8

Let these two equation be named as 1 and 2 respectively.

Taking equation 2 and making x stay one side and all others on other side of the equation. We get,

x = 8 -2y

Substituting this value of x in equation 1.

2x - 4y = -4

2(8 - 2y) - 4y = -4

y = 2.5

substituting this value of y in equation 2,

x + 2y = 8

x = 8 - 5

x = 3

Therefore, The expression should be substituted into the first equation is "x = 8 -2y"  and also the value of x = 3 and y = 2.5

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Complete Question

Using substitution to solve the system below, what expression should be substituted into the first equation? 2x-4y=-4 and x+2y=8

Answer:

x = -2/3  x=1

Step-by-step explanation:

We cant solve by substitution with just one equation

-3x^2 + x +2=0

Factor out a negative

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

Divide by negative 1

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

Factor

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

Using the zero product property

3x+2 =0   x-1 =0

3x= -2   x=1

x = -2/3  x=1

Answer:

\(x = \frac{2}{3} \\ x = - 1\)

Step-by-step explanation:

\(x - 3 {x}^{2} + 2 = 0 \\ - 3 {x}^{2} + x + 2 = 0 \\ - 3 {x}^{2} - 3x + 2x + 2 = 0 \\ - 3x(x + 1) + 2(x + 1) = 0 \\ ( - 3x + 2)(x + 1) = 0\)

\( - 3x + 2 = 0 \\ - 3x = - 2 \\ \frac{ - 3x}{ - 3} = \frac{ - 2}{ - 3} \\ x = \frac{2}{3} \)

\(x + 1 = 0 \\ x = - 1\)

hope this helps

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The percentage of people playing basketball is approximately 86.67%.

To determine the percentage of people playing basketball, we need to find the number of people playing basketball.

Given that there are 14 people who play football, 5 people who play both football and basketball, and a total of 30 people playing one sport, we can use this information to calculate the number of people playing basketball.

Let's denote the number of people playing basketball as 'B'.

From the given information, we know that:

The number of people playing football only = 14 - 5 = 9

The number of people playing basketball only = 30 - 9 = 21

The number of people playing both football and basketball = 5

To find 'B', we sum up the number of people playing basketball only and those playing both sports:

B = 21 + 5 = 26

Now, to calculate the percentage of people playing basketball, we divide the number of people playing basketball by the total number of people and multiply by 100:

Percentage of people playing basketball = (26 / 30) \(\times\) 100 = 86.67%

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We  can be 95% confident that the true population mean falls within a range of 100 ± 9.31 days, or between 90.69 and 109.31 days.

To determine when it is optimal to put their house on the market, the family should consider their personal circumstances and financial needs, as well as market conditions in St. Louis.

Assuming the family wants to sell their house as soon as possible, they may want to consider listing their house for sale before the average time it takes for houses to sell in their neighborhood, which is 100 days. Since the standard deviation of this sample is 20 days, we can assume that the true population standard deviation is also around 20 days.

One common way to determine the optimal time to put a house on the market is to use a statistical technique called a confidence interval. A confidence interval can give us a range of values within which we can be reasonably confident that the true population mean (i.e., the average time it takes for houses to sell in the neighborhood) falls.

Assuming a normal distribution and a 95% confidence level, we can calculate the confidence interval as follows:

Margin of error = z-score * (standard deviation / square root of sample size)
where z-score = 1.96 (for a 95% confidence level)

Using the information provided, we can calculate the margin of error as:

Margin of error = 1.96 * (20 / sqrt(18)) = 9.31

This means that we can be 95% confident that the true population mean falls within a range of 100 ± 9.31 days, or between 90.69 and 109.31 days.

Based on this analysis, the family may want to consider listing their house for sale before the lower end of this confidence interval, which is around 90 days. However, it's important to keep in mind that this is just a statistical estimate and may not necessarily reflect actual market conditions. Other factors, such as the local economy, interest rates, and housing demand, can also affect the timing of a home sale.

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Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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