Answers
Answer:
a)
Step-by-step explanation:
[tex]\dfrac{3p-1}{p^2-1}[/tex]
Factorize the denominator:
[tex]\implies \dfrac{3p-1}{(p+1)(p-1)}[/tex]
Therefore,
[tex]\implies \dfrac{3p-1}{(p+1)(p-1)}=\dfrac{A}{p+1}+\dfrac{B}{p-1}[/tex]
[tex]\implies 3p-1=A(p-1)}+B(p+1)[/tex]
When p = 1:
[tex]\implies 2=A(0)}+B(2)[/tex]
[tex]\implies B=1[/tex]
When p = -1:
[tex]\implies -4=A(-2)}+B(0)[/tex]
[tex]\implies A=2[/tex]
Therefore,
[tex]\implies \dfrac{3p-1}{(p+1)(p-1)}=\dfrac{2}{p+1}+\dfrac{1}{p-1}[/tex]
Related Questions
For f(x) = 2x-1 and g(x)= x+3, find f(g(x))
Answers
Answer:
C
Step-by-step explanation:
Plug in g(x) into the variable x of f(x), we get:
[tex](fog) = 2(x+3)-1 = 2x+6-1=2x+5[/tex]
Help please!! I know 4/9 is greater but what is the common denominator.
Answers
Answer: 36
Step-by-step explanation:
Just find the lowest common multiple of the denominators, which in this case are 4 and 9
You can just multiply 4 and 9 together so that gives you 36
Ashley painted 1/2 of her bathroom ceiling. Alex painted 1/4 of the ceiling in the school library. Who painted the larger fraction of their ceiling? Use a picture to demonstrate you answer.
Answers
Answer:
Ashley painted the larger fraction of their ceiling.
Step-by-step explanation:
I have no idea how large this ceiling is in this problem or what rate they are painting at; However, 1/2 is considered larger than 1/4.
Answer:
Ashley: 1/2 = 0.5
Alex: 1/4 = 0.25
0.25 < 0.5 Therefore Ashley painted more of their ceiling.
What is the missing reason?
Answers
Answer:
D
Step-by-step explanation:
you distribute the 2 to both numbers in the parentheses, and you get 2x+6=10 I HOPE THIS HELPS
pls show work
Thank youuu I’ll appreciate it <3
Answers
Answer:
x = 5
Step-by-step explanation:
15. When working with the expression 6(2+.03) if we multiply first before adding, that is an example
of using the
property?
Answers
Answer:
Distributive Property
Step-by-step explanation:
If you multiply first,
6(2 + .03)
6•2 + 6•.03
You must multiply the 6 times BOTH of the terms inside the parenthesis.
This is using the Distributive Property.
Mr. Morris is going to save money and replace his sailboat's mainsail himself. He must determine the area of the mainsail in order to buy the correct amount of material. Calculate the area of the parallelogram to determine how much material should be purchased. Be sure to explain how to decompose this shape into rectangles and triangles. Describe their dimensions and show your work.
Answers
Answer:
The area of the parallelogram is equal to 300 square feet.
Step-by-step explanation:
How many oranges does Heidi need to make one large orange
juice? Show your work.
Answers
Answer:
Heidi needs to make 9 oranges to make one large orange juice, give me brainliest answer:)
Given the triangles are similar. Solve for x.
1st
3.5 cm
8.4 cm
2nd
2x cm
5 cm
Answers
Answer:
6
Step-by-step explanation:
By CSSTP,
2x/8.4 = 5/3.5
2x=(8.4)(5/3.5)
2x=12
x=6
Which of the following are solutions to the equation below?
Check all that apply.
x2 + 6x + 9 = 20
O A. X = 215 + 3
B. X = -2,5 - 3
O c. x= -1/3 + 20
O D. x = -2.75 +3
O E. x = 215 - 3
h
O F. X = _3 + 20
Answers
Wah value of c makes the equation 15-8+c=11
Answers
[tex]\mathbb{FINAL\;ANSWER:}[/tex]
[tex]\huge\boxed{\sf{c=4}}[/tex]
[tex]\mathbb{SOLUTION:}[/tex]
Hi! Hope you are having a nice day!
Let's solve the equation for c.
First, subtract 15 and 8:
15-8+c=11
7+c=11
We can actually solve this equation using mental maths.
7+4=11, right? :)
Hope you could comprehend everything.
#CarryOnLearning
By rounding to one significant figure, estimate the answers to these questions:
a)
59 +25
b)
682
71
C)
91 x 18
58
Answers
find the product of 0.54x2.8
Answers
Answer:
The answer is 1.512
Step-by-step explanation:
0.54x2.8= 1.512
Select the graph of the solution set that would represent the following expression. 2 ( x + 1 ) > 3 x − 2
Answers
Hey there!
2(x + 1) > 3x - 2
DISTRIBUTE 2 WITHIN the PARENTHESES:
2(x) + 2(1) > 3x - 2
CONVERSION:
2x + 2 > 3x - 2
SUBTRACT 2 to BOTH SIDES:
-x + 2 - 2 > -2 - 2
SIMPLIFY IT!
NEW EQUATION:
-x > -4
CONVERSION 2:
-1x > -4
DIVIDE -1 to BOTH SIDES
-1x/-1 > -4/-1
SIMPLIFY IT!
x < 4
Therefore, your answer is: x < 4
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
We are given with an inequality and need to find it's solution set and need to represent it on number line too. Let's start !!!!
[tex]{:\implies \quad \sf 2(x+1)\> 3x-2}[/tex]
[tex]{:\implies \quad \sf 2x+2\> 3x-2}[/tex]
Subtracting 2x from both sides ;
[tex]{:\implies \quad \sf \cancel{2x}+2-\cancel{2x}\> 3x-2-2x}[/tex]
[tex]{:\implies \quad \sf 2\> x-2}[/tex]
Adding 2 to both sides :
[tex]{:\implies \quad \sf 2+2\> x-\cancel{2}+\cancel{2}}[/tex]
[tex]{:\implies \quad \sf 4\> x }[/tex]
[tex]{:\implies \quad \sf x\< 4}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{x\in (-\infty,4)}}}[/tex]
Refer to the attachment for representation
Please help
Use the distributive property to fill in the blanks below. 9x(7-2)=(_x7)-(_x2)
Answers
Answer:
9x(7-2)=(9x7)-(9x2)
Step-by-step explanation:
You're just multiplying 9 by the numbers inside the parenthesis... I hope this helps you :)
Evaluate the integral. (Use C for the constant of integration.)
2x^2+ 5x + 2/(x² + 1)2 dx
Answers
Answer:
[tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x - \frac{5}{2(x^2 + 1)} + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Method: U-Substitution
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx[/tex]
Step 2: Integrate Pt. 1
[Integrand] Rewrite [Factor]: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = \int {\frac{2(x^2 + 1) + 5x}{(x^2 + 1)^2}} \, dx[/tex]Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = \int {\frac{2(x^2 + 1)}{(x^2 + 1)^2}} \, dx + \int {\frac{5x}{(x^2 + 1)^2}} \, dx[/tex][Left Integral] Simplify: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = \int {\frac{2}{x^2 + 1}} \, dx + \int {\frac{5x}{(x^2 + 1)^2}} \, dx[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \int {\frac{1}{x^2 + 1}} \, dx + 5 \int {\frac{x}{(x^2 + 1)^2}} \, dx[/tex][Left Integral] Trigonometric Integration: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + 5 \int {\frac{x}{(x^2 + 1)^2}} \, dx[/tex]Step 3: Integrate Pt. 2
Identify variables for u-substitution for the remaining integral.
Set u: [tex]\displaystyle u = x^2 + 1[/tex][u] Differentiate [Derivative Properties and Rules]: [tex]\displaystyle du = 2x \ dx[/tex]Step 4: Integrate Pt. 3
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + \frac{5}{2} \int {\frac{2x}{(x^2 + 1)^2}} \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + \frac{5}{2} \int {\frac{1}{u^2}} \, du[/tex]Apply Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + \frac{5}{2} \bigg( \frac{-1}{u} \bigg) + C[/tex][u] Back-substitute: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + \frac{5}{2} \bigg( \frac{-1}{x^2 + 1} \bigg) + C[/tex]Simplify: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x - \frac{5}{2(x^2 + 1)} + C[/tex]∴ the integration of the given integral [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx[/tex] is equal to [tex]\displaystyle \bold{2 \arctan x - \frac{5}{2(x^2 + 1)} + C}[/tex].
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Learn more about integration: https://brainly.com/question/21023287
Learn more about calculus: https://brainly.com/question/23558817
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
What is the area of this polygon ?
Answers
Answer:
51
Step-by-step explanation:
ΔABC: AC = 5 - (-1) = 6
height = (-1) - (-4) = 3
Area = 6*3/2 = 9
Rectangle ACDE, length AE = 6 - (-1) = 7
height DE = 5 - (-1) = 6
Area = 7 * 6 = 42
So the area of this polygon = 9 + 42 = 51
Please please someone help me with this question!!! math question !!!!
Answers
In the graph we can identify two local minimums, with values y = 0, and at the x-values:
x = -3 and x = 3.
What is a local minimum?For a function f(x), we define a local minimum on an interval (a, b) if for a value c ∈ (a, b), then:
f(c) ≤ f(x) ∀ x ∈ (a, b)
a) On the image we can see two local minimums (the two lowest points on the graph). The values of the minimums are both 0.
b) The values of x where we have the minimums are:
x = -3 and x = 3.
If you want to learn more about minimums, you can read:
https://brainly.com/question/2118500
A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 7 marbles, each of diameter 3 inches. The vase is filled with water up to a height of 12 inches. Which of the following could be used to calculate the volume of water in the vase?
π(12in)2(3in) − 7(four over threeπ(1.5in)3)
π(3in)2(12in) − 7(four over threeπ(1.5in)3)
π(12in)2(3in) − 1.5(four over threeπ(7in)3)
π(3in)2(12in) − 1.5(four over threeπ(7in)3)
Answers
Answer:
Step-by-step explanation:
Vase:
h = 12 in
r = diameter/2 = 6/2 = 3 in
Volume of vase = πr²h
= π(3)²*12
Marbles:
r = 3/2 = 1.5 in
[tex]Volume \ of \ marbles = \dfrac{4}{3}\pi r^{3}\\\\\\Volume \ of \ 7 marbles=7*\dfrac{4}{3}\pi (1.5)^{3}[/tex]
Volume of water = Volume of vase - volume of 7 marbles
[tex]= \pi (3)^{2}*12 - 7*\dfrac{4}{3}\pi (1.5)^{3}[/tex]
Answer:
second choice
Step-by-step explanation:
the volume of water in the vase
= volume of the vase up to the height 12 inches - volume of 7 marbles
= π(6/2)²(12) - 7(4/3)π(3/2)³
so answer is the second choice
Jose has 3/5 kilogram of prepped mints and 2/3 kilogram of candy canes. How many kilograms of candy does he have?
Answers
Answer:
1 4/15
Step-by-step explanation:
Fractions are added using a common denominator. When the denominators have no common factors, the least common denominator is their product.
[tex]\dfrac{3}{5}+\dfrac{2}{3}\\\\=\dfrac{3}{5}\cdot\dfrac{3}{3}+\dfrac{2}{3}\cdot\dfrac{5}{5}\\\\=\dfrac{9+10}{15}=\dfrac{19}{15}=\boxed{1\dfrac{4}{15}}[/tex]
Jose had 1 4/15 kilograms of candy.
Who Logarithmic equation is equivalent to the exponential equation below? e^4c=5
A. Log 5= 4x
B. In 5= 4x
C. Log 4x= 5
D. In 4x= 5
Answers
Step-by-step explanation:
option a 5 = 4x
please mark me as brainlist pleaseAnswer:
ln 5 = 4x
Step-by-step explanation:
four properties of a trapezoid
Answers
Opposite sides of a trapezoid (isosceles) are of the same length.
Angles next to each other sum up to 180°
The median is parallel to both the bases.
Median's length is the average of both the bases i.e. (a +b)/2. You’re welcome!
Answer:
The bases are parallel to each other.
Angles next to each other sum up to 180°
The lower base angles are congruent.
The upper base angles are congruent.
Step-by-step explanation:
Seeta is organising a concert to raise money for a school and for a hospital.
A total of 1/20 of the money received from selling tickets will be spent on hiring a hall.
The rest of the money received from selling tickets will be given to the school and to the
hospital in the ratio 2 : 3.
Seeta expects to sell 1000 tickets at £23.50 each.
Work out the amount of money that Seeta expects to give to the school and to the
hospital.
You must show all your working.
Answers
Step-by-step explanation:
MATH QUESTION SCREEN SHOT DOWN BELOW
Answers
f(x)=(x-1)²-2
min point is (1,-2)
the answer is first picture
How can 10% of 45 be used to determine 30% of 45?
Enter your answers in the boxes to correctly complete the sta
10% of 45 is
so 30% of 45 is
Answers
Answer: 10% of 45 is 4.5
So 30% of 45 is 13.5
Step-by-step explanation:
Consider the work sample and statements below. Select ALL that apply.
Answers
Answer:
A, B, D, F
Step-by-step explanation:
The work of solving the standard-form equation that is the difference of squares is properly shown except for Line 4. Statement [F] correctly describes the proper solution, which results in the solution set shown in Statement [B].
The first step was necessary to put the equation into standard form (Statement [D]). That form is the difference of squares (Statement [A]).
The statements that correctly describe the work are A, B, D, F.
which number comes next 10 7 11 12 9 13 14 ___
Answers
Answer:
11
Step-by-step explanation:
the pattern is
-3 +4 +1 -3 +4 +1
What is the volume of the
rectangular prism?
Answers
Answer:
We are already given the length of the prism, so now we need to find the height and width.
4 units across is the width, and 2 units up is the height
In order to find the volume of a rectangular prism we must multiply the length, width, and height.
In this case, 4 is our width, 2 is our height, and 7 is obviously our length.
Now let's multiply;
4 x 2 x 7 = 56 cubic centimeters
to make this easier to multiply we could also do
(4 x 2) x 7 or 4 x (2 x 7)
In what quadrant is the point (5,4)?
Answers
Step-by-step explanation:
1st quadrant
hope it helps you
Jesse has five meters of twine and needs to cut it into lengths that are each 1/4 of a meter long. How many lengths will he have? Express this problem in a number sentence that uses division.
Answers
Answer:
20
Step-by-step explanation:
use the keep, change, flip method to solve fraction division