Answer:
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{5}{9(x-4)}+\frac{4}{(x+5)}[/tex]
Step-by-step explanation:
Given
[tex]\frac{x - 20}{ x^2 + x - 20}[/tex]
Required
Decompose into partial fraction
Start by factorizing the denominator:
[tex]x^2 + x - 20 =x^2 + 5x -4x- 20[/tex]
[tex]x^2 + x - 20 =x(x + 5)-4(x+5)[/tex]
[tex]x^2 + x - 20 =(x-4)(x+5)[/tex]
So, we have:
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A}{x-4}+\frac{B}{x+5}[/tex]
Take LCM
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A(x+5)+B(x-4)}{(x-4)(x+5)}[/tex]
Cancel out the denominator
[tex]x - 20 = A(x+5)+B(x-4)}[/tex]
Open brackets
[tex]x - 20 = Ax+5A+Bx-4B[/tex]
Collect Like Terms
[tex]x - 20 = Ax+Bx+5A-4B[/tex]
[tex]x - 20 = (A+B)x+5A-4B[/tex]
By comparison;
[tex](A +B)x = x[/tex] ==>[tex]A + B = 1[/tex]
[tex]5A - 4B = 1[/tex]
Make A the subject in [tex]A + B = 1[/tex]
[tex]A = 1 - B[/tex]
Substitute 1 - B for A in [tex]5A - 4B = 1[/tex]
[tex]5(1-B) -4B = 1[/tex]
[tex]5-5B -4B = 1[/tex]
[tex]5-9B = 1[/tex]
Collect Like Terms
[tex]-9B = 1 - 5[/tex]
[tex]-9B = - 4[/tex]
[tex]B = \frac{4}{9}[/tex]
[tex]A = 1 - B[/tex]
[tex]A = 1 - \frac{4}{9}[/tex]
[tex]A = \frac{9-4}{9}[/tex]
[tex]A = \frac{5}{9}[/tex]
So:
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A}{x-4}+\frac{B}{x+5}[/tex]
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{5}{9(x-4)}+\frac{4}{(x+5)}[/tex]
Write the fraction in lowest terms.
14/37
Answer:
14/37
Step-by-step explanation:
14/37 is already in the simplest form. It can be written as 0.378378 in decimal form (rounded to 6 decimal places).
Steps to simplifying fractions
Find the GCD (or HCF) of numerator and denominator
GCD of 14 and 37 is 1
Divide both the numerator and denominator by the GCD
14 ÷ 1
37 ÷ 1
Reduced fraction:
14/37
Therefore, 14/37 simplified to lowest terms is 14/37.
Find the missing sides to the triangle seen below.
Answer:
95
Step-by-step explanation:
you got to eat it and then division then multiple
Answer:
95
Step-by-step explanation:
Mr. Morales owns a tour bus company and just received the news that fuel prices are going to increase by 125% it is currently $3.40 per gallon what will the cost per cost per gallon after the increase
Answer:
Step-by-step explanation:
Your answer
Let me think. 125 %,,,. So 1.25* 3.4= 4.25
New price = 7.65
Mark it as Brainlist answer. Follow me.
[tex] \sqrt{25} [/tex]
pls help i just want the answer T-T.
Answer:
5
Step-by-step explanation:
S 4xy
when x = 2, y = 5
Answer: 40
Step-by-step explanation:
Plug in the known values:
4(2)(5) = 8(5) = 40
Answer:
its 40 hope this helps you
Step-by-step explanation:
have a nice day/night
User will enter three grades averages (exam, project, and lab). Determine which of the three grades (consider any ties) is the highest grade and display the results. Determine which of the three grades (consider any ties) is the lowest grade and display the results. Check for any grades failing below 70% and display each individual grade. Calculate the average grade using the three grades and display the average grade. If they are all 70 and above then display the fact that they are all 70% or above.
Answer:
In Python:
exam = int(input("Exam: "))
project = int(input("Project: "))
lab = int(input("Lab: "))
if exam >= project and exam >= lab:
print("Highest Grade: "+str(exam))
elif project >= exam and project >= lab:
print("Highest Grade: "+str(project))
else:
print("Highest Grade: "+str(lab))
if exam <= project and exam <= lab:
print("Lowest Grade: "+str(exam))
elif project <= exam and project <= lab:
print("Lowest Grade: "+str(project))
else:
print("Lowest Grade: "+str(lab))
print("\nGrades below 70")
if exam < 70:
print("Exam: "+str(exam))
if project < 70:
print("Project: "+str(project))
if lab < 70:
print("Lab: "+str(lab))
print("\nAverage: "+str((exam+project+lab)/3))
if exam > 70 and project >70 and lab > 70:
print("All grades are above 70")
Step-by-step explanation:
The next three lines get input for exam, project and lab
exam = int(input("Exam: "))
project = int(input("Project: "))
lab = int(input("Lab: "))
This condition checks if exam is the highest grade
if exam >= project and exam >= lab:
If true, exam is printed as the highest grade
print("Highest Grade: "+str(exam))
This condition checks if project is the highest grade
elif project >= exam and project >= lab:
If true, project is printed as the highest grade
print("Highest Grade: "+str(project))
If otherwise
else:
lab is printed as the highest grade
print("Highest Grade: "+str(lab))
This condition checks if exam is the lowest grade
if exam <= project and exam <= lab:
If true, exam is printed as the lowest grade
print("Lowest Grade: "+str(exam))
This condition checks if project is the lowest grade
elif project <= exam and project <= lab:
If true, project is printed as the lowest grade
print("Lowest Grade: "+str(project))
If otherwise
else:
lab is printed as the lowest grade
print("Lowest Grade: "+str(lab))
This prints the header "Grades below 70"
print("\nGrades below 70")
This checks if exam is below 70.
if exam < 70:
If true, exam score is printed
print("Exam: "+str(exam))
This checks if project is below 70
if project < 70:
If true, project score is printed
print("Project: "+str(project))
This checks if lab is below 70
if lab < 70:
If true, lab score is printed
print("Lab: "+str(lab))
This calculates and prints the average
print("\nAverage: "+str((exam+project+lab)/3))
This checks if all three scores are above 70
if exam > 70 and project >70 and lab > 70:
If true, the the message that all are above 70, is printed
print("All grades are above 70")
This year 0.3 of the x students at Mega Middle School are in 7th grade. There are 294 students in 7th grade.
Answer:
is that even a question ?
Step-by-step explanation:
3/10x=294
x=294*10/3
x=980 students
if you found my answer helpful please mark as brainliest.
A math teacher was frustrated at the number of students leaving their graphing calculator behind in her classroom at the end of class without a way to locate the student. A random sample of 50 students is selected, and of the students questioned, 32 had their names written on their graphing calculators.
Required:
What would be a 99% confidence interval for the proportion of all students at this school who have their names written on their graphing calculators?
Answer:
The 99% confidence interval for the proportion of all students at this school who have their names written on their graphing calculators is (0.4652, 0.8148).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
A random sample of 50 students is selected, and of the students questioned, 32 had their names written on their graphing calculators.
This means that [tex]n = 50, \pi = \frac{32}{50} = 0.64[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.64 - 2.575\sqrt{\frac{0.64*0.36}{50}} = 0.4652[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.64 + 2.575\sqrt{\frac{0.64*0.36}{50}} = 0.8148[/tex]
The 99% confidence interval for the proportion of all students at this school who have their names written on their graphing calculators is (0.4652, 0.8148).
an arfican elephant weighs 6 tons what is the weight of the elephant in pounds? 2000 pounds = 1 ton
HELP EMERGANCY FAST ANSWERS TIME LIMIT
Assume Sheila's nominal salary increases from $42,000 in 2003 to $69,000 in 2004.
If the Deflator increased from 106 in 2003 to 109 in 2004 and the CPI increased
from 184 in 2003 to 190 in 2004, what was Sheila's percentage increase in real
income?
6
Answer:
E)
Step-by-step explanation:
1 - (69,000 / 42,000) = .64285 * 100% = 64.3%
43,5 multiplicado por 8,6 y que la explicación o la operación venga incluida porfavor
Answer:
la respuesta correcta es 374.10
Divide.
14)4210
O A. 300 r 10
O B. 300 r 7
O C. 300
O D. 310
no rush at all lolz.!
300 with a remainder of 10
3 0 0
1 4 | 4 2 1 0
4 2
1 0
Therefore, 4210 / 14 = 300 with a remainder of 10.
300 with a remainder of 10
The checker piece near the middle of the board can move diagonally in any directions between shaded squares. On how many different squares can the piece be located at the end of one turn?
URGENT I REALLY NEED HELP ANYONE? PLEASE
Find the slope of the line passing through each of the following pairs of points. (0,0) (4,3)
Answer:
Step-by-step explanation:
Slope or m is defined as
m=(y2-y1)/(x2-x1) in this case
m=(3-0)/(4-0)
m=3/4
3. Evaluate and graph
the solution.
3. E
the
"the
5x + 9-3x s 21
+
++
Answer:
x=6
Step-by-step explanation:
5x+9-3x=21
5x-3x=21-9
2x=12
x=6
The ice cream store offers schools a discount of 12% for the month of June. The school decides to purchase ice cream bars for the end of the year picnic.
a. How much money would the school save if the school purchased 55 boxes of ice cream? Show your work and write your answer in the space below.
b. What is the total price with the discount for 55 boxes of ice cream?
PLS HELP ME!!!
Answer:
Divide the number of ice-cream bars into the number of people. Example: say you have 20 ice cream bars and 10 people you divide 20/10 and get 2 ice cream bars per person
Step-by-step explanation:
Are you also a simp for draco? :3
Which of the following is most likely the next step in the series?
Answer:
I need more info to answer this question.
Step-by-step explanation:
a total of 40 percent of the voters in a city classify themselves as independents, whereas 35 percent classify themselves as liberals, and 25 percent as conservatives. in a recent election, 40 percent of the independents, 75 percent of the liberals, and 65 percent of the conservatives voted. given that a person voted in the election, what is the probability that the person is an independent
Answer:
Probability = 0.088 ie 8.8%
Step-by-step explanation:
P (I) = 40% = 0.4
P (L) = 35% = 0.35
P (C) = 25% = 0.25
P (EV / I) = 40% = 0.4
P (EV / L) = 75% = 0.75
P (EV / C) = 65% = 0.65
P (I / EV) = [ P (EV / I) . P (I) ] / [ P ( EV) ]
[ P (EV / I) . P (I) ] / [ P (EV / I) + P (EV / L) + P (C / L)
[(0.4) (0.4)] / [ 0.4 + 0.75 + 0.65 ]
0.16 / 1.8
= 0.088 ie 8.8%
1.99 ÷ 3 =
2. 125 ÷ 5 =
3. 288 ÷ 36=
4. 540 ÷ 12=
5. 999 ÷ 111=
pls answer ngayon ko na po ito ipapasa explain the answer
Plz help I’m stuck on this question
Answer:
the answer is C
Step-by-step explanation:
bhl
2
i hope it will help you
HELP ASAP PLS SHOW WORK
Answer:
42
dnndndndndndnd
dndndndndj
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
5 a) 22.6
b) 67.8
6 a) 9 miles
b) 18 miles
7. Alicia
Hope this helps pls mark me brainliest thx that took me ages
Evaluate the expression for x= -4.
4x2 - 6x + 7
When x= -4,4x2 - 6x +7=
Why is your amount owed considered when determining your credit score? BI U S
Aaron usually runs 1 1/2 miles each day. However, on
Tuesday he only ran 2/3 of that distance. How far did
Aaron run on Tuesday?
Isabella invested $500 at 6% annual interest, compounded quarterly. How much will her Investment be after 25 years.
Answer:
$2216.02
Step-by-step explanation:
Compound interest formula:
[tex]FV=PV(1+\frac{i}{n})^{nt}\\\\FV=500(1+\frac{.06}{4})^{25*4}\\\\500(1.015)^{100}\\=2216.02[/tex]
Without making any calculations, which data set has the smallest standard deviation?
O 1, 1, 2, 2, 3,3
O 1, 3,5
O 0, 1, 5, 6, 9, 10
O 1, 1, 1, 1, 2, 2, 2, 2
Answer:
the last set: {1, 1, 1, 1, 2, 2, 2, 2}
Step-by-step explanation:
Notice the smallest standard deviation will come from the addition of the differences between the average value and each individual number in the set.
We notice that there is one set where all values are very close to the average . This is the set:
{1, 1, 1, 1, 2, 2, 2, 2} whose clear average is 1.5 , and therefore the deviations from the mean will produce contributions of 0.5 for each of the elements.
Can the triangles be proven similar by AA?
Question options:
A)
No, similar triangles cannot contain a pair of parallel lines.
B)
Yes, because ∠QUR ≅ ∠TUS (vertical angles) and ∠R ≅ ∠S (alternate interior angles).
C)
Yes, because || .
D)
No, the triangles contain no angles marked congruent.
Answer:
No, similar triangles cannot contain a pair of parallel lines. Yes, because || . Yes, because ∠QUR ≅ ∠TUS (vertical angles) and ∠R ≅ ∠S (alternate interior angles).
Step-by-step explanation:
Yes, because ∠QUR ≅ ∠TUS (vertical angles) and ∠R ≅ ∠S (alternate interior angles).
What is similarity?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Both triangles are similar as,
∠QUR ≅ ∠TUS (vertical angles)
∠R ≅ ∠S (alternate interior angles).
So, By AA similarity criteria triangles are similar.
Learn more about similarity here:
https://brainly.com/question/17170212
#SPJ5
I dont understand it
Answer:
30xy
Step-by-step explanation:
I divided this shape into a square and a rectangle.
Solve:
First I multiplied 2x and 3y
2x*3y= 6xy
Then I multiplied 6x and 4y
6x*4y= 24xy
Then I added them together
24xy+6xy= 30xy
Hope this helps!
what is the solution f/4 = 12/5
Step-by-step explanation:
cross multiply
4(12) = 5f
48 = 5f
48/5 = f
9 3/5
