Answers
Answer:
Horizontal Asymptote: None (degree of numerator is larger than denominator)
Vertical Asymptote: None (domain of function is \(\mathbb{R}\))
x-intercept: (0, 0)
y-intercept: (0, 0)
Hole: (-2, 1)
Step-by-step explanation:
HA: Since the degree of the numerator (2) is larger than the degree of the denominator (1), no HA exists.
VA: Since the domain of the function of is \(\mathbb{R}\) (all real numbers), no VA exists. *no real value of x will make the denominator equal to 0 and numerator \(\neq\) 0
x-intercept:
The x-intercept occurs at \(y=0\).
Solving for x:
\(0=\frac{-2x^2-4x}{4x+8}\):
\(0=-2x^2-4x,\\x=0\). Therefore, the x-intercept is (0, 0).
y-intercept:
The y-intercept occurs when \(x=0\).
Solving for y:
\(\frac{-2x^2-4x}{4x+8}, x=0,\\\frac{-2(0)^2-4(0)}{4(0)+8}=0\). Therefore, the y-intercept is (0, 0).
Hole:
When looking for a hole, we are looking for a factor that occurs in both the numerator and denominator:
\(\frac{-2x^2-4x}{4x+8}=\frac{-2x(x+2)}{4(x+2)}\)
Rewriting our function here, we see that the term \((x+2)\) occurs in both the numerator and denominator. Thus, when this term is set to 0, it will make both the numerator and denominator 0, thus rendering an undefined value (since we cannot divide by 0). We call this a hole. *Note: Usually when an x-value makes the denominator zero, this will create a vertical asymptote. However, if the x-value also makes the numerator zero, it's considered a hole, not an asymptote. The x-value of this hole will be the value of when the common term is equal to 0:
\(x+2=0,\\x=-2\)
To find the y-value of the hole, remove the common term and plug in your x-value:
\(\frac{-2x^2-4x}{4x+8}=\frac{-2x(x+2)}{4(x+2)}=\frac{-2x}{4},\\\frac{-2(-2)}{4}=\frac{4}{4}=1\)
Therefore, the hole of this function is at (-2, 1).
Related Questions
A class planted 130 seeds. 52 seeds grew into plants. What percent of the seeds grew into plants?
Answers
Answer:
40%
Step-by-step explanation:
52/130 =.4
.4 x 100=40
Answer:
40%
Step-by-step explanation:
40%
Oprah looks at this histogram of a distribution with a mean of 6.7 grams
and a standard deviation of 1 gram. She claims that approximately 68% of
the data is between 5.7 and 7.7 grams. What is the error in her thinking?
Answers
Answer:
68% of the data is between 5.7 and 7.7 grams.
Step-by-step explanation:
According to the empirical rule for a normal distribution, 68% of data falls within one standard deviation, 95% of data falls within two standard deviation and 99.7% of data falls within three standard deviation.
Given that:
mean (μ) = 6.7 grams, standard deviation (σ) = 1 gram.
From the empirical rule:
68% of the data is between one standard deviation i.e μ ± σ = 6.7 ± 1 = 5.7, 7.7
Therefore 68% of the data is between 5.7 and 7.7 grams.
en una granja hay comida para alimentar a 300 conejos durante 60 días. Cuántos conejos hay que vender si se quieren alimentar durante 15 días más?
Answers
The number of rabbits that must be sold if they want to be fed for 15 more days is 150 rabbits.
In a farm, there is food to feed 300 rabbits for 60 days.
Let x be the number of rabbits that must be sold if they want to be fed for 15 more days.
From the given data, we have the following equation:
300 * 60 = (300 - x) * 75
The equation represents the amount of food for 300 rabbits that can last 60 days is equal to the amount of food for 300 - x rabbits that can last 75 days.
Solving for x, we get:
x = 150 rabbits
Hence, the number of rabbits that must be sold if they want to be fed for 15 more days is 150 rabbits.
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Fill in the blank. methods used that summarize or describe characteristics of data are called _______ statistics.
Answers
The methods used to summarize or describe characteristics of data are called descriptive statistics.
Descriptive statistics refers to the branch of statistics that focuses on summarizing and describing the main features or characteristics of a dataset. These statistics provide a way to organize, present, and analyze data to gain insights and understand the data's properties. Here are some key points about descriptive statistics:
Data summarization: Descriptive statistics aim to summarize the main aspects of a dataset, including measures of central tendency (such as mean, median, and mode) that provide information about the typical or average value of the data. Measures of dispersion (such as range, variance, and standard deviation) describe the spread or variability of the data points.
Presentation and visualization: Descriptive statistics often involve presenting data in a meaningful and concise manner. This can be done through various graphical representations, such as histograms, bar charts, box plots, or scatter plots. These visualizations help to provide a clear understanding of the distribution, patterns, and relationships within the data.
Sample statistics and population parameters: Descriptive statistics can be calculated for either a sample or an entire population. Sample statistics are calculated based on data from a subset of the population, while population parameters describe the entire population. Sample statistics, such as sample mean or sample standard deviation, provide estimates or approximations of the population parameters.
Descriptive statistics are widely used in various fields, including social sciences, business, healthcare, finance, and many others. They offer a concise and informative summary of data, enabling researchers, analysts, and decision-makers to gain insights, communicate findings, and make informed decisions based on the characteristics of the data.
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Helpppp please!!!!!!
Answers
mai poured 2.6 of water into a partially-filled pitcher. the pitcher now contains 10.4.mai wants to know how many liters of water was originally in the pitcher.
Answers
Answer:
Step-by-step explanation:
Let's call the original volume of water in the pitcher "V". Then, after Mai added 2.6 liters, the total volume of water in the pitcher became V + 2.6 = 10.4 liters.
To find the original volume of water in the pitcher, we can isolate V by subtracting 2.6 from both sides of the equation:
V + 2.6 = 10.4
V = 10.4 - 2.6
V = 7.8 liters
So the original volume of water in the pitcher was 7.8 liters.
Answer: 7.8
Step-by-step explanation:
really sorry if im wrong
1. Francis was biking up the hill in the image to the right. The hill made a 45° angle with the
ground. How high off of the ground was Francis when he reached the top of the hill?
Answers
I cant put the Problem here But just look up "PUZZLE TIME 7.3 What Kind Of Ship Can Last Forever?"
If both pairs of opposite sides of a quadrilateral are ___________, then the quadrilateral is a parallelogram.
Answers
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram
What is a quadrilateral?A quadrilateral is a closed shape that has four sides, four vertices, and four angles. It's made by connecting four non-collinear points. The sum of quadrilateral interior angles is always 360 degrees. A quadrilateral is a four-sided polygon with four edges and four corners in geometry.
A parallelogram is formed when both pairs of opposite sides of a quadrilateral are congruent. A parallelogram is formed when one pair of opposite sides of a quadrilateral are parallel and congruent.
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What value of x makes the following equation true?
31 = x + 14
A)45
B)27
C)25
D)17
Answers
Answer:
D) 17
Step-by-step explanation:
31 = x + 14
x = 31 - 14
x = 17
Pls help math!!!!!!!
Answers
What is negative 1 and negative 16 =
Answers
Answer:
-17
Step-by-step explanation:
-1 + (-16) =
-1 - 16 =
- (1 + 16) = -17
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(›)
Which is more, 1 tablespoon or 2 teaspoons?
Answers
Answer: 1 tablespoon
Step-by-step explanation:
Multiply.
1/8(-4/5)
Write your answer in simplest form.
Answers
Answer:
2.5
Step-by-step explanation:
-4X5 is -20 negative 20 divided by 1/8 is 2.5.
i need help with this
Answers
Answer:
D
Step-by-step explanation:
Multiply everything on the bottom by -2 and then they are the same so infinite answers
Find the distance and midpoint for the points (7, 10) and (1,2).
Answers
= sqrt 36+64
=sqrt 100
=10
Midpoint= (7+1)/2 , (10+2)/2
= (4, 6)
Hope this can help.
Guys pls help me!!!!!
Answers
what is the value of the expression below 2816 * 7
Answers
Answer:
2816 x 7 is 19712.
Step-by-step explanation:
I'm not going into detail, but simply, use a calculator
Answer:
the answer is 19,712
Step-by-step explanation:
ur welcome
what equation can be used to find the radius of a circle with an area of 50.24 square inches
Answers
The equation that can be used to find the radius of a circle with an area of 50.24 square inches is the square root of the area divided by pi, i.e.
r = √(A/π).
The area of a circle can be calculated using the formula: Area = π * r^2
where π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
To find the area of a circle, simply square the radius and multiply it by π.
Given that the area of the circle is 50.24 square inches.
We know that the formula for the area of a circle is given by A = πr²
Where,
A is the area of the circle
r is the radius of the circle.
Rewrite the given formula in terms of r, we get;
r² = A/π
Taking square root both sides of the equation, we get;
r = √(A/π)
Therefore, the radius of a circle with an area of 50.24 square inches is
r = √(50.24/π).
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Calculate the Breakaway points are roots of the equation. 4s³ +15s² +18s +5=0 Since, there are no zeros on the real axis, the breaking points are absent. Breakaway points are as follows: −1.6785+ j0.6028 –1.6785 – j0.6028 -0.3930 Since, the first two points are not as root locus breakaway point is -0.3930
Answers
The breakaway point of the root locus is -0.3930. To find the breakaway points of the root locus, we need to find the values of s at which the real part of the transfer function poles or zeros becomes zero.
This means that we need to find the roots of the equation 4s³ + 15s² + 18s + 5 = 0.
Using numerical methods such as the Routh-Hurwitz criterion or the root locus method, we can determine that there are no real roots of the equation. Therefore, the breakaway points must be complex conjugate pairs.
Using a numerical solver or a quadratic formula, we can find that the complex conjugate roots are -1.6785+ j0.6028 and -1.6785 – j0.6028. However, these roots do not lie on the real axis, so they are not breakaway points.
To find the breakaway point, we need to look for the point on the real axis between the two complex roots where the real part of the transfer function poles or zeros becomes zero. Using a numerical solver or by inspection, we can find that this point is -0.3930. Therefore, the breakaway point of the root locus is -0.3930.
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4. What is the output of the following Java code? int abc []={5,9,19,28,21}; abc[6]=11
Answers
The given Java code will result in an ArrayIndexOutOfBoundsException because the array abc has a length of 5, and attempting to access index 6 is beyond the bounds of the array.
The given Java code declares an array named abc and initializes it with five integers: 5, 9, 19, 28, and 21. The array has a length of 5, which means it has indices from 0 to 4.
However, in the next line of code, abc[6] = 11; tries to assign a value of 11 to the element at index 6. Since the valid indices for the abc array are from 0 to 4, attempting to access index 6 is beyond the bounds of the array.
As a result, the code will throw an ArrayIndexOutOfBoundsException at runtime, indicating that the index 6 is out of range for the array abc. This exception is thrown to prevent accessing memory locations that are not part of the array, which helps avoid potential errors or data corruption.
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pls help with my homework
Answers
The area of the trapezoid is 65.16 metres squared.
How to find the area of a trapezoid?The area of a trapezoid can be found as follows:
area of a trapezoid = 1 / 2 (a + b)h
where
a = top baseb = bottom baseh = height of the trapezoidTherefore,
a = 5metres
b = 13.1 metres
h = 7.2 metres
Hence,
area of a trapezoid = 1 / 2 (5 + 13.1) 7.2
area of a trapezoid = 1 / 2 (18.1)7.2
area of a trapezoid = 130.32 / 2
Therefore,
area of a trapezoid = 65.16 metres squared
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plz help brainliest to first answer **HELP** plz
Answers
Answer:
Angle UST= 180
Step-by-step explanation:
Im not so sure but angle U= 25 degrees+ angle S=95 degrees+ angle T=60 degrees. Dont rely on me too much I'm only a middle school kid that got put in a highschool course for some apparent reason.
On every three hamburgers that McDonalds makes, they use 9 pickles. How many pickles would they use on 100 burgers?
Answers
Answer:
300 pickles
Step-by-step explanation:
9/3=3, 3*100=300
Answer:
11.1 repeating
Step-by-step explain
You would figure out that they have 3 pickles on each burger so do 100/9 and 11.1 repeating.
A radioactive substance has an initial mass of 475 grams and a half-life of 20 days. What equation is used to determine the number of days, x, required for the substance to decay to 63 grams?
Answers
The equation used to determine the number of days, x, required for the substance to decay to 63 grams is: x ≈ 83.60
To determine the number of days, x, required for a radioactive substance to decay to 63 grams, we can use the exponential decay formula. The equation that represents the decay of a radioactive substance over time is:
N(t) = N₀ * (1/2)^(t/h)
Where:
N(t) is the remaining mass of the substance at time t
N₀ is the initial mass of the substance
t is the time elapsed
h is the half-life of the substance
In this case, we have an initial mass of 475 grams, and we want to find the number of days required for the substance to decay to 63 grams. We can set up the equation as follows:
63 = 475 * (1/2)^(x/20)
To solve for x, we can isolate the exponential term on one side of the equation:
(1/2)^(x/20) = 63/475
Next, we can take the logarithm (base 1/2) of both sides to eliminate the exponential term:
log(base 1/2) [(1/2)^(x/20)] = log(base 1/2) (63/475)
By applying the logarithmic property log(base b) (b^x) = x, the equation simplifies to:
x/20 = log(base 1/2) (63/475)
Finally, we can solve for x by multiplying both sides of the equation by 20:
x = 20 * log(base 1/2) (63/475)
Using a calculator to evaluate log(base 1/2) (63/475) ≈ 4.1802, we find:
x ≈ 20 * 4.1802
x ≈ 83.60
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6a-5=4a+2
Can someone help me
Answers
-4a -4a
2a-5=2
+5 +5
2a=7
/2 /2
a=3.5
Consider the relation (9,8) (2,6) (1,5) (8,3) (5,7)
What is the domain of the relation?
Enter each value on the same line, separated by commas.
Domin =
Answers
Answer:
Step-by-step explanation:
Given the relation (9,8) (2,6) (1,5) (8,3) (5,7),
Domain= {9,2,1,8,5}
Plz Brain-list or subscribe to my channel " ZK SOFT&GAMING" THANKS...
help me please.....
Answers
Answer: I believe its Option 2
Step-by-step explanation: Sory if im wrong
——
1. Write down the formula:
y=a(x-h)^2+k
2. Find the coordinates.
(H, K is the vertex form)
H, K= (0,4)
X, Y= (1,3)
3. Plug in the numbers into the formula
y=a(x-h)^2+k
3=a(1-0)^2+4
4. Solve for “a”
a= -1
Answer: y= -x^2+4
Pssst.... you can also use Desmos to help you with graphs. :)
Also Desmos is a great way to double check your work.
It is y= -x^2+4 because if you put it into Desmos it gives you the same coordinates and the same graph.
I hope this helped you!
Use the limit comparison test to determine if the series converges or diverges. 2√n 9n3/2-10m+1 O Converges Diverges
Answers
The given series, ∑(2√n)/(9n^(3/2) - 10n + 1), diverges according to the limit comparison test.
To apply the limit comparison test, we compare the given series with the series 1/n^(3/2), which is a known series that converges. Taking the limit as n approaches infinity of the ratio of the terms of the two series, we find:
lim(n→∞) [(2√n)/(9n^(3/2) - 10n + 1)] / [1/n^(3/2)]
Simplifying this expression, we get:
lim(n→∞) 2√n * n^(3/2) / (9n^(3/2) - 10n + 1)
By dividing the numerator and denominator by n^(3/2), we obtain:
lim(n→∞) 2 / (9 - 10/n^(1/2) + 1/n^(3/2))
As n approaches infinity, both 10/n^(1/2) and 1/n^(3/2) tend to 0. Therefore, the limit becomes:
lim(n→∞) 2 / (9 + 0 + 0) = 2/9
Since the limit is a nonzero finite value, the given series diverges by the limit comparison test.
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Evaluate the expression when x = 4 and y = 5.
3x2 + 4y0 • x –1
Answers
Answer:
60
Step-by-step explanation:
The evaluated expression of 3x² + 4y⁰(x - 1) when x = 4 and y = 5 is 60.
What is Substitution?
Substitution simply means to put in place another. Therefore, let's substitute the value of x and y in the mathematical expression.
3x² + 4y⁰(x - 1)
Therefore,
y⁰ = 1
3x² + 4y⁰(x - 1)
3x² + 4y⁰(x - 1)
3x² + 4(x - 1)
3x² + 4x - 4
Therefore, when x = 4 and y = 5
3(4)² + 4(4) - 4
48 + 16 - 4 = 60
HOPE THIS HELPED!
Answer:
B
Step-by-step explanation:
what is the length of the radius of the circle 15^2
Answers
Answer:
the length of the radius of the circle = 15.
Step-by-step explanation: