The form of the partial fraction decomposition of the given function is:
[tex]\frac{A}{x+5}+\frac{B}{x-4}[/tex]
What do we mean by rational expression?The ratio of two polynomials is a rational expression.If f is a rational expression, it can be expressed as p/q, where p and q are polynomials.To find the form of the partial fraction:
The rational expression given is: [tex]\frac{x-20}{x^2+x-20}[/tex]
Factor the provided rational expression's denominator:
[tex]\begin{aligned}\frac{x-20}{x^2+x-20} &=\frac{x-20}{x^2+5 x-4 x-20} \\&=\frac{x-20}{x(x+5)-4(x+5)} \\&=\frac{x-20}{(x+5)(x-4)}\end{aligned}[/tex]
Apply the partial fraction decomposition method now:
[tex]\begin{aligned}\frac{x-20}{x^2+x-20} &=\frac{x-20}{(x+5)(x-4)} \\&=\frac{A}{x+5}+\frac{B}{x-4}\end{aligned}[/tex]
Therefore, the form of the partial fraction decomposition of the given function is:
[tex]\frac{A}{x+5}+\frac{B}{x-4}[/tex]
Know more about rational expression here:
https://brainly.com/question/25292194
#SPJ4
The correct question is given below:
Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficients.
[tex]\frac{x-20}{x^2+x-20}[/tex]
please solve this question (and explain how it works) thank you!
Answer:
Equation is 15(x-20) = 945
x = $83
Step-by-step explanation:
The cost of each lesson is $x
The discounted cost = x-20
Since 15 lessons cost 945,
the equation is
15(x-20) = 945
Simplifying by multiplying the term in brackets by 15:
15x - 15(20) = 945
15x - 300 = 945
Adding 300 on both sides isolates the 15 x term
15x = 945 + 300 = 1245
15x = 1245
Dividing both sides by 15 ,
x = 1245/15 = 83
So cost of lesson before discount is $83
A cat is in the top of a tree so you will save it you are standing 23 m away from the tree the angle of elevation to the cat is 54 how long does the ladder need to be fro you to get to get the cat?
The ladder needs to be 34.3m long from tree you to get to get the cat.
We must determine the hypotenuse in this right triangle, which is the side that is opposite the triangle's 90° angle. When the neighboring side is 23 meters away, the elevation angle is 54°
Suppose Hypotenuse equals h.
Given, the base is 23m
Using trigonometry,
tan θ = Base / hypotenuse
tan 54° = 23 / h
⇒ 0.67 = 23 / h
⇒ h = 23 / 0.67
⇒ h = 34.3
So, the ladder needs to be 34.3m away in order to reach cat.
To learn more about trigonometric problems from given link
https://brainly.com/question/24349828
#SPJ4
1/5(10x−5)=5x−1 is the problem.
some one help please.
9th grade math
Solution of the equation [tex][\frac{1}{5(10x-5)} =(5x-1)][/tex] is [x = (-0.512788205961), (-0.187211794039)].
As per the question statement, our concerned equation is [tex][\frac{1}{5(10x-5)} =(5x-1)][/tex].
We are required to find the value of "x" that satisfied the equation. First, we will have to convert the given equation to the form of quadratic equation.
[tex][\frac{1}{5(10x-5)} =(5x-1)]\\or, 1=5(10x-5)*(5x-1)\\or, 1=5*5(2x-1)*(5x-1)\\or,1=25[(2x-1)(5x-1)]\\or,1=25(10x^{2} -2x-5x+1)\\or,1=25(10x^{2} -7x+1)\\or,1=250x^{2} -175x+25\\or,250x^{2} -175x+24=0\\[/tex]
Now, [(250x² - 175x + 24) = 0] is in the form of a quadratic equation.
Also, the formula to calculate the solutions of a standard quadratic equation [ax² + bx +c = 0] goes as [tex][x=(\frac{-b+\sqrt{(b^{2}-4ac) } }{2a}), (\frac{-b-\sqrt{(b^{2}-4ac) } }{2a}) ][/tex]
Comparing [ax² + bx +c = 0] with [(250x² - 175x + 24) = 0], we get
(a = 250), (b = 175) and (c = 24), and using these values in the above mentioned formula to calculate the solutions of quadratic equations, we get, [x = (-0.512788205961), (-0.187211794039)].
Quadratic Equations: In algebra, any polynomial equation whose highest degree is two and can be rearranged to the standard form of [ax² + bx + c = 0], where (a ≠ 0), is known as a quadratic equation.To learn about Quadratic Equations, click on the link below.brainly.com/question/1863222
#SPJ9
please help
10101010101000
Answer:
I did this and I got it wrong so i did some so it said x=10 so im suggesting interpolation
9643x48 paso a paso a paso
Answer: 462,864
Step-by-step explanation:
[tex]9614 \\x\\8\\\\\\=\\77144\\\\9643\\x\\4\\38572\\\\77144+38572 = 77144[/tex]
Pleaseeee hellp meeeee
Answer:
57,600 ft
Step-by-step explanation:
The table below shows the number of gallons of gasoline used and the miles driven for different types of cars.
Type of Car Gallons of Gasoline Used Miles Driven
A
5 : 106
B
10 :204
C
15 : 298
D
20 : 392
Which type of car had the HIGHEST number of miles per gallon?
A
Type A
B
Type B
C
Type C
D
Type D
Type A car has the highest number of miles per gallon.
Given that the miles driven by a Type A car is 106 miles for 5 Gallons of Gasoline.
⇒ miles per gallon for a Type A car = 106/5 = 21.2 miles/gallon
Given that the miles driven by a Type B car are 204 miles for 10 Gallons of Gasoline.
⇒ miles per gallon for a Type B car = 204/10 = 20.4 miles/gallon
Given that the miles driven by a Type C car are 298 miles for 15 Gallons of Gasoline.
⇒ miles per gallon for a Type A car = 298/15 = 19.87 miles/gallon
(approximate to the two places of decimal value)
Given that the miles driven by Type D car are 392 miles for 20 Gallons of Gasoline.
⇒ miles per gallon for a Type D car = 392/20 = 19.6 miles/gallon
Therefore we have the following:
Type A - 21.2 miles/gallon
Type B - 20.4 miles/gallon
Type C - 19.87 miles/gallon
Type D - 19.6 miles/gallon
It is clear from the above data, that type A car has the highest number of miles per gallon.
Learn more at:
https://brainly.com/question/24787693
#SPJ9
SOS PLEASE, I DONT UNDERSTAND
Answer:
8ft
Step-by-step explanation:
i believe it's eight feet?
Is the following relation a function? Justify your answer. Two circles are shown, one labeled x and the other labeled y. The x circle contains the numbers 6, negative 2, 4, and negative 1. The y circle contains the numbers 2, negative 2, and 1. Arrows map numbers from x to numbers from y. There are arrows going from 6 to negative 2, from negative 2 to 2, from 4 to 1, and from negative 1 to 1. Yes, because each output value has only one input value Yes because each input value has only one output value No, because there is an input value with more than one output value No, because there is an output value with more than one input value
each input is mapped into only one output, so this is in fact a function.
Is the following relation a function?A relation is a function if and only if each input is mapped into only one output.
Remember that an ordered pair is of the form (x, y), where x is the input and y the output.
In this case, the relation is defined by the ordered pairs:
(6, -2), (2, 2), (4, 1), (-1, 1)
We can see that each input is mapped into only one output, so this is in fact a function.
If you want to learn more about functions:
https://brainly.com/question/2328150
#SPJ1
Toni & Warren are collecting foods for their
school's canned food drive. Toni started with 400
cans and collected 13 more each day. Warren
started with 40 cans and collected 22 more each
day. How long before Toni & Warren have the
same number of cans for their food drive?
Answer:
40 days
Step-by-step explanation:
Let d be the number of days.
[tex]400 + 13d = 40 + 22d[/tex]
[tex]360 = 9d[/tex]
[tex]d = 40[/tex]
Use the drawing tools to form the correct answer on the graph.
Graph this function.
f(x) = - 1/3x + 8
Answer: Use Desmos Graphing Calc, helps for graph like these
Step-by-step explanation:
1. Place a point on (0,8)
2. Then go down -1/3
P.S: REMEMBER RISE OVER RUN
Find a polynomial f(x) of degree 5 that has the following zeros. 9,8,0,4,-3 leave your answer in factored form
Step-by-step explanation:
x(x-4)(x+1) is a 3 degree polynomial in factored form with zeros 0,4 and -1
Just take each zero and change its sign, then stick an x in front of it to get the 3 factors
(x-0)(x-4)(x- -1) = x(x-4)(x+1)
= x(x^2-3x-4)
= f(x) = x^3 -3x^2 -4x
f(0) = 0
f(4) = 64-3(16)-4(4) = 0
f(-1) = -1 -3(-1)^2 -4(-1) = 0
graph the polynomial and it intersects the x axis in 3 places, the origin (0,0), (4,0) and (-1,0)
solve these simultaneous equations
2x+3y=13
and 4x+6y=26
Answer:
2x + 3y = 13
4x - y = -2
In the second equation, subtract 4x from both sides.
-y = -2 - 4x
Divide both sides by -1.
y = 2 + 4x
Put this into the first equation in place of y.
2x + 3(2 + 4x) = 13
Multiply everything in the parenthesis by 3.
2x + 6 + 12x = 13
Combine like terms.
14x + 6 = 13
Subtract 6 from both sides.
14x = 7
Divide 14 on both sides.
x = 7 / 14
x = 0.5
Put this into the second equation in place of x.
4(0.5) - y = -2
2 - y = -2
Subtract 2 from both sides.
-y = -4
Divide both sides by -1.
y = 4
So x = 0.5 and y = 4.
Step-by-step explanation: I hope this helps.
A student's four test grades are stored in cells a10, b10, c10, and d10. which excel statement will calculate the test average of these 4 grades?
The excel statement to estimate the test average of these 4 grades is -
Click a cell just below column or on the right of the row containing the numbers you want to average.Click the arrow next to AutoSum > Average on the HOME tab, then press Enter.What is termed as average function?An average is the sum of many numbers divided by the total of numbers. It is also known as the arithmetic mean.
Assume we have the following sequence of numbers: 1, 2, 3, 4, 1, 2, and 3. The sum of the these numbers is 16, and the number of numbers divided by 7 is 2.28. As a result, the average of the these numbers is 2.28.In Microsoft Excel, how do you find the average?The average of multiple cells in Microsoft Excel and other spreadsheets can be calculated using the appropriate formula. The formula in the following example calculates the average of the values found in cells A1 through F1 of the first column : =AVERAGE(A1:F1)You would use the same row but modify the cells to cells in a row to calculate the average of cells in one row. For instance, the formula recognizes the average value in cells A1 via A20 when placed in cell A21. =AVERAGE(A1:A20)To know more about the Microsoft Excel, here
https://brainly.com/question/23501096
#SPJ4
there are blank vaues in the data set which are greater than or equal to 10 and less than or equal to 19. there are blank vlaues in the data set which are greater than or equal to 30 and less than or equal to 39. there are blank values in the data set which are greater than or equal to 20 and less than or ewual to 29
According to the given data set:
values10,11,12,13,14,17,17,18,18,19,19,19,21,23,23,25,26,27,27,27,31,32,33,33,36,37,37,38,38more than 20 and less than or equal to 29 values21,23,23,25,26,27,27,27more than 20 and less than or equal to 29 values.
What is an example of a data set?A data set is a group of figures or values related to a specific topic. A data set might include, for instance, each student's test results in a certain class. A data set is the number of fish that each dolphin consumes in an aquarium.
According to the given data:There are eight values that are both bigger than 20 and less than 29.The data collection has 12 values that are both higher than or equal to 30 and lower than or equal to 39.Values greater than nor equal to 30 and less than or equal to 3931,32,33,33,35,36,37,37,37,38,38The data collection has 12 values that are both higher than or equal to 30 and lower than or equal to 39.
To learn more about data set visit:
https://brainly.com/question/16300950
#SPJ4
Which figure has a significant zero?
A) 2000
B) 506
C) 0.00412
D) 70
A boys weighs 90 pounds on earth and 34.5 pounds on mars how much would a 600 pound man weigh on mars
Answer:
about 230lbs
Step-by-step explanation:
I think
WILL GIVE 12 POINTS AND BRAINLIEST IF ANSWERED IF ANSWERED CORRECTLY
Solve for t: d=rt-g
Answer:
d=rt-g
First, add G to both sides
d=rt-g
+g +g
----------
dg=rt
Then divide by r since you're solving for t
dg rt
---=-----
r r
Your answer should be t=dg/r
Hope this helps!
Step-by-step explanation:
I don’t understand how to do this equation 12x when x =6
Answer:
72
Step-by-step explanation:
when x = 6
then replace x with 6 in the equation
12x
= 12(6)
= 72
Josiah has a job washing cars. He earns $35 for each car he washes. On Monday, he washed 7 cars. On Tuesday, he forgot to count how many cars he washed. He earned $560 for the two days. Josiah wants to find how many cars he washed on Tuesday.
Write the equation that Josiah can use for the situation above. (Use the variable x)
How many cars did Josiah wash on Tuesday?
( I know that the answer would be X=9 but how do I write the equation.)
Answer:
245 + 35x = 560
Step-by-step explanation:
35 x 7 = 245 (for monday)
Then the equation should be
245 + 35x = 560
It looks like you solved it too, your answer is correct btw! Lmk if you need help with the steps, or anything
Also, how you make this equation is this, you put how much he earned for monday, and then add it to 35x (x being the amount of cars he did) make sure to do = 560 at the end so you can solve it :)
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
Step-by-step explanation:
Since he gets 35$ for every car he washes and washed seven cars on Monday, he got 35*7=245. Now, you can minus the amount from it to 315. 315/35 is 9, so nine is your answer.
To phrase it into an equation, you can do when x=amount of cars washed, 35x=560-7*35.
Hope this helped!
If OM=103 MN=108 ON=84 PQ=54 RQ=42 find the perimeter of pqr
By additive property of line segments, the length of the line segment PR is equal to a length of 96 units.
What is the perimeter of a combination of line segments?
According to geometry, the perimeter of a figure, closed or not, is the sum of the lengths of its sides, each represented by a line segment. In this question, we must determine the perimeter of two line segments, whose definition is found by additive property of line segments:
PR = PQ + QR (1)
Where PR, PQ and QR are the lengths of the three line segments. If we know that PQ = 54 and QR = 42, then the length of the line segment PR is equal to:
PR = PQ + QR
PR = 54 + 42
PR = 96
Therefore, the length of the line segment PR is equal to a length of 96 units.
To learn more on perimeters: https://brainly.com/question/6465134
#SPJ1
There are 5 white balls,8 red balls ,7 yellow balls and 4 green balls in a container a ball is choosen at random.what is the probabilty of chooseing neither white or green? .
15/19 + 14/19 = 29/19
Step-by-step explanation:
Add the number of balls in the basket together.
Subtract the number of white balls from the sample space ( the total amount of balls) your answer is written over the sample space and the same process is done for the green ball
Y is inversely proportional to the cube of x when x=1/2,y=24 find the formula for y in terms of x
The formula for y in terms of x is y = 3/x³.
Inversely Proportional:
When two variables are inversely proportional to each other, then the value of one quantity increases with respect to decrease in other or vice-versa.
So, it can be written as,
y = k/x
where,
y is inversely proportional to x and k is the constant of proportionality.
Given,
Y is inversely proportional to the cube of x.
Here we need to find the formula for y in terms of x.
We know that, y is inversely proportional to the cube of x.
So, it can be written as
=> y = k / x³
Where k is the constant.
To find the formula of y,
First we need to find the value of k,
By applying the value of x and y,
So,
=> 24 = k / (1/2)³
=> 24 = k / 1/8
=> 24/8 = k
=> k = 3
Therefore, the formula for y in terms of x is,
=> y = 3/ x³
To know more about Inversely Proportion Problems here.
https://brainly.com/question/14318761
#SPJ4
the equation 1.2+61=2r(4-6) HELP MEEEEEEEEEEEEEEEE PLEASE
The value of "r" in the given equation is -15.55.
The equation given is,1.2 + 61 = 2r(4-6)Add the two numbers present on the left hand side of the equation.62.2 = 2r(4-6)Subtract the two numbers present on the right hand side of the equation in brackets.62.2 = 2r(-2)Multiply the two numbers present on the right hand side of the equation.62.2 = -4rDivide both the sides of the equation by the common factor, i.e., -4.62.2/(-4) = (-4r)/(-4)Cancel terms that are in both the numerator and denominator.-15.55 = rMove the variable to the left hand side of the equation.r = -15.55To learn more about equations, visit :
https://brainly.com/question/10413253
#SPJ9
What is the slope, y intercept and equation
to get the equation of any straight line, we simply need two points off of it, let's use those points from the picture below.
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{4 +2}{3 -1} \implies \cfrac{ 6 }{ 2 }\implies 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{3}(x-\stackrel{x_1}{1}) \implies y +2= 3 (x -1) \\\\\\ y+2=3x-3\implies {\LARGE \begin{array}{llll} y=3x\underset{(0~~,~~-5)}{\stackrel{\stackrel{y-intercept}{\downarrow }}{-5}} \end{array}}[/tex]
Suppose there are 1000 lockers in a school hallway and they are all closed. Only 50 students
come through the hallway and start opening and closing the lockers. The first student opened all
the lockers. The second student closed every second locker and so forth. The Third student
changes the state of every 3rd locker. The fourth student changes the state of every 4th locker,
the fifth student changes the state of every 5th locker and so on, until the 50th student.
a. What is the state of the following locker numbers: #91, #1505, #625, #1000?
i. How do you know? (please show how you know)
Answer:
Suppose there are 1000 lockers in a school hallway and they are all closed. Only 50 students
come through the hallway and start opening and closing the lockers. The first student opened all
the lockers. The second student closed every second locker and so forth. The Third student
changes the state of every 3rd locker. The fourth student changes the state of every 4th locker,
the fifth student changes the state of every 5th locker and so on, until the 50th student.
a. What is the state of the following locker numbers: #91, #1505, #625, #1000?
i. How do you know? (please show how you know)
Pablo finished his English assignment in 1/4
hours. Then he completed his history assignment in 4/5 hours. How much more time did Pablo spend on his history
4
assignment?
Write your answer as a fraction in simplest form.
Answer:
11/20
Step-by-step explanation:
Answer:
33/60 might be correct.
Step-by-step explanation:
1/4 hours is 15 minutes. 4/5 hours is 48 minutes
48-15=33 more minutes
Deon cut away 1.52 meters of rope. Before that, he had 3 meters of rope. How much rope does Deon have left?
Answer:
1.48
Step-by-step explanation:
first find the half of 3 and then minus 2
Answer:
1.48 meters
Step-by-step explanation:
3.00-1.52= 1.48m
Why do you think calculators change the way of scientists notation appears
Answer:
Yes because, Maybe because it's sometimes of technology occurs many things such as we no longer using old stuffs and living because. Even the calculator it's similar
Finding an angle measure given extended angles
Answer:
thanks for the points
Step-by-step explanation:
thanks for the points