Answer:
[tex]\frac{1}{x-1}[/tex] - [tex]\frac{1}{x+2}[/tex] - [tex]\frac{3}{(x+2)^2}[/tex]
Step-by-step explanation:
Expressing as a partial fraction
[tex]\frac{9}{(x-1)(x+2)^2}[/tex] = [tex]\frac{A}{(x-1)}[/tex] + [tex]\frac{B}{(x+2)}[/tex] + [tex]\frac{C}{(x+2)^2}[/tex] ( A, B, C are numerical values to be found )
Multiply both sides by (x - 1)(x + 2)²
9 = A(x + 2)² + B(x - 1)(x + 2) + C(x - 1)
Choose value for x that are zeros of the factors and substitute into right side
x = - 2 : 9 = - 3C ⇒ C = - 3
x = 1 : 9 = 9A ⇒ A = 1
x = 0 : 9 = 4A - 2B - C , that is
9 = 4 - 2B + 3 = - 2B + 7 ( subtract 7 from both sides )
2 = - 2B ⇒ B = - 1, then
A = 1, B = - 1, C = - 3
Thus
[tex]\frac{9}{(x-1)(x+2)^2}[/tex] = [tex]\frac{1}{x-1}[/tex] - [tex]\frac{1}{x+2}[/tex] - [tex]\frac{3}{(x+2)^2}[/tex]
Isabel wrote 10 letters to friends each month for x months in a row. Write an expression to show how many total
letters Isabel wrote.
Answer:
10x
X = Months
10 = letters each month
5. Theresa decides to donate money to cancer
research each year. Her brother, Tony, also decides
to contribute. Together, they donate $1,000 per
year to cancer research. If Tony is able to donate
1 1/2 times the amount that Theresa is able to
donate, what is the amount in dollars that Tony
will donate after 5 years, assuming the amount
and proportions remain the same cach year?
A. $2.000
B. $2.100
C. $2.450
D. $3.000
E. $3.600
Answer:
3000
Step-by-step explanation:
Tony will donates $3000 after 5 years.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Donated amount= $1000
Tony is able to donate 3/2 times the amount that Theresa donates.
let Theresa donates x dollar each year
So, x+ 3/2x = 1000
5x/2 = 1000
5x = 2000
x= 400
Thus, Tony donate = 3/2 x 400 = $600
Hence, After 5 years Tony will donate= 600 x 5= $3000
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Need help with this, thank you
Answer:
65
Step-by-step explanation:
40 + 75 = 115
180 - 115 = 65
Answer:
x=65
Explaination
x+75+40=180
or,x+ 115=180
or, x=180-115
or x= 65
A 28 -inch board is to be cut into three pieces so that the second piece is twice as long as the first piece and the third piece is four times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.
What is the length of the first piece?
Answer:
4
Step-by-step explanation:
4 (First piece)
4*2=8(Second piece)
4*4=16
16+8+4=28
Which of the following expresses the sum of 54 and 30 as a product? * O 6 (54 + 30) O 6(9+5) O 9 (6+5) O 9 (54 + 30)
6(9+5)
Step-by-step explanation:
-3 + (-7)
Someone give me an explanation but use another example to show me
-3+-7....The answer is minus 10
para alumbrar un parque, se colocan luminarias a lo largo de una longitud de 100 metros, si la primera se coloca en el metro 1, la siguiente en el metro 4, la que sigue en el metro 7, y así sucecibamente. en las siguientes posiciones se colocará una luminaria exepto en el metro: a)13 b)19 c) 21 d)28 ayudaaaaaaa
Answer:
c)21
Step-by-step explanation:
"To light a park, luminaries are placed along a length of 100 meters, if the first is placed in meter 1, the next in meter 4, the next in meter 7, and so on. in the following positions a luminary will be placed except in the subway:
a)13 b)19 c) 21 d)28? "
-------------
Luminaries position:
1, 4, 7, ...It makes an AP with the first term of 1 and common difference of 3
The formula for this AP is:
aₙ = 1 + 3(n-1) = 1 + 3n - 3 = 3n - 2From the given options, only one is not in the same format:
c) 21because
21 = 3n - 2 ⇒ 3n = 23 and n= 23/3 is not an integerAnswer is: c) 13
distance, midpoint, and angle measurement a walk in the park
Answer:
Step-by-step explanation:
The distance between to things is how far apart those two things are.
The Distance Formula is
d = √[(x1 - x2)² + (y1 - y2)²]
Midpoint: This is the point that bisects a segment in the middle.
The Midpoint formula is:
M = [(x1 + x2)/2, (y1 + y2)/2]
Angle is a point where two straight lines meet.
27. 8 minus the product of 9 and r
find the slope of the line containing the points (3,-2) and (-1,6)
Answer: the answer is -2
Step-by-step explanation: use slope formula
What are the domain and range of this function ? Help plz
Answer:
Hey there!
The domain, or possible x values are (-4, -1, 2, 9).
The range, or possible y values are (-3, 0, 6)
Let me know if this helps :)
Answer:
Domain: { -4, -1, 2,9}
Range: {-3, 0, 6}
Step-by-step explanation:
Domain is the x-values and range are the y-values. You can write it out in an x, y table to be able to see it better. Like shown below,
x y
-1 6
2 0
9 -3
-4 6
If you need further explanation let me know, but I hope this helps!
Have a great day!
What is the equation for the kind of reflection?
Answer:
A vertical reflection is given by the equation y=−f(x) y = − f ( x ) and results in the curve being “reflected” across the x-axis. A horizontal reflection is given by the equation y=f(−x) y = f ( − x ) and results in the curve being “reflected” across the y-axis.
I need help with these two problems please
Problem 2
Plot point L anywhere that isn't on segment JK. Draw a line through point L. I find it helps to make the lines parallel.
Next, use a compass to measure the width of segment JK. Keeping this same width, transfer the nonpencil end of the compass to point L. Draw an arc that crosses the line through L.
Mark this intersection point M. Lastly, use a pen or marker to form segment LM and erase everything else of that line.
======================================================
Problem 3
The ideas of the previous problem will be used here. We copied segment JK to form congruent segment LM. So JK = LM.
The same steps will be used to form segment GN where GN = EF. In other words, segment GN is a perfect copy of segment EF.
If you repeat these steps again, you'll get another segment of the same length. This segment goes from point N to point H. So NH = GN = EF
Then we can say,
GH = GN + NH
GH = EF + EF
GH = 2*EF
PLEASE HELP! this is due today!
Answer:
For question 9 = 54
Step-by-step explanation:
54 + 67 = 121
67 - 54 = 13
Answer:1.)k+2x 2.)54 3.) i think is n+n=145
Step-by-step explanation:
I don’t exactly know what the answer is. I would appreciate it if someone could help :)
Answer:
d
Step-by-step explanation:
its inverse so it will be the oppisite of 2/5
Give the equation of a line that goes through the point ( − 24 , 2 ) and is perpendicular to the line 8 x + 3 y = − 6 . Give your answer in slope intercept form
Answer:
[tex]y=\frac{3}{8}x+11[/tex]
Step-by-step explanation:
To find a line that is perpendicular to 8x + 3y = -6 and goes through (-24, 2), lets first find what the line's slope would be.
We can find this by finding the slope of 8x + 3y = -6 and taking the negative reciprocal of it.
We can find the slope of that line by putting it in slope-intercept form:
8x + 3y = -6
Subtract 8x from both sides.
3y = -6 - 8x
Divide both sides by 3.
[tex]y=-\frac{6}{3}-\frac{8}{3}x[/tex]
[tex]y=-\frac{8}{3}x-2[/tex]
So the slope of that line would be -8/3.
The negative reciprocal of -8/3 would be 3/8.
Now we know that the new line would have to pass through the point (-24, 2). We can use this point and write the equation in point-slope form:
[tex]y-2=\frac{3}{8}(x+24)[/tex]
Now lets change this into slope-intercept form. Add 2 to both sides.
[tex]y=\frac{3}{8}(x+24) +2[/tex]
Distribute the 3/8.
[tex]y=\frac{3}{8}x+9+2[/tex]
Simplify.
[tex]y=\frac{3}{8}x+11[/tex]
And now we have our equation in slope-intercept form.
I hope you find this helpful.
73% of what is 7.1?
a. 5.2
b. 518.3
C. 9.7
d. 38

Answer:
Answer is 9.7
I used calculator
what steps do i take to solve this?
Answer:
B; The second answer
Step-by-step explanation:
The question is asking about the associative property of addition. This involves the rearranging of the parenthesis. If you were to solve the given equation, and solve the the answer, then you will get the same answer. In this property, it says that you will get the same result if you were to move/switch the parenthesis from the values; This means that order doesn't matter.
Valentino wants to estimate the product (5.2)(9.9). Which expression shows each factor rounded to the nearest whole
number?
(5)(9)
(6)(10)
(6)(9)
(5)(10)
Answer:(5)(10)
Step-by-step explanation:
Answer:
(5)(10)
Step-by-step explanation:
Please help! will give brainliest!!
Answer:
c
Step-by-step explanation:
tHE ANSWER IS C
Given a circle with endpoints of a diameter at –10 – 1i and 6 + 11i, answer the questions below. 1. The center of the circle is at ---+ --- i.
The center of the circle is at -2 + 5i.
What are Complex Number?Complex Numbers. Complex numbers are those that are expressed as a+ib, where a and b are actual numbers and I is a fictitious number called a "iota."
Complex numbers are numbers that consist of two parts — a real number and an imaginary number.
Given:
Diameter = –10 – 1 i = (- 10, - 1)
6 + 11 i = (6, 11)
Given that we are aware that these are the diameter's endpoints, it follows that the circle's center is the place that lies midway between the endpoints.
Then,
x = (-10 + 6) / 2
= - 4 / 2
= -2
y = (- 1 + 11) / 2
= 10 / 2
= 5
Hence, the center is located at (- 2, 5).
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Please help me
Which of the following is not equivalent to
3/4
A. 0.75
B. 3:4
С. 75%
D. 4:3
Answer:
C: 75%
D. 0.75
Step-by-step explanation:
Both numbers are the same and they both are equivalent to 3/4.
PLEASE HELP WILL MARK AS BRAINLIEST THE QUESTION IS BELOW
Answer:
Step-by-step explanation:
First you have to split the shape into 2. I split the box so that the little one's length is Z and width is x. Find the area of both boxes:
Box 1:
Z x X = ZX
Box 2:
Y x (Z + X) = Y(Z + X)
So the overall area of the box is:
ZX + Y(Z + X)
I'm not quite sure how to explain this without pictures to show you but i hope this helps. Let me know if you have any questions
A store sells the basic model of a phone for $60 and the upgraded model for $200. It costs the store $10 to buy each
basic model and $50 to buy each upgraded model from the phone company, On Tuesday, the store has $1,800 in
sales for these two models, and it paid the phone company $400 to buy these phones. How many upgraded models
did the store sell on Tuesday?
O 6 upgraded phones
10 upgraded phones
15 upgraded phones
42 upgraded phones
Answer: A, 6
Step-by-step explanation:
Edg
Decide whether 0 is a solution of the inequality: a.) 2x – 1 9 c.) x – 3 > 1
Step-by-step explanation:
How to check a solution: Just as you can check the solution to an equation, you can check a solution to an inequality. First, you check the end point by substituting it in the related equation. Then you check to see if the inequality is correct by substituting any other solution to see if it is one of the solutions.
How to tell if its true or false: An inequality is a statement that shows the relationship between two (or more) expressions with one of the following five signs: <, ≤, >, ≥, ≠. Like an equation, an inequality can be true or false. 34 - 12 > 5 + 2 is a true statement. 1 + 3 < 6 - 2 is a false statement.
Find the distance between (11, 10) and (1,3). Round your answer to
the nearest tenth.
Answer:
12.2Step-by-step explanation:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(1-11)^2+(3-10)^2}=\sqrt{(-10)^2+(-7)^2}=\sqrt{149}\\\\d=12.2065...\approx12.2[/tex]
What is the value of 4s2+10 if s=9?
Answer:
82
Step-by-step explanation:
4x9=36x2=72+10=82
Answer:
82
Step-by-step explanation:
Plug in the 9 for s
4(9)2+10
Remember PEMDAS
Parentheses first, then multiply the 2
72+10=82
What is the sign of 39 11/13 + (-41 1/13) ?
Answer:
negative
best of luck!
The sign of the expression is Negative, the correct option is B.
What is an Expression?An expression is a mathematical statement which consists of variables, constants and mathematical operators.
The expression is
39 11/13 + (-41 1/13)
[tex]=\rm 39\dfrac{11}{13} -41\dfrac{1}{13}\\\\=\dfrac{518}{13} - \dfrac{534}{13}\\\\=\dfrac{ 518 - 534} {13}\\\\=\dfrac{ -16}{13}\\\\=- 1 \dfrac{3}{13}[/tex]
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Evaluate the function f(x)=3x+12 with x+6.
f(x+6) = 6x + 60
f(x+6) = 2x - 30
f(x+6) = 3x + 30
f(x+6) = 30
Answer:
f(x+6)= 3x + 30
Step-by-step explanation:
Whenever you have to evaluate a function with a certain value, replace the variable x with a certain value. In this case, substitute x with the value of (x+6). You get the equation f(x+6)= 3(x+6) + 12, which simplifies into f(x+6)= 3x + 18 +12, which further simplifies into f(x+6)= 3x + 30.
5,432 to nearest tens
5430. Since 2 is smaller than 5, we will not round 32 to 40.