Write out the form of the partial fraction decomposition of the function (as in this example). Do not determine the numerical values of the coefficients. (a) x − 20 x2 + x − 20 Incorrect: Your answer is incorrect. (b) x2 x2 + x + 20 Incorrect: Your answer is incorrect.
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]
Jane needs to miss fewer than 1__6of the words on her spelling list. If there are 18 words, how many can she miss? Explain.
Answer:
Assuming that you mean 1/6, the answer would be 3 .
Step-by-step explanation:
1/6 x 18 is equal to three.
alternate exterior angles theorem
vertical angles theorem
corresponding angles postulate
same side interior angles theorem
alternate interior angles theorem
are all the second awsner which one is it
i need this awnser
117°
same side interior angles theorem
ss of
3. In a class of 50 students, 40 % are girls. Find the number of girls and
number of boys in the class?
Solution:
Answer:
20 boys in the class
Step-by-step explanation:
40% of 50 is 20
What is a in the parallelogram
Vaughn threw the shot put 9 yards at a track meet. The official used a tape measure to measure the distance in feet. How many feet did he throw the shot put?
Answer:
27 feet
Step-by-step explanation:
There are 3 feet in 1 yard. 9×3=27
How do you solve for a variable?
A. Use the alphabet
B. Displacement
C. Get it by itself
Answer:
C. Get it by itself
Step-by-step explanation:
When solving for a variable, whether it be an inequality, a factor, or an algebraic expression. Getting the specified variable by itself is the most effective and best way to get that answer to your question. The other two answers here do not make any sense whatsoever.
it’s MATH who knows how to do this i’m down bad
Answer/Step-by-step explanation:
1. 7x + 2 = 5x + 22 (alternate interior angles are congruent)
Collect like terms
7x - 5x = -2 + 22
2x = 20
2x/2 = 20/2
x = 10
2. 13x - 6 = 10x + 24 (alternate interior angles are congruent)
Collect like terms
13x - 10x = 6 + 24
3x = 30
3x/3 = 30/3
x = 10
3. (12x + 26)° + 46° = 180° (same side interior angles are supplementary)
12x + 26 + 46 = 180
12x + 72 = 180
12x + 72 - 72 = 180 - 72
12x = 108
12x/12 = 108/12
x = 9
4. (5x + 5)° + 135° = 180° (same side interior angles are supplementary)
5x + 5 + 135 = 180
5x + 140 = 180
5x + 140 - 140 = 180 - 140
5x = 40
5x/5 = 40/5
x = 8
Write the measure 29° 6'6" as a decimal to the nearest thousandth.
a. 29.1020
C. 29.485
b. 27.5949
d. 27.682°
Please select the best answer from the choices provided
Answer:
A. 29.1020
Step-by-step explanation:
Rewrite it:
29°6'6"
29° + 6(1/60)° + 6(1/3600)°
Simplify:
29° + 0.1° + 0.002°
= 29.102
So, the correct answer is A, 29.1020
what's the correct choice please help
Year. 2006. 2007. 2011 . 2012. 2013
CPI. 201.6. 207.342. 224.939. 229.594 232.957
Suppose you bought a house in 2013 for $90,000. Use the table above to calculate the 2006 value adjusted for inflation. which is the correct answer below
$90,314
$91,398
$103,999
$77,886
Answer:
$77,886
Step-by-step explanation:
We solve this question by proportions, using a rule of three.
The table states that:
$201.6 in 2006 is worth $232.957 in 2013.
We want to find:
The value of $90,000 in 2013 in 2006:
$201.6 - $232.957
x - $90000
Applying cross multiplication
[tex]232957x = 201.6*90000[/tex]
[tex]x = \frac{201.6*90000}{232957}[/tex]
[tex]x = 77886[/tex]
$77,886 is the answer
Pls help extra points and mark brainlist
Answer:
80 + 30h
Step-by-step explanation:
(10 * 8) + (10 * 3h)
=80 + 30h
[tex]\Large\boxed{\tt Anwer:~80+30h}[/tex]
[tex]\tt Step-by-step~explanation:[/tex]
We need to distribute the 10 to 8 and 3h. In order to do this, we can multiply 10 by 8 and 10 by 3h.
[tex]\tt 10*8=80\\10*3h=30h[/tex]
Then, we add them together to get the answer.
[tex]\tt 80+30h[/tex]
Linda can drive 180 miles in 3 hours. On Tuesday, she drove for 7 hours at that rate. How many miles did she drive on Tuesday?
Answer: 420
Step-by-step explanation:
I took the test and got it right lol
Urgently need help please . Thanks
Answer:
224 feet^3
Step-by-step explanation:
Cube -> Volume = 4×7×7 = 196 feet^3
Prism -> Volume = 2×7×2 = 28 feet^3
196+28=224
please helppp
Simplify.
(-2)^-3
Answer:
-1/8 <----- FRACTION
Step-by-step explanation:
If the tax rate in a certain city is 8.75%, how much tax is added to the purchase of carpeting that costs $1,500?
Answer:$1312.5
Step-by-step explanation:
1500x1.875=2812.5
2812.5-1500=1312.5
Solve the equation
2x2 + 12x - 7 = 0
by completing the square.
Give your answers correct to 2 decimal places.
Show step by step please!!!!
Step-by-step explanation:
4+12x=7
12x=7-4
12x=3
X=3/12
X=0.25
I would like anyone to help me with this, please!
Answer:
the sencond and the last one
Answer:
125 • 125
Step-by-step explanation:
5⁶ = 5 × 5 × 5 × 5 × 5 × 5 = 15,625
125 • 125 = 15,625
They give the same result so both expressions are equivalent to each other.
Brady is conducting an experiment using a spinner with four different colors: red, orange, blue, and green. He spun the spinner 40 times and recorded the following data.
Based on the data in the table, if Brady spins the spinner 240 times, he predicts the spinner will land on red roughly A. 48, B. 24, C. 12, D. 36 times. He also predicts the spinner will land on green roughly A. 108, B. 72, C. 48, D. 36
more times than it will land on red.
Answer:
out of 240, the prediction of landing on Red would be 36
out of 240, the prediction of landing on Green would be 108
Step-by-step explanation:
out of 240, the prediction of landing on Red would be 36 because:
240 x 0.15 = 36
out of 240, the prediction of landing on Green would be 108 because:
240 x 0.45 = 108
Journal: Explain how you can check your answers on algebraic equations to know that you are right! Example: 2x = 12*
um if someone could help that would be great this one is not a big deal;-;
Simplify (3^z)^6 in exponent notation
Answer:
3^6z
Step-by-step explanation:
you multiply 6 and z since they are exponets and one is in a (
Answer:
3 to the power of 6z of 3^6z
Step-by-step explanation:
Pls help me I’ll brainlest I need a good grade on this
Answer:12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
find y and round to the nearest tenth. thank you
Answer and Step-by-step explanation:
31 degrees on the top would be equal to the angle in between x and 600ft, by the interior angles theorem.
That means we can solve for y using the trigonometric function of tangent.
[tex]tan(31) = \frac{y}{600}[/tex]
Multiply by 600 to both sides, then use a calculator to solve.
600(tan(31)) = x
x = 360.5163714
x ≈ 360.5 is the answer.
exact volume of this cylinder
I am taking this quiz but I'm pretty sure its....c
Answer:
Volume=πr2h=π·42·8≈402.12386
Step-by-step explanation:
Write the slope intercept form for an equation that has an equation of -2x + y = 7 and passes through (4,5). *
SLOPE INTERCEPT FORM: y = 7x −23
Skylas research Shows at eight empty cans make 1/ 4th pound of aluminum
she
wants to know how many cans it takes to make 5 pounds of aluminum how many kids are there per pound of aluminum
Answer:
160 cans for 5 pounds of aluminum
Step-by-step explanation:
If x= 9 in what is the surface area of the geometric shape formed by this net?
Answer:
D
Step-by-step explanation:
Surface Area = 2×(9×9 + 9×27 + 9×27) = 1134 inches2
how many odd _2-digit positive integers can be written using the numbers 2,4,5, and 8?
Answer:
4 different odd integers: 25, 45, 55, 85
Step-by-step explanation:
5 for $4.45 or 8 for $7.28
Answer:
5 for $4.45
Step-by-step explanation:
A- g(x)=|x+5|+5
B-g(x)=|x-5|+5
C-g(x)=|x|+5
D-g(x)=|x-5|
Answer:
if anything, I would say C. I can't see the image too clearly, but I can see what you typed out
Step-by-step explanation:
Hello - I'm trying to find the answer for $6,000 x 10% x (1/12) to find the monthly interest rate
Answer:600
Step-by-step explanation:
Make the number 6 x 1000
Take 10% of the 1000
Now put the 6 and the 100 together