The partial fraction of the rational function is 5/(x + 1) + 9/(x + 5).
To begin, let's first check if the given rational function can be factored or simplified. In this case, the denominator, x² + 6x + 5, can be factored as (x + 1)(x + 5). Therefore, we can express the given rational function as:
(14x + 34)/((x + 1)(x + 5))
Now, we aim to express this rational function as a sum of partial fractions. To do this, we assume that the rational function can be written in the form:
(14x + 34)/((x + 1)(x + 5)) = A/(x + 1) + B/(x + 5)
where A and B are constants that we need to determine.
To find the values of A and B, we need to eliminate the denominators in the equation above. We can do this by multiplying both sides of the equation by the common denominator, (x + 1)(x + 5). This gives us:
(14x + 34) = A(x + 5) + B(x + 1)
Now, let's simplify this equation by expanding the right side:
14x + 34 = Ax + 5A + Bx + B
Next, we group the x terms and the constant terms separately:
(14x + 34) = (A + B)x + (5A + B)
Since the coefficients of the x terms on both sides must be equal, and the constants on both sides must also be equal, we can equate the corresponding coefficients:
Coefficient of x:
14 = A + B (Equation 1)
Constant term:
34 = 5A + B (Equation 2)
We now have a system of two equations with two unknowns (A and B). Let's solve this system to find the values of A and B.
From Equation 1, we can express B in terms of A:
B = 14 - A
Substituting this into Equation 2, we have:
34 = 5A + (14 - A)
Simplifying further:
34 = 5A + 14 - A
20 = 4A
A = 5
Now that we have found the value of A, we can substitute it back into B = 14 - A to find B:
B = 14 - 5
B = 9
Therefore, the constants A and B are A = 5 and B = 9.
Substituting these values back into the partial fraction decomposition, we have:
(14x + 34)/((x + 1)(x + 5)) = 5/(x + 1) + 9/(x + 5)
This is the expression of the given rational function in terms of partial fractions.
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The students at a High School earned money for an international animal rescue foundation. 82 seniors earned an average $26.75 per student, 74 juniors earned an average $12.25 per student, 96 sophomores earned an average $15.50 per student, and 99 freshmen earned an average $10.85 per student. What was the average collection for a student in this school?
Using the mean concept, the average collection for a student in this school was of $16.13.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
The number of students is given as follows:
82 + 74 + 96 + 99 = 351.
The sum is:
82 x 26.75 + 74 x 12.25 + 96 x 15.50 + 99 x 10.85 = $5662.15
Hence the mean is:
M = $5662.15/351 = $16.13.
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Which equation is the inverse of Y equals 9X Square -4
[tex]y = 9x {}^{2} - 4 \\ flip \: x \: and \: y \\ x =9 (y ) {}^{2} - 4 \\ solve \: for \: the \: inverse \: of \: y \\ x + 4 = 9(y ) {}^{2} \\ y {} {}^{2} = \frac{x + 4}{9} \\ you \: can \: split \: it \: into \: two[/tex]
[tex]y {}^{(1)} = \sqrt{ \frac{x + 4}{9} } \\ y {}^{(2)} = - \sqrt{ \frac{x + 4}{9} } [/tex]
PLEASE HELP FAST!
A figure has rotational symmetry if a rotation of 180°
or less produces an image that fits exactly on the original figure. Select each degree of rotation that shows the figure below has rotational symmetry.
30 °
45 °
60 °
90 °
120 °
135 °
150 °
180 °
Answer:180 °
Step-by-step explanation:
Answer:
90 degrees
Step-by-step explanation:
The only numbers that are possible to be divided into 180 are these: 30, 45, 60, 90, & 180.
Now to figure out if this figure is symmetrical. It is. Why? Because you can put at least one line through each triangle. 8 in total but 180 cannot be divided by 8. So you could maybe split it in half. 180/4= 45
45x2= 90
Easy: Since there are now, two halves, since it is split up, it could be possible that the answer could be 90. Because 180/2 halves= 90.
The answer is 90
Determine whether the function f(x) = 3x is even or odd.
The function is even because f(-x) = f(x).
The function is odd because f(-x) = f(x).
The function is even because f(-x) = -f(x).
The function is odd because f(-x) = -f(x).
Answer: The function is even because [tex]f(x)=f(-x)[/tex].
Step-by-step explanation:
[tex]f(x)=3x^4 \\\\f(-x)=3(-x)^4 = 3x^4\\\\\therefore f(x)=f(-x)[/tex]
So, the function is even.
Find the surface area of the composite figure. Round to the nearest tenth if necessary.
The surface area of the composite figure shown in the figure attached is 233.6 cm²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The surface area of the composite = (6 * 8) + 2(8 * 3.6) + 2(0.5)(6 + 2 + 6 + 2)(3) + (8)(2 + 6 + 2) = 233.6 cm²
The surface area of the composite figure shown in the figure attached is 233.6 cm²
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An economist is studying salaries for high technology companies and wants to test the claim that the average salary for high
tech employees is less than $70,000.
The economist selects a sample of 35 random employees from various high tech companies and records their salaries.
Based on past studies, the economist determines that the population standard deviation is $8,500.
The economist conducts a one-mean hypothesis test at the 5% significance level to test the claim that the average salary for
high tech employees is less than $70,000.
The setup for the null and alternative hypothesis is given as:
Hoμ = 70,000; Ha < 70,000, which is a left-tailed test.
The sample data for 35 salaries is shown in the dataset below.
Use Excel to test the claim that the average salary for high tech employees is less than $70,000, where a = 0.05. Calculate
the test statistic, z, and the p-value, rounding to three decimal places.
The decision would be to fail to reject the null hypothesis and conclude that there is insufficient evidence.
How to solve for the mean of the data setThe formula is fx/n
To get fx we have to sum all of the values of x = 2430161
The total number in the data set = 35
Mean = 2430161/35
= 69433.17
This test is a left tail test.
sd = 8500
We have to make the hypothesisH0: u = 70000
H1 : U < 70000
z0.05 = 1.645
The decision would be to reject if z < critical value
Z= (69433.17 - 70000)/(8500/√35)
= -0.395
P-value can be gotten from the z score = 0.348
Given that the p value is > 0.05, we would have to fail to reject the null. The conclusion would be that there is insufficient evidence to support claim.
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If the term of arthematic progression decrease in magnitude then common difference must be
We can say that if the term of arithmetic progression decrease in magnitude then the common difference must be negative.
An arithmetic progression is a sequence where every term is a sum of the previous term and a common difference.
If we suppose the first term of an arithmetic progression to be a, and the common difference to be d, then the arithmetic progression goes like this:
The first term, a₁ = a,
Second term, a₂ = a₁ + d = a + d,
Third term, a₃ = a₂ + d = a + 2d,
Fourth term, a₄ = a₃ + d = a + 3d, and it goes so on up to,
The n-th term, aₙ = aₙ₋₁ + d = a + (n - 1)d.
In the question, we are asked if the term of arithmetic progression decrease in magnitude then what can we say about the common difference.
As the magnitude of the term decreases, we can show that as:
The n-th term < The first term,
or, aₙ < a₁,
or, a + (n - 1)d < a,
or, a + (n - 1)d - a < a - a {Subtracting a from both sides},
or, (n - 1)d < 0.
Since, n > 1, (n - 1) > 0, thus we get the common difference, d < 0, that is, the common difference is negative.
Thus, we can say that if the term of arithmetic progression decrease in magnitude then the common difference must be negative.
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When given an inverse variation, how do you find k?
Considering an inverse proportional relationship, you find k taking a point (x,y), and multiplying the values of x and y.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
For an inverse relationship, the function is:
[tex]y = \frac{k}{x}[/tex].
Then:
k = xy.
Which means that to find k, you take a point (x,y), and multiply the values of x and y.
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can someone please help me
answer choices:
A - sin(0°)
B - cos(0°)
C - sin(180°)
D - cos(180°)
E - sin(270°)
F - cos(270°)
Answer:
B
Step-by-step explanation:
Cos(0)=1
since the diagram shows x as (1,0)
(-4,-2) (0,2) (-2,1) find the domain and range and can you tell me if it’s a function ?? PLS HELPPP
Answer:
domain means -4,0,-2 and range is -2,2,1
Need help in this pls
Answer:
6
Step-by-step explanation:
The arc length is (2)(pi)(27)(40/360)=6pi.
So, k=6.
Please help and explain how to solve
Answer:
$ 7.52
Step-by-step explanation:
Find charge per minute
59 - 23 min = 36 minutes cost 16.32 - 10.56 = $ 5.76
or $5.76 / 36 min = 16 cents per min
from 59 to 78 = 19 more minutes x .16/min = $ 3.04
so from 59 to 78 will leave 10.56 - 3.04 = $7.52
In a bag of 10 marbles, there are 4 blue, 3 red, 2 green,
and 1 yellow. What is the probability that you draw one
marble that is green, DO NOT replace it, and draw another
marble that is yellow?
1
30
O b. 139
OC. 15
45
a.
O d. 7/19
2
Answer: 1/45
Step-by-step explanation: 10 total marbles. 4 are blue 3 are red 2 are green and 1 is yellow. The chance of drawing a green is 2/10 or 1/5. Then there are only 9 marbles left in the bag. So the chance of a yellow marble is 1/9. 1/5 x 1/9 = 1/45.
2x⁴ - 4-7x - 38x²/x - 4
Answer:
2x⁴-45x-8
Step-by-step explanation:
What is 3r2 – 48r + 192?
Gabrielle is baking large batches of brownies and cookies to share with her friends and family. Among other ingredients, her brownie recipe calls for 1 cup of sugar and 2 eggs and her cookie recipe calls for 3 cups of sugar and 2 eggs. Gabrielle has 20 eggs and 21 cups of sugar, and she would like to know how many batches of brownies and cookies she can bake without getting more of these ingredients. Part A Question Which system of inequalities can model Gabrielle’s situation, where x represents batches of brownies and y represents batches of cookies?
The system of inequalities can model Gabrielle’s situation is;
x + 2y ≤ 20
x + 2y ≤ 203x + 2y ≤ 21
InequalityIt follows from the task content, that the inequalities which can be used to model Gabrielle's situation be determined.
By setting variables as follows;
batches of brownies = x batches of cookies = yBrownie:
Sugar = 1 cup
Eggs = 2
Cookie:
Sugar = 3 cups
Eggs = 2
x + 2y ≤ 20
x + 2y ≤ 203x + 2y ≤ 21
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If u are 13, and ur birthday is 21 of october, how old will you be in 2050?
Answer:
41 years old
Step-by-step explanation:
2050-2022=28 years
13years old +28years = 41 years old (sorry if wrong)
Answer: Based on today's date of 7/19/2022, you will be 41 until October 21, 2050. On October 21, 2050 you will turn 42. You were born in 2008
Step-by-step explanation:
If Sam has 4 times as many nickels as dimes and they have a combined value of 120 cents, how many of each coin does he have
Answer:
Step-by-step explanation:
If Sam has 4 times as many nickels as dimes and they have a combined value of 120 cents, how many of each coin does he have
La siguiente tabla muestra el saldo de las tres cuentas bancarias de Dmitri.
Ahorros........$573.73
Retiro............$294.43
Cheques --$435.24
Ayuda a Dmitri a ordenar sus cuentas de menor a mayor valor absoluto del saldo.
Las cuentas de Dmitri de menor a mayor se ordenan: retiro, cheques y ahorros.
¿Cómo organizar las cuentas bancarias de Dmitri?Para organizar las cuentas bancarias de Dmitri de menor a mayor debemos observar cuidadosamente los valores de cada una. Adicionalmente para organizarlas por valor absoluto nos fijamos únicamente en el número sin tener en cuenta el símbolo, en ese caso el valor de cheques pierde su símbolo negativo.
Entonces las cuentas quedarían organizadas así:
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Function g is defined as g(x) = k f(x). What is the value of k?
What is the value of k?
Answer: Pick an x value like x = 2
Note that f(2) = 1 and g(2) = 2. This shows we've doubled the f(x) value to get g(x). Therefore k = 2.
Or you could pick on x = 4 to see f(4) = 2 and g(4) = 4. The output of f(x) has been doubled as well.
It doesn't matter what x is since we'll have this doubling effect go on. I recommend picking x values where the points on the blue graph land perfectly on a grid location. Something like x = 5 seems a bit tricky.
:
15. If 3x + 10 = 3y - 2(y + 4), what is the value of y in terms of x? (A) x + 18 (B) 3x+6 (C) 3x + 14 (D) 3x + 18
Answer:
3x + 18
Step-by-step explanation:
3x + 10 = 3y - 2(y + 4)
3x + 10 = 3y - 2y - 8
3x + 18 = y
Answer:
D, 3x + 18.
Step-by-step explanation:
3x + 10 = 3y - 2(y + 4)
3x + 10 = 3y - 2y - 8
3x + 10 = y - 8
y = 3x + 10 + 8
y = 3x + 18.
a big water tank contained 200 litres of water. during the day, 88 l 580 ml of water was used and 200 ml leaked. how much water was left in the water tank?
The quantity of water left in the tank as described in the task content is; 111 l 220ml.
What is the amount of water left in the tank?The tank described in the task content initially contains 200 liters, in which case, 1 liter corresponds to 1000ml.
Hence, when 88l 580ml was used, the remaining quantity of water is; 200l - (88l 580ml) = 111 l 420ml.
And finally, since 200 ml leaked, the quantity of water left is; 111l 220ml.
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Write an equation of the line point(2,-1) and parallel passing through y=3x-5 write in slope-intercept form
Answer:
y = 3x - 7
Step-by-step explanation:
Since the lines are parallel, the slopes will be the same. In this case 3. Now we have to find the y-intercept. We will use the slope (3), the x (2) and y (-1) to help us do this. We get the x and the y from the ordered pair given(2,-1).
y = mx + b
-1 = 3(2) + b Plug in what you know
-1 = 6 + b Subtract 6 from both sides
-7 = b
Now we can write the equation
y = 3x -7
ANSWER THIS QUESTION FIRST=BRANIEST
Answer:
18
Step-by-step explanation:
first we divide both parties by 5 making it so that 1/6 =3 and then we multiply by 6 to make it 6/6 = 18
The ratio of boys to girls who play soccer in Mr. Fraser’s class is 14:6. If there were 400students in the school, how many boys would likely play soccer?
Answer:
280
Step-by-step explanation:
Set up a ratio to solve.
Mr. Fraser's class has 20 soccer playing students, and 14 are boys.
14/20 = x/400
Cross multiply. 20x= 5600
Divide by 20 to solve
x= 280
Please help me fast
What is the equation of this graph
Answer-4,5
Step-by-step explanation:
If the ratio of areas of two similar solids is 25:36, what is the linear ratio.
Answer: Hi here go your answer is
25 divides by 36 is 0.69444 or 0.69
Step-by-step explanation:
Find the least positive integer, written only by numbers 0, 1, and 2, which is divisible by 225.
The least positive integer, written only by numbers 0, 1, and 2, which is divisible by 225 is 1,222,200.
A number (A) is divisible by another number (K) when the division of A by K, leaves a remainder of 0.
In the question, we are asked to find the least positive integer, written only by numbers 0, 1, and 2, which is divisible by 225.
Now, we need to know that the multiples of 225 end with 00, 25, 50, and 75.
So, to have a multiple with digits 0, 1, and 2, we need the last digits to be 00.
The smallest multiple of 225, ending with 00 is 225*4 = 900.
So, we need to have the least multiple of 900, with digits 0, 1, and 2.
We know that a multiple of 9, has a sum of its digit as 9.
The smallest multiple of 9, with digits 1, and 2, will be 12222.
Adding the last 00 to this, we get the least multiple as 1,222,200.
Thus, the least positive integer, written only by numbers 0, 1, and 2, which is divisible by 225 is 1,222,200.
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Find the zeros of: [tex]f(x)=-\frac{1}{1500} (x^3+10x^2-275x-1500)[/tex], and the use them to find all of the linear factors of the polynomial function
The function f(x) = -(1/1500)(x³ + 10x² - 275x - 1500) the zeros are at (-20, 0), (-15, 0) and (15, 0). Hence the factors of the function are x + 20, x + 15 and x - 15.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the graph of the function f(x) = -(1/1500)(x³ + 10x² - 275x - 1500) the zeros are at (-20, 0), (-15, 0) and (15, 0). Hence the factors of the function are x + 20, x + 15 and x - 15.
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What is the length of the hypotenuse of the triangle?
Triangle A B C. Side A C is 7 centimeters and side B C is 3 centimeters. Hypotenuse A B is unknown.
StartRoot 20 EndRoot cm
StartRoot 23 EndRoot cm
StartRoot 40 EndRoot cm
StartRoot 58 EndRoot cm
The length of the hypotenuse of the triangle as given is; √58 cm.
What is the length of the hypotenuse of the triangle described?It follows from the task content that the triangle described in the task content is a right triangle with two other side lengths; 7cm and 5cm.
Hence, it follows from Pythagoras theorem that the length of the hypotenuse side of the triangle is;
Hypotenuse = √(5² + 7²)
Hypotenuse = √58 cm.
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