Suppose the rational function f(x) has: a) a vertical asymptote of x = -5 b) a slant asymptote of y = x - 11. Write a function that can satisfy the property of f(x). 2. (10 points): Let f(x) = x³ + 7x² + 10x - - 6 and x = -3 is one root of f(x). Find the remaining roots of f(x).
Answers
a) To have a vertical asymptote at x = -5, we can introduce a factor of (x + 5) in the denominator of the rational function. The function f(x) = 1 / (x + 5) satisfies this property. b) To have a slant asymptote of y = x - 11, we need the numerator of the rational function to have a degree one higher than the denominator. A function that satisfies this property is f(x) = (x² - 11x + 30) / (x - 1).
a) For a vertical asymptote at x = -5, the denominator of the rational function must have a factor of (x + 5). This ensures that the function approaches infinity as x approaches -5. The simplest function that satisfies this property is f(x) = 1 / (x + 5).
b) To have a slant asymptote of y = x - 11, the degree of the numerator must be one higher than the degree of the denominator. One way to achieve this is by setting the numerator to be a quadratic function and the denominator to be a linear function.
A function that satisfies this property is f(x) = (x² - 11x + 30) / (x - 1). By dividing the numerator by the denominator, we obtain a quotient of x - 12 and a remainder of -18. This indicates that the slant asymptote is indeed y = x - 11.
For the second part of the question, to find the remaining roots of f(x) = x³ + 7x² + 10x - 6, we can use synthetic division or factoring methods. Since it is given that x = -3 is a root, we can divide the polynomial by (x + 3) using synthetic division.
By performing the division, we find that the quotient is x² + 4x - 2. To find the remaining roots, we can set the quotient equal to zero and solve for x. Using factoring or the quadratic formula, we find that the remaining roots are approximately -2.83 and 0.83. Therefore, the roots of f(x) are -3, -2.83, and 0.83.
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Related Questions
Which of the following equations have exactly one solution?
Choose all answers that apply:
A. −5x+12=−12x−12
B. −5x+12=5x+12
C. −5x+12=5x−5
D. −5x+12=−5x−12
Answers
Answer:
A, B, & C
Step-by-step explanation:
A: -5x +12 = -12x - 12
+12x +12x
7x + 12 = -12
-12 -12
7x = -24 [Divide both sides by 7 to get x]
x = -24/7
B: −5x + 12 = 5x + 12
-5x -5x
-10x + 12 = 12
-12 -12
-10x = 0 [Divide both sides by -10 to get x]
x = 0
C: −5x + 12 = 5x − 5
-5x -5x
-10x + 12 = -5
-12 -12
-10x = -17 [Divide both sides by -10 to get x]
x = 17 / 10
D: −5x + 12 = −5x − 12
+5x +5x
12 ≠ -12 [The statement is false, so it isn't the correct answer]
Simplify and explain (x^3+8)/(x+2)
Answers
answer:
x^2 - 2 x + 4
explanation: you want to factor the expression using a^3 + b^3= (a+b) (a^2 - ab+b^2)
then
(x,2) x (x^2 - 2x+4)
_________________
x+2
then reduce so,
(x+2) x (x^2- 2x +4)
_________________
x+2
then cross out repeating which is x+2
then you get your answer!
What are the values of r and a1 for 1/4(2)k-1
Answers
Given:
\(\sum_{k=1}^{6}\dfrac{1}{4}(2)^{k-1}\)
To find:
The values of r and \(a_1\).
Solution:
We have,
\(\sum_{k=1}^{6}\dfrac{1}{4}(2)^{k-1}\)
Here,
\(a_k=\dfrac{1}{4}(2)^{k-1}\) ...(i)
We know that, kth term of a GP is
\(a_k=a_1(r)^{k-1}\) ...(ii)
From (i) and (ii), we get
\(a_1=\dfrac{1}{4}\) and \(r=2\)
Therefore, the correct option is C.
Answer:
c
Step-by-step explanation:
Work out 4 1/7 + 1 1/2
Answers
Answer:
5 9/14
Step-by-step explanation:
Answer:
5 9/14
Step-by-step explanation:
(4+1) + ( 1/7 + 1/2)
\ /
5 9/14
= 5 9/14
I hope this helps.
FILL IN THE BLANK a/an ____________________________ diagram can be used to show how the tables in a database are defined and related..
Answers
A/an database schema diagram can be used to show how the tables in a database are defined and related.
This type of diagram provides a visual representation of the structure and organization of the database. It illustrates the tables ,and their attributes, and the relationships between them.
The database schema diagram helps in the understanding the logical design of the database, including primary keys, for foreign keys, and the connections between different tables. It allows developers, database administrators, and stakeholders to visualize the database structure and serves it as a reference for in designing, modifying, and querying the database effectively.
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What is the Domain and Range of the following Graph?
Answers
Answer:
This is a square function with its maximum at (-3, 2).
The domain is:
x ∈ [-3, + ∞)The range is:
y ∈ (- ∞, 2]help please!!!!!!
what is 3/10+1/3
Answers
Answer: 19/30
Answer:
First you make 3/10=0.3 the 1/3=0.33 then 0.3+0.33=0.63
Plssss help it's my last assignment
Answers
(1) 6.1 x 10⁷ is approximately 2.9 x 10¹¹ times larger than 2.1 x 10⁻⁴ as estimated.
(2) 1.9 x 10⁻⁸ is approximately 4.5 x 10⁴ times larger than 4.2 x 10⁻¹³ as estimated.
What is the estimation of the numbers?
To estimate how many times larger 6.1 x 10⁷ is than 2.1 x 10⁻⁴, we can divide the two numbers:
6.1 x 10⁷ ÷ 2.1 x 10⁻⁴
= 6.1 x 10⁷ ÷ (2.1/10⁴)
= 6.1 x 10⁷ x (10⁴/2.1)
≈ 2.9 x 10¹¹
To estimate how many times 1.9 x 10⁻⁸ is than 4.2 x 10⁻¹³, we can divide the two numbers:
1.9 x 10⁻⁸ ÷ 4.2 x 10⁻¹³
= 1.9/4.2 x 10⁵
≈ 4.5 x 10⁴
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What is the solution to this rational equation? 24-x-8=4 A. x = -2 B. x = 2 C. x = 4 D. x = 14
Answers
Answer:x=14
Step-by-step explanation:
for plato users
The solution of the rational equation 24/(x-8) = 4 is x = 14.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
A rational equation,
24/(x-8) = 4.
Simplifying,
x - 8 = 6
x = 8 + 6
x = 14.
Therefore, the value of x is 14.
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2/3 x 3/4 x 4 x 3 x 100
Answers
Answer:
600
Step-by-step explanation:
2/3 x 3/4 =
1/2 x 12 =
6 x 100
Which would be: 600
Number of miles driven in a week.
Person. Miles
Vani 30
Ryan 18
Fatoumata 42
For every ___ miles Vani drove, Ryan drove __ miles.
Answers
The number of miles driven by Taub in a week is 3 times the number of miles driven by Valeria in a week.
How to express ratio in simplest form?The United States Department of Transportation Federal Highway Administration said that the average driver traveled 12,724 miles in 2020. That's down from 14,263 average annual miles in 2019. The 2020 average equates to 1,060 miles per month per driver, or about 35 miles per day.Although it's possible, you cannot drive 1000 miles in a day safely with a single driver. This would involve approximately 16 hours of driving before accounting for traffic and rest stops. Assuming a total travel time of 20 hours, you would need to depart in the early hours and share the driving.Often, 100,000 miles is considered a cut-off point for used cars because older vehicles often start requiring more expensive and frequent maintenance when mileage exceeds 100,000.The average American spends 18 days driving per year, with an average of eight hours and 22 minutes per week, a OnePoll study conducted on behalf of Cooper Tire found.Number of miles driven by each person in a week:
Valeria = 7
Taub = 21
Ruby = 35
Number of miles driven by Taub : Number of miles driven by Valeria
= 21 : 7
= 21/7
= 3/1
= 3 : 1
Therefore, the number of miles driven by Taub : number of miles driven by Valeria in a week is 3 : 1 in it's simplest form.
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100 students went on a field trip. 6 buses were filled and 10 students traveled to the destination in cars with their parents. How many students were on each bus?
Answers
Answer:
15 students on each bus!
Step-by-step explanation:
100-10(with parents)
90÷6(how many busses)
15 students on each
The students travelling on each bus are 15.
What are arithmetic operations?The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.
Total number of students is given as 100.
The students to travel on car are 10.
Then, the students to travel on bus are given by following operation as,
Total students - Students to travel on car
⇒ 100 - 10 = 90
Now, the students on each bus can be obtained by using the division operation as below,
Students to travel on bus ÷ Total number of bus
⇒ 90 ÷ 6 = 15
Hence, the number of students on each bus is obtained as 15.
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NEED HELP ASAP! THANK YOU!
To get to Checkpoint C, Helena needs to run north 6 units, crawl through a 4-unit-long tube to the east, hopscotch south 3 units, jump 1 unit to the east, and run south 3 units.
1. Since she began at Checkpoint B, what are the coordinates for Checkpoint C?
2. What would be an easier way to get from Checkpoint B to Checkpoint C?
3. How might you be able to figure this out just by reading the description of the translations? (Hint: It may help you to plot these points on a graph or draw a picture.)
Answers
Helena's motions, including the 6 units north, 4 and 1, east, 3 and 3 south gives;
(5, 0)5 units to the southAdding the motions based on their directionsHow can the position of Helena be found?1. Let the coordinates of checkpoint B be (0, 0), using vectors, we have;
\(6 \times j \: + 4 \times i - 3 \times j \: + i - 3 \times j = 0 \times j \: + 5 \times i\)
The coordinates of checkpoint C is therefore; (5, 0)
2. The easier way to get to checkpoint C from point B is to go south 5 units.
3. How it is possible to figure out the shortest route is by taking the northwards and eastwards motions as positive numbers, and the motions to the south as negative.
The motions to the north can only be added to the motions to the south (motions in the same straight line) and the motions towards east are to be added to themselves.
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Answer:
5, 0
5 units south
adding motions based on direction
Step-by-step explanation:
Ratios equivalent to 1:7
Answers
Answer:
2:14
Step-by-step explanation:
\(\frac{1 \times 2}{7 \times 2} = \frac{2}{14}/2:14\)
When we conclude that the results we have gathered from our sample are probably also found in the population from which the sample was drawn, we say that the results are:
Answers
When we conclude that the results we have gathered from our sample are probably also found in the population from which the sample was drawn, we say that the results are statistically significant.
In statistical analysis, we use hypothesis testing to determine whether the results of a sample are likely to be representative of the population as a whole. If the results are statistically significant, we can infer that there is a low probability that the observed differences between the sample and the population occurred by chance alone.
This allows us to generalize the findings from the sample to the larger population with a reasonable degree of confidence.
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simplify : 8x - 4(x -1)
Answers
We want to simplify:
\(8x-4(x-1)\)For doing so, we use the distributive property, and we get:
\(8x-(4x-4)\)And we break the parenthesis to obtain:
\(8x-4x+4\)Lastly, we simplify the similar terms and we get:
\(4x+4\)This means that the expression simplified is 4x+4.
4. The sides of a triangle are in the ratio of 2:7:3. The perimeter of the triangle is 114 centimeters. What is the length of the longest side? Show your reasoning
Answers
Answer:
66,5 sm
Step-by-step explanation:
The sides of a triangle: 2x+7x+3x=114
12x=114
x=9,5
2×9,5=19,
7×9,5=66,5
3×9,5=28,5
Answer: 66,5
QUESTION ONE [25]Brozierz Ltd, operate in the engineering industry. They feel that some of their older equipment need to be replaced. They seek your help to calculate their cost of capital.Their present capital structure is as follows:• 300 000 R2 ordinary shares now trading at R2,40 per share.• 100 000 preference shares trading at R2,50 per share (issued at R3 per share). 10 % p.a. fixed rate of interest.• A bank loan of R 500 000 at 12 % p.a. (payable in 5 years’ time).Additional information:a. The company’s beta is 1,4. A return on market of 15% and a risk free rate of 6%.b. Its current tax rate is 28%.c. Its current dividend is 50c per share and they expect their dividends to grow by 7% p.a.Required:1.1 Assuming that the company uses the Capital Asset Pricing Model (CAPM) to calculate their cost of equity, calculate their weighted average cost of capital.
Answers
The weighted average cost of capital WACC = (0.375 x 0.165) + (0.125 x 0.12) + (0.5 x 0.12) x (1 - 0.28)
= 0.120 or 12.0%
To calculate the cost of capital for Brozierz Ltd, we need to calculate the cost of each component of their capital structure and weight them according to their proportion in the overall capital structure.
First, let's calculate the cost of equity using the Capital Asset Pricing Model (CAPM):
Cost of equity = risk-free rate + beta x (return on market - risk-free rate)
= 0.06 + 1.4 x (0.15 - 0.06)
= 0.165 or 16.5%
Next, let's calculate the cost of preference shares:
Cost of preference shares = (fixed dividend rate / market price of preference shares) + flotation costs
= (0.1 x 3 / 2.5) + 0
= 0.12 or 12%
The cost of debt is simply the interest rate on the bank loan, which is 12% per annum.
Now, we can calculate the weighted average cost of capital (WACC) using the formula:
WACC = (proportion of equity x cost of equity) + (proportion of preference shares x cost of preference shares) + (proportion of debt x cost of debt) x (1 - tax rate)
Let's calculate the proportion of each component:
Proportion of equity = 300,000 x 2.40 / (300,000 x 2.40 + 100,000 x 2.50 + 500,000) = 0.375
Proportion of preference shares = 100,000 x 2.50 / (300,000 x 2.40 + 100,000 x 2.50 + 500,000) = 0.125
Proportion of debt = 500,000 / (300,000 x 2.40 + 100,000 x 2.50 + 500,000) = 0.5
Therefore, the WACC is:
WACC = (0.375 x 0.165) + (0.125 x 0.12) + (0.5 x 0.12) x (1 - 0.28)
= 0.120 or 12.0%
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got a question that needs an answer look at teh photo
Answers
Answer:
I see no photo so ill put the steps on how to
Step-by-step explanation:
Just click on that attachment icon below your answer or question box . You can attach pictures to your answers by selecting pics from your gallery or by clicking from your camera. But remember you cannot crop your picture once you have selected it. So keep your pic ready in your gallery and just select it
You want your daily sodium intake to be less than 2300 milligrams. For breakfast, you eat a cereal bar with the nutrition label shown. What are the possible amounts of sodium you can eat during the rest of the day? Nutrition Facts Serving Size Servings Per Container Amount Per Serving Calories 120 Total Fat 3g 1 Bar (37g) Calories from Fat 30 % Daily Value* 5% 3% Saturated Fat 0.5g Trans Fat Og Cholesterol Omg Sodium 125mg 0% 5% The possible amounts of sodium you can eat during the rest of the day should be less than mg
Answers
According to the information in the nutritional table, it can be inferred that the amount of milligrams of sodium that we should consume during the rest of the day must be less than 2,175mg,
How to calculate the amount of sodium we can consume?To calculate the amount of sodium that we can consume during the rest of the day after breakfast, we must subtract the value of sodium consumed to the amount of total sodium that we want to ingest as shown below:
2300mg - 125mg = 175mgAccording to the above, it can be inferred that after consuming the cereal bar at breakfast, we should consume an amount less than or equal to 2,175mg of sodium in the other meals of the day (lunch, dinner and snacks).
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¿Cuál de los siguientes valores de n hace CIERTA
la ecuación n^3-125=0 ?
(A) 121
(B) 5
(C) 0
(D) 3
(E) 12
Answers
Answer:
B
Step-by-step explanation:
n³-125=0
n³=125
n= ³√125
n=5
Two sides of a triangle measure 8 cm and 15 cm. Which could be the length of the third side? O 6 cm O18 cm O 24 cm O 28 cm
Answers
Answer:
18
Step-by-step explanation:
It's the only size that works.
A chi-square test of independence is a one-tailed test. The reason is that Multiple Choice we are testing whether the frequencies exceed their expected values. we square the deviations, so the test statistic lies at or above zero. hypothesis tests are one-tailed tests when dealing with sample data. the chi-square distribution is positively skewed.
Answers
A chi-square test of independence is indeed a one-tailed test. The reason for this is that we are testing whether the observed frequencies of two categorical variables are significantly different from the expected frequencies.
We square the deviations between the observed and expected frequencies, and since deviations can only be positive, the test statistic always lies at or above zero. Hypothesis tests are one-tailed when dealing with sample data because we have a specific direction for our research question. In the case of a chi-square test of independence, we are interested in whether one variable is dependent on the other variable, so we have a directional hypothesis. Furthermore, the chi-square distribution is positively skewed, meaning that the majority of the distribution is on the right-hand side. This is important to consider when interpreting the results of a chi-square test.
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What is the solution to this equation? log6(x) + log6(3) = log6( x+1)
Answers
Answer:
A
Step-by-step explanation:
got it right
The solution to this equation log₆(x) + log₆(3) = log₆( x+1) is x = 1/2.
What is a logarithm?A logarithm is an exponent or power to which a base must be raised in order to produce a given number. If aˣ = n, then x is the logarithm of n to the base a, which is expressed mathematically as x = logₐn.
How to solve this problem?We know that logₐx + logₐy = logₐ(xy)
Here, log₆(x) + log₆(3) = log₆( x+1)
i.e. log₆(3x) = log₆( x+1)
i.e. 3x = x + 1
i.e. 3x - x = 1
i.e. 2x = 1
i.e. x = 1/2
Therefore, the solution to this equation log₆(x) + log₆(3) = log₆( x+1) is x = 1/2. So, option A is correct.
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Which symbol should go into the box to make the statement true?
|17| |17
Answers
Answer: equals 17
Step-by-step explanation:
Answer:
The answer is = for 17 and |17|
Tracy answered all of the questions on the math test correctly. She scored 100 points, or 100%.
Marcel answered the extra-credit questions on the test and scored 120 points.
Which percent, fraction, and decimal shows Marcel's score in relation to Tracy's score?
Answers
Answer:
120% = 120/100 = 1.2
Step-by-step explanation:
100 points = 100%, so 120 points = 120%
120% = 120/100 = 1.2
Anelle is in charge of bringing in dry erase markers for everyone in her math group to use to work on a project. She brings 3 markers for each person in her group and 5 extra markers for everyone to share. If Janelle brings in 23 markers in all, which equation represents the information?
Answers
Answer:
3x + 5 = 23
Step-by-step explanation:
Let x represents the number of persons in her group.
Since she brings 3 markers for each person, then number of markers brought for persons in her group = 3x.
She brings 5 extra markers for each person to share.
Thus, total markers she brought is now;
3x + 5
She brought 23 markers in all.
Thus, equation that represents the information is;
3x + 5 = 23
Which sequence is arithmetic? A- 2,6,18,54... B- 3,6,12,24... C- 11,14,17,20... D- 7,11,13,18
Answers
I think B. 3,6,12,24 is the answer
Answer:
C
Step-by-step explanation:
the pattern is add 3
11 + 3 = 14
14 + 3 = 17
17 + 3 = 20
in your taining routine each week you bike five times as far as you run and you run four times as far as you swim. you train a total of 200 miles each week. how far do you bike? how far do you run? how far do you swim?
Answers
Train a total of 200 miles each week. 160 miles I bike, 32 miles I run, 8 miles I swim.
What do you mean by Simultaneous linear equations?
A system of simultaneous linear equations is any pair of linear equations or more that have the same unknown variables in common. To solve such a system, one must identify values for the unknown variables that simultaneously satisfy each of the equations. A system of simultaneous linear equations is any pair or group of linear equations where each equation has the same unknown variables. Finding values for the unknown variables that simultaneously satisfy each equation in such a system is the first step in its solution.
according to the question,
you bike five times as far as I run and you run four times as far as iswim. you train a total of 200 miles each week.
let, I swim x miles then I run 4x times and I bike 20x miles.
so, 4x+x+20x=200
by solving linear equations,
we get, x=8
hence,160 miles I bike.
32 miles I run.
8 miles I swim.
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5. In one game, the final score was Falcons 3, Hawks 1. What fraction and
of the total goals did the Falcons score? Show your work in the space
percent
below. Remember to check
your
solution.
Answers
Step-by-step explanation: