The rational functions that have an oblique asymptote are:
are:
f(x) = x^2 + 1/X
f(x) =4x^2 - 6/x + 1
f(x) =x^5/x^3 +1
f(x) =x² +2/ x^2+ 3x
How can the functions have an oblique asymptote be gotten?The concept that will be used here is finding the function one after the other.
The first function:
f(x) = x^2 + 1/X
The degree of numerator is seen to be 2, which can be considered to be is greater than the degree of denominator which is one, the, we can consider this function as oblique asymptote.
Second function:
f(x) =4x^2 - 6/x + 1
The degree of numerator which can be seen to be 2 is greater than the degree of denominator which is 1 and can be considered as an oblique asymptote.
Third function:
f(x) =-x/x^2
The degree of numerator can be seen as 1 which can be considered to be less than the degree of denominator which is 2, and we can not considere this as an oblique asymptote.
The fourth function:
f(x) =x^5/x^3 +1
The degree of numerator can be seen as 5 which can be considered to begreater than the degree of denominator which is 3 and this function can be considered to be an oblique asymptote.
Fifth option:
f(x) =x² +2/ x^2+ 3x
The degree of numerator can be seen as 3 which can be considerd to be greater than the highest degree of denominator which is seen as 2 and can be considered to be oblique asymptote.
Therefore, the 1st, 2nd, 4th, and 5th options are correct.
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missing options:
f(x) = x^2 + 1/X
f(x) =4x^2 - 6/x + 1
f(x) =-x/x^2
f(x) =x^5/x^3 +1
f(x) =x² +2/ x^2+ 3x
ms tunnicliffe is making jam for the county fair blackberries cost 5.50 per kg sugar cost 65c per kg 15 glass jars cost 5.85 she uses 16kg of blackberries and 10kg of sugar to make 15 jars of jam calculate the total cost to make the 15 jars
Therefore , the solution of the given problem of unitary method comes out to be total cost for to make 15 jars is 12,386.25 euroes.
What exactly is a unitary method?After calculating the size of a small slice, multiply the quantity by two to complete a task using the unitary technique. Simply expression, the unit variable technique works to separate a coded item from a certain group or collection of groups. For instance, 40 pens would cost Rs. 400 (or 400 pounds, $1.01). It's possible that one country will have total control over the method employed to do this. Almost every living creature has a distinctive quality.
Here,
Given :
cost of blackberry = 88 euroes
cost of sugar = 650 euroes
Jam bottles costs =87.75
total cost for to make 15 jars is
=> 15 * (87.75+650+88)
=> 15 * 825.75
=> 12,386.25 euroes
Therefore , the solution of the given problem of unitary method comes out to be total cost for to make 15 jars is 12,386.25 euroes.
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9. the scenario in problem 14 generates an extraneous solution. neither solution makes a denominator equal zero. why can we not use both solutions?
An extraneous solution is not part of the solution set because it is not valid in the original problem context and may not satisfy the problem's constraints.
The scenario in problem 14 generates an extraneous solution because it is a solution obtained by squaring both sides of an equation, which can lead to extraneous solutions. These extraneous solutions may not satisfy the original equation, and hence, cannot be considered as a valid solution. To determine if a solution is extraneous, we must check if it satisfies the original equation. If it does not, then it is considered extraneous and should not be used.
In other words, an extraneous solution is an extraneous or unintended answer that is obtained as a result of an error in the solution method, but it may not satisfy the original equation or problem. This can occur when using algebraic methods that involve squaring, square roots, or other operations that can cause the equation to change in such a way that some solutions are no longer valid. To ensure that a solution is valid, it is always important to check that the solution satisfies the original equation, and not just the simplified or transformed equation.
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Marcy works as a server at the Cass Restaurant. The amount of money she earns during a shift depends on the number of tables she serves. m = the amount of money Marcy earns t = the number of tables Marcy serves Which of the variables is independent and which is dependent?
If you divide $320 by 40 your answer is 8, so Mary probably earns 8 dollars an hour.
Can I please get help anyone
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 3000e^{0.06\cdot 2} \implies A \approx 3382.49~\hfill \underset{interest~only}{\stackrel{3382.49~~ - ~~3000}{\approx\text{\LARGE 382.49}}}[/tex]
1. Simplify the following expression. (84x + 82y) - (14x + 38y)
Answer:
70x+44y
Step-by-step explanation:
step 1: distribute
84x+82y−(14x+38y)
84x+82y−14x−38y
step 2: combine like terms
84x+82y−14x−38y
84+82−14−38
70x+44y
Find a solution to the system of equations 
The solution to the system of equations is (-2, -2)
How to determine the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have two lines that intersect at the point (-2, -2)
The point of intersection represent the solution
This means that the solution to the system of equations is (-2, -2)
Hence, the required solution is (-2, -2)
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What is the lateral surface area of the triangular prism shown below?
150 cm2
40 cm 2
190 cm2
170 cm2
The area of the triangular prism is calculated as; 170 cm²
How to find the Lateral Surface Area of the Prism?The given triangular prism when broken down is made up of;
2 triangles (top and bottom)
2 side rectangles
1 back rectangle
Formula for area of triangle = ¹/₂ * base * height
Formula for area of rectangle = length * width
Thus;
Area of trapezoid = 2(¹/₂ * 5 * 4) + 3(10 * 5)
Area = 20 + 150
Area = 170 cm²
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Mia had $22 Then she started to receive $4 a week as an allowance. She plans to save all of her money for a bicycle and draws a graph of her planned savings. Mia lets x represent the number of weeks she has received her allowance, and y represent her total amount of money. Which of the following ordered pairs is on Mia's graph?
A. (2,44)
B. (1,22)
C. (6,24)
D. (5,42)
Answer:
(5, 42)
Step-by-step explanation:
22 + 4x= 42
There is only one that will work.
42 - 22 = 20
4x = 20
x= 5
" X is the number of weeks they have gotten the allowance "
Answer: D. (5,42)
Step-by-step explanation:
If x is representing the weeks that she received her allowance, this means that we would need to add 4 to her starting amount (22) for every week.
So, if she got an allowance for 5 weeks, we would need to multiply her earning amount (4 per week) by the number of weeks (5).
5 x 4 = 20
But, we aren't done just yet! We still need to add this amount to her starting balance, which is $22. So, 20 + 22 = 42.
So, if x is 5, y would be 42, just like in the answer!
Another way of solving this answer would be 22 + 4x = 42.
I hope this helped you :)
Cheers!
5. Rewrite each of the following in simplest form by combining like terms.
(b) -2n+10n
(c) 8y-14y
(a) 9x+14x
CONS
(d) -6w-11w
(B) 8n (C) -6y (A) 23x (D) -17w
Evaluation:
B. 10 + (-2) is the same as 10 - 2, the answer is 8.
C. 8 - 14 could be rewritten as -14 + 8, depending on which is easier to comprehend. The answer is -6
A. 9 + 14 = 23.
D. -6 - 11 is the same as -11 + (-6), which is -17.
Cheers,
qxxi
PLS PLS ANWSer ASAP ITS GRADED I NEEd at least
Answer:
The third angle is 60
Step-by-step explanation:
The interior angle of a triangle is equal to the 180 minus the exterior angle.
[tex]180-80=100[/tex]
So one of the interior angles is equal to 100
All of the interior angles of a triangle add up to 180
[tex]180=100+20+x[/tex]
[tex]x=60[/tex]
an urn contains 5 red and 3 green balls. the balls are chosen at random, one by one, from the urn. if a red ball is chosen, it is removed. any green ball that is chosen is returned to the urn. the selection process continues until all of the red balls have been removed from the urn. what is the mean duration of the game?
The mean duration of the game will be 70%.
The likelihood of not receiving any color will be equal to the likelihood of receiving one fewer ball of each hue:
P(green) = 2/5 P(red after green) = 3/6
P(green after yellow after red) = 1/4 0.5 x 0.4 x 0.25 = 0.05
Suppose we follow a different order:
Yellow has the following probabilities: P(yellow) = 1/6, P(red after yellow) = 3/5, and P(green after red after yellow) = 2/4.
As you can see, we also get denominators of 4,5,6, and numerators of 1, 3, and 2!
Therefore, the result probably will be 0.05 for any feasible combination (believe me on this one)!
How many possible combinations exist?
RGY\sRYG\sYGR\sYRG\sGRY\sGYR
6 combinations are thus feasible. The likelihood of each at 0.05 times 6 equals 0.3.
6 combinations are thus feasible. The likelihood of each at 0.05 times 6 equals 0.3.
The likelihood of all outcomes minus the ones we discovered, or 1 - 0.3 = 0.7, is the probability of not receiving distinct colors.
So 70% is the answer.
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state the degree and leading coefficient of each polynomial in one variable. if it is not a polynomial in one variable, explain why
The degree and leading coefficient of each polynomial in one variable is given below :- (2). degree 3; leading coefficient 8 | (4). degree 6; leading coefficient | (6). not a polynomial
The "leading coefficient" is the coefficient of the highest-degree term in the sum of terms that makes up a polynomial.
These expressions all have one variable, so the number of variables is not an issue in any case. All of the exponents are positive integers, so that is not an issue in any case. However, the variable appears in the denominator in the expression of problem 6, so that sum is not a polynomial.
______
(2). In order to put this into the form we recognize as a polynomial, the expression must be "simplified' by performing the multiplication of the two factors:
= 8x³ -4x² +6x -3
The leading coefficient is the coefficient of the highest-degree term, which is the product of the highest-degree terms of the factors. That product is ...
(2x)(4x²) = 8x³
so the leading coefficient is 8. The variable is to the 3rd power, so the degree is 3.
______
(4). The expression is already written as a sum, so we only need to find the term of highest degree. That is the last one: 7y^6. Its degree is 6 and its leading coefficient is 7.
_____
(6). Variables are not allowed in the denominator of a polynomial. This expression is not a polynomial.
Hence the degree and leading coefficient of each polynomial in one variable is given below :-
(2). degree 3; leading coefficient 8 | (4). degree 6; leading coefficient | (6). not a polynomial
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----------- Correct format of the question is given below --------
(Q). State the degree and leading coefficient of each polynomial in one variable. if it is not a polynomial in one variable, explain why?
*equations of each polynomial is given below in image.*
A management dilemma defines the research question.True or False
A management conundrum is an issue or difficulty that a manager faces that necessitates a choice. This difficulty or challenge frequently defines the study question and motivates researchers to conduct research to discover a solution that is the given statement is true.
What is research?Mathematics research is the long-term, open-ended investigation of a series of connected mathematical issues, the answers to which connect to and build upon one another. Because students always come up with new questions to ask based on their observations, problems are open-ended. Mathematics research is the long-term, open-ended investigation of a series of connected mathematical issues, the answers to which connect to and build upon one another. Because students always come up with new questions to ask based on their observations, problems are open-ended. Student research also has the following characteristics: Students create questions, tactics, and outcomes that are, at least for them, unique. Students employ the same broad techniques as research mathematicians. They go through data collection, visualization, abstraction, conjecture, and proof cycles.
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HELP pls will mark you the brainliest. Please show your work too.
Answer:
Below
Explanation:
y = 1/2 x + 1
y = 3/2x + 4 Use first equation to sub in for y ( equate the equations)
1/2 x + 1 = 3/2 x + 4 solve for 'x'
-3 = x then use this value in one of the equations to calculate 'y'
y = 1/2 x + 1
y = 1/2 (-3) + 1 = - 1/2
assuming the number of arrivals per time period is poisson distributed with a mean arrival rate of 6 customers per hour, what is the mean interarrival time? a. 10 minutes b. 3 minutes c. 6 minutes d. 20 minutes
If the mean arrival rate is 6 customers per hour, then the mean inter-arrival time is calculated to be 10 minutes.
The mean arrival rate of customers = 6 customers/ hour.
Therefore, the mean inter-arrival rate is given as:
Mean inter-arrival rate = 1/ mean arrival rate = 1/6 hour = 1/6 * 60 minutes = 10 minutes.
The inter-arrival time is the time between two consecutive arrivals and is often modeled as an exponential random variable. The exponential distribution has a mean equal to the reciprocal of the rate parameter, which in this case is 6 customers per hour. So, the mean inter-arrival time is 1/6 hour or 10 minutes.
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What are the new coordinates of the following image after a reflection over the x-axis and a translation of -2 vertically and 5 horizontally? PLEASE HELP
the answer is in the picture.. if you have any questions feel free to ask
The distance a bus travels varies directly with time as shown in the table.
Time (h), x Distance (mi), y
1.5 93.75
3 187.5
4.5 281.25
6 375
Write the constant variation and the mph
The constant variation rate is given as follows:
62.5 miles per hour.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
Hence we can solve for the constant as follows:
k = y/x.
In the context of this problem, the constant variation rate is the constant of the proportional relationship, obtained dividing one output by it's respective input, hence:
k = 375/6
k = 62.5 miles per hour.
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Which equations could verify the solution to the equation − 48 = − 7 x − 13 ? Select two answers.
A.-48 = -7(-5) - 13
B.-48 = -35 - 13
C.-48 = 7(-5) - 13
D.-48 = -7(5) - 13
E.48 = 35 + 13
F.48 = 7(5) + 13
The equations that can verify the solution.
-48 = -35 - 13
-48 = 7(-5) - 13
-48 = -7(5) - 13
Options B, C, and D are the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 6 is an equation.
We have,
-48 = -7x P - 13
-48 + 13 = -7P
-35 = -7P
P = 5
The solution is 5.
This means,
-48 = - 7 x 5 - 13
-48 = -35 - 13
-48 = -48
Verified.
Now,
A.
-48 = -7(-5) - 13
-48 = 35 - 13
-48 = 22
Not true.
B.
-48 = -35 - 13
-48 = -48
Verified.
C.
-48 = 7(-5) - 13
-48 = -35 - 13
-48 = -48
Verified.
D.
-48 = -7(5) - 13
-48 = -35 - 13
-48 = -48
Verified.
E.
48 = 35 + 13
48 = 48
True.
F.
48 = 7(5) + 13
48 = 35 + 13
48 = 48
True.
Thus,
-48 = -35 - 13
-48 = 7(-5) - 13
-48 = -7(5) - 13 equations can verify the solution.
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draw similar rectangles that are in the ratio of 2/3. What is the ratio of the areas of the rectangles you drew.
The ratio of the areas of the rectangles will be 4:9.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
We know that the sides cannot be the same because it is a rectangle, therefore there is a width and length.
For the width, which is the shortest side, we will keep the radius as it is, that is, for rectangle 1 it will be 2 and for rectangle 2 it will be 3.
For the length, which is the longest side, we multiply the radius by two, which means that rectangle 1 will be 4 (2 x 2) and for rectangle 2 it would be 6 (2 x 3)
If we calculate the area it would be:
Rectangle 1:
2 x 4 = 8
Rectangle 2:
3 x 6 = 18
This means that the radius is 8/18 = 4/9
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Do the ratios 6:10 and 10:60 form a proportion?
Answer:
No, the following ratios are not proportional, because they are not equal, nor can be reduced.
Step-by-step explanation:
Hope it helps! =D
Write a
linear function f with f (5) = -1 and
f (0) = -5.
f(x) =
[tex]\huge\begin{array}{ccc}f(x)=\dfrac{4}{5}x-5\end{array}[/tex]
The linear function.
We have:
[tex]f(5)=-1\\\\f(0)=-5[/tex]
therefore we have two points on the line:
[tex](5,-1),\ (0,-5)[/tex]
Use the two points-slope formula:
[tex]A(x_a,\ y_A),\ B(x_B,\ y_B)\\\\y-y_A=\dfrac{y_B-y_A}{x_B-x_A}(x-x_A)[/tex]
Substitute:
[tex](5,-1)\to x_A=5,\ y_A=-1\\(0,-5)\to x_B=0,\ y_B=-5[/tex]
[tex]y-(-1)=\dfrac{-5-(-1)}{0-5}(x-5)\\\\y+1=\dfrac{-5+1}{-5}(x-5)\\\\y+1=\dfrac{-4}{-5}(x-5)\\\\y+1=\dfrac{4}{5}(x-5)\\\\y+1=\dfrac{4}{5}x-4\\\\y+1-1=\dfrac{4}{5}x-4-1\\\\\boxed{y=\dfrac{4}{5}x-5}[/tex]
Answer:
f(x) = 0.8x - 5
Step-by-step explanation:
the equation of a linear function is of the form
f(x) = ax + b
to find a and b use the given points
f(5) = - 1 ⇒ (5, - 1)
f(0) = - 5 ⇒ (0, - 5 )
substituting into the standard form , (0, - 5 )
- 5 = a(0) + b
- 5 = b
then
f(x) = ax - 5
substitute the other point (5, - 1 )
- 1 = 5a - 5 ( add 5 to both sides )
4 = 5a ( divide both sides by 5 )
[tex]\frac{4}{5}[/tex] = a
f(x) = [tex]\frac{4}{5}[/tex] x - 5
or
f(x) = 0.8x - 5
an obtuse triangle has integer length sides. if two sides of the triangle are 16 and 21, how many possible lengths are there for the third side?
For the obtuse triangle with 16 and 21 as two sides of the triangle there are 18 possible lengths for the third side
What is an angle?An angle is the opening formed by two half-straights (sides) with the same origin called vertex. For example, within a triangle there are three angles, which in total add up to 180°.
With the obtuse triangle we have the following rule:
a^2 + b^2 < c^2
a + b > c
So, lets called the third side (c)
c + 16 > 21 = c > 5
c+21 > 16 = c > - 5
21 + 16 > c = 37 > c
The third side must be: 5 < c < 37
To be an obtuse triangle we have:
c^2 > 21^2 +16^2
c^2 > 697
c > 26 (positive integer)
Calculating if the other angles are obtuse:
21^2 > c^2 + 16^2
c^2 < 185
c < 14
16^2 > c^2 + 21^2
c^2 < a negative integer, not possible
This means that for the angle opposite the third side to be obtuse should be:
26 < c < 37
27,28,29,30,31,32,33,34,35,36 = 10 possible lengths
And for the angle opposite the side 21 to be obtuse, should be:
5 < c < 14
6,7,8,9,10,11,12,13 = 8 possible lengths
Total possible lengths = 10 + 8 = 18 possible lengths
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Triangle ABC has vertices A(−5, 6), B(−3, 2), and C(−1, 2). If △ABC is reflected across the x-axis and translated using the following rule (x, y) (x+4, –y). What are the vertices of the image of △ABC ?
The image of △ABC is the triangle with vertices (-1, -6), (1, -2) and (3, -2)
How to Solve for Vertices?The image of point (x,y) after reflecting across the x-axis is (x, -y) and after the translation it is (x + 4, -y).
Applying these transformations to each vertex of △ABC:
A(−5, 6) becomes (-5, -6) after reflection, which becomes (-1, -6) after translation.B(−3, 2) becomes (-3, -2) after reflection, which becomes (1, -2) after translation.C(−1, 2) becomes (-1, -2) after reflection, which becomes (3, -2) after translation.So, the image of △ABC is the triangle with vertices:
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# 7.
5 years ago Riley bought a dryer. Every year
for the past 5 years the dryer has lost 15 percent
of its value. The current value of the dryer is
$100. How much did Riley pay for the dryer 5
years ago?
The amount that Riley paid for the hair dryer is $225.37.
How much was paid for the hair dryer?Given the information in the question, the dryer is depreciating in value. Depreciation is when the value of an asset declines with the passage of time.
The formula that can be used to determine the amount paid for the hair dryer is:
p = FV / (1 - r)^n
Where:
p = current price of the dryer r = rate of depreciation n = number of yearsp = $100 / (1 - 0.15)^5
p = $100 / 0.85^5
p = $225.37
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A rectangular prism has a width of 4 inches, a height of 6 inches, and a total volume of 192 cubic inches. What is the length of the rectangular prism?
A. 6
B. 8
C. 12
D.15
(Please tell me how to show my work)
If x1 and x2 are solutions to 3x^2+15x+9=0 quadratic equation, then
x1+x2=
Answer:
[tex]x_1 + x_2 = \boxed{-5}[/tex]
Step-by-step explanation:
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]
[tex]x_{1,\:2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\implies x_{1,\:2}=\dfrac{-b}{2a}\pm\dfrac{\sqrt{b^{2}-4ac}}{2a}[/tex]
Let's have
[tex]x_{1}=\dfrac{-b}{2a}+\dfrac{\sqrt{b^{2}-4ac}}{2a}[/tex]\
[tex]x_{2}=\dfrac{-b}{2a}-\dfrac{\sqrt{b^{2}-4ac}}{2a}[/tex]
[tex]x_1 + x_2 =\dfrac{-b}{2a}+\dfrac{\sqrt{b^{2}-4ac}}{2a} + \dfrac{-b}{2a}-\dfrac{\sqrt{b^{2}-4ac}}{2a}\\[/tex]
[tex]\dfrac{\sqrt{b^{2}-4ac}}{2a} - \dfrac{\sqrt{b^{2}-4ac}}{2a} = 0\\\\[/tex]
Leaving us with
[tex]\dfrac{-b}{2a} + \dfrac{-b}{2a}\\\\\implies 2 \cdot \left(\dfrac{-b}{2a}\right)\\\\\implies -\dfrac{b}{a}\\\\[/tex]
The given equation is
[tex]3x^2+15x+9=0[/tex]
Here a = 3, b = 15
So
[tex]-\dfrac{b}{a} = --\dfrac{15}{3} = -5\\[/tex]
Answer:
[tex]x_1 + x_2 = \boxed{-5}[/tex]
What is the image of (−4,−4) after a dilation by a scale factor of 5 centered at the origin?
The required image of (−4,−4) after dilation by a scale factor of 5 centered at the origin is (-20, -20).
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
A dilation with a scale factor of k, centered at the origin, will take a point (x,y) in the pre-image to the point (kx,ky) in the image.
Given the required image of (−4,−4) after dilation by a scale factor of 5 centered at the origin.
For x-coordinate:
- 4 × 5 = -20
For y-coordinate:
- 4 × 5 = -20
Thus, the required coordinates are (-20, -20).
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an aircraft carrier made a trip to dry dock and back. the trip took ten hours and the trip back took 11 hours. what was the aircraft carriers average speed on the trip there if it averaged 20 km/h on the return trip?
(please provide a step by step in simple terms, I'm about to cry)
The average speed of aircraft to dry dock on the trip is given by the equation S₁ = 8 km/h
What is Speed?Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude
Speed = Distance / Time
Given data ,
Let the average speed to dry dock be represented as S₁
The time for aircraft for dry docking = 10 hours
Now , the equation will be
The average speed on the return trip S₂ = 20 km/h
The time for aircraft for the return trip = 11 hours
So , Speed = Distance / Time
Substituting the values in the equation , we get
The distance = average speed on the return trip S₂ x time
On simplifying the equation , we get
The distance D = 20 x 11 = 220 km
And , the average speed to dry dock S₁ = 220 km / 10 hour
On simplifying the equation , we get
The average speed to dry dock S₁ = 22 km/hr
Hence , the average speed is 22 km/hr
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(3^3-6.8)divided by 7
Answer:
Yurrrr Tha answer to your question is 2.8
Step-by-step explanation:
now tha full Answer is 2.88571429
but hope this help and hope you pass type xhii
Is the equation x+5=8 balanced
Answer: Yes
Step-by-step explanation: The value of x is 3 therefore the equation is balanced.