Answers
Answer:
-2x(5x²-6)
Step-by-step explanation:
hope this helps you
Answer:
First, express the fraction in partial fractions
Write it out as an identity:
\(\dfrac{2x-10}{x(x+1)(x-1)} \equiv \dfrac{A}{x}+\dfrac{B}{(x+1)}+\dfrac{C}{(x-1)}\)
Add the partial fractions:
\(\dfrac{2x-10}{x(x+1)(x-1)} \equiv \dfrac{A(x+1)(x-1)+Bx(x-1)+Cx(x+1)}{x(x+1)(x-1)}\)
Cancel the denominators from both sides of the original identity, so the numerators are equal:
\(2x-10 \equiv A(x+1)(x-1)+Bx(x-1)+Cx(x+1)\)
Now solve for A, B and C by substitution.
Substitute values of x which make one of the expressions equal zero (to eliminate all but one of A, B and C):
\(\begin{aligned}x=0 \implies 2(0)-10 & =A(0+1)(0-1)+B(0)(0-1)+C(0)(0+1)\\-10 & = -A\\\implies A & = 10\end{aligned}\)
\(\begin{aligned}x=1 \implies 2(1)-10 & =A(1+1)(1-1)+B(1)(1-1)+C(1)(1+1)\\-8 & = 2C\\\implies C & = -4\end{aligned}\)
\(\begin{aligned}x=-1 \implies 2(-1)-10 & =A(-1+1)(-1-1)+B(-1)(-1-1)+C(-1)(-1+1)\\-12 & = 2B\\\implies B & = -6\end{aligned}\)
Replace the found values of A, B and C in the original identity:
\(\implies \dfrac{2x-10}{x(x+1)(x-1)} \equiv \dfrac{10}{x}-\dfrac{6}{(x+1)}-\dfrac{4}{(x-1)}\)
Now integrate:
\(\begin{aligned}\displaystyle \int \dfrac{2x-10}{x(x+1)(x-1)}\:dx & =\int \dfrac{10}{x}-\dfrac{6}{(x+1)}-\dfrac{4}{(x-1)}\:\:dx\\\\& =10\int \dfrac{1}{x}\:dx\:\:-6 \int\dfrac{1}{(x+1)}\:dx\:\:-4 \int \dfrac{1}{(x-1)}\:dx\\\\& = 10 \ln |x|-6 \ln |x+1|-4 \ln |x-1|+C\end{aligned}\)
Related Questions
can you help me with this problem
Answers
Answer:
Step-by-step explanation:
You are helping your little brother pick up his toy blocks. The blocks are cubes and each side measures 5 in. The toy chest that you have to put them in measures 12 1/3 in by 10 and 3/4 in by 12in. Your brother has 10 blocks to put away, will they all fit in the toy chest?
Since you have 10 blocks to put away, what is the volume of all 10 blocks
Answer:
85
Step-by-step explanation:
check the lower answer
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
The percentage of vehicles that are returned with less than 30000 miles are given as follows:
b) 2.5%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is obtained by the equation presented as follows:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
\(\mu = 36400, \sigma = 3200\)
The proportion is the p-value of Z when X = 30000, hence:
Z = (30000 - 36400)/3200
Z = -2.
Z = -2 has a p-value of 0.028 -> percentage rounded to 2.5%.
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you are helping your sister plan her sweet 16. the venue you want to host it at charges $75 for every 3 guest as well as a rental deposit of $200 write an equation to determine the total party cost
Answers
Answer:
y = 25x + 200
Step-by-step explanation:
y = the total cost of the party
x = the number of guests
75/3 = 25
25 is the cost per guest.
Helping in the name of Jesus.
-5p+11 > 43-9p
sorry. but I need help on all of these questions please help.
Answers
Answer:
Step-by-step explanation:
Hey, again!
So, first, get the 43 isolated. So, add -9p on both sides.
This will give you 4p+11>43
Next, subtract 11 on both sides.
You will get 4p>32
Next, divide 4 on both sides
This will give you p>8.
Hope this helps!!!
For the following vectors, (a) find the dot product v•w ; (b) find the angle between v and w , (c) state whether the vectors are parallel, octagonal, or neither. V=-3i-4j, w=6i+8j
A- v•w
B-the angle between v and w is theta ^•?
C- the vectors v and w are?
Answers
B) The angle between vectors v and w can be found using the formula: cos(theta) = (v • w) / (||v|| ||w||), where ||v|| and ||w|| are the magnitudes of vectors v and w respectively.
First, we need to find ||v|| and ||w||:
||v|| = sqrt((-3)^2 + (-4)^2) = 5
||w|| = sqrt((6)^2 + (8)^2) = 10
Now, we can substitute in the values to get:
cos(theta) = (-50) / (5 * 10) = -1
theta = arccos(-1) = pi radians or 180 degrees.
Therefore, the angle between vectors v and w is 180 degrees.
C) Two vectors are parallel if their directions are the same, which can be determined by comparing their unit vectors.
The unit vector of v is:
v_hat = v / ||v|| = (-3/5)i + (-4/5)j
The unit vector of w is:
w_hat = w / ||w|| = (6/10)i + (8/10)j = (3/5)i + (4/5)j
We can see that the unit vectors are in opposite directions, which means that the vectors are anti-parallel or opposite. Therefore, the vectors v and w are neither parallel nor orthogonal.
write an equation in slope-intercept form that meets the criteria described slope =3,through (5,2)
Answers
Answer:
y = 3x - 13
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs.
Match each power of i to its equivalent expression.
Tiles
1
Pairs
81
¡52
*99
166
-1
i
111
-i
Answers
The equivalent expressions based on the information will be:
i^81 = I
i^52 = 1
i^99 = -i
i^66 = -1
How to calculate the expressionAn expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
For i^81, 81 will be 4 × 20 + 1
i^81 = i
i^52 will be:
52 = 13 × 4
i^52 = 1
i^99 will be:
99 = 24 × 4 + 3
i^99 = -i
i^66 will be;
66 = 16 × 4 + 3
i^66 = -1
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Solve 25=q+14.
Q=?
Can someone help please?
Answers
Answer:
11
Step-by-step explanation:
just flip the problem around 14+q=25
then do 25-14
Thats your Q
Alice is selling bracelets to earn money for a new bike. On Monday she sold 30 bracelets. On Friday she sold 54 bracelets. Calculate the percent change in bracelets sold.
Answers
Answer:
24 she sold 24 more so it would be 24 percent more
Lines that appear to be tangent are tangent. O is the center of each circle.
What is the value of x? Show all work to receive full credit.
Answers
Note that in the prompt above, the value of x is given as: 16°
To answer the issue, we will first name all of the points supplied to us on the isosceles triangle, then identify O, and last discover the value of x. See the attached image.
What is an isosceles triangle?As a result, an isosceles triangle has two equal sides and two equal angles. The term is derived from the Greek words iso (same) and skelos (skull) (leg). An equilateral triangle has all of its sides equal, whereas a scalene triangle has none of its sides equal.
In ΔAOB
OA = OB = R, the radius of the circle O,
therefore, the ΔAOB is an isosceles triangle, with OA, OB as the congruent sides and AB as the base of the triangle.
Thus, ∠OAB = ∠OBA = 53°
Sum of all the angles of a triangle = 180°
∠O + ∠AOB + ∠OBA = 180°
We know ∠AOB = ∠OBA, therefore,
∠O + 2(∠AOB) = 180°
∠O + 2(53°) = 180°
∠O = 180 - 106
∠O = 74°
In ΔOBC,
BC is the tangent to the circle O, therefore,
∠OBC = 90°
Sum of all the angles of a triangle = 180°
∠O + ∠OBC + ∠OCB = 180°
74° + 90° + ∠OCB = 180°
∠OCB = 180° - 74° - 90°
∠OCB = 16°
Hence, the value of x is 16°.
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1 The figure shows a rectangle inscribed in a circle.
Determine the area of the shaded region. Use 3.14
for and round to the nearest tenth.
Answers
Answer:
46.8 cm²
Step-by-step explanation:
The diagonal of the square has length \(\sqrt{6^2+10^2}=2\sqrt{34}\). Therefore, the radius of the circle is \(\sqrt{34}\), meaning the area is \(\pi(\sqrt{34})^2 \approx 34(3.14)=106.76\).
The area of the rectangle is \((6)(10)=60\) cm².
Subtracting the areas, the answer is 46.76 cm², which is 46.8 cm² to the nearest tenth.
Please helpp!!!!!!!!!!!!!!! I will mark brainlist
Answers
If you into 0 for x you get 4. It is not straight line or constant rate of change because slope is x^2 which is a parabola. If you input -3 you don’t get -5 you get 13. And lastly, y is a function of x means y changes according to the x input, which is the case here.
Answer:
statements 2 & 5 are true
Step-by-step explanation:
1. False because is a quadratic nonlinear equation
2. True, 4 is the ordered to the origin
3. False, the rate not being linear is not constant
4. False, because when the input is -3 the output is 13
\(y = (-3)^{2} +4=9+4=13\)
5. True, y depends on x
Hope this helps
what number is greater than 6 but less than 7? 20 40 60 or 80
Answers
6.5 or 65 :ppppppp I get those goosebumps every time
just number 3, i dont rly need an explanation
Answers
Answer:
L=(-2,4)
Step-by-step explanation:
I just had this homework over the weekend. And there are the rest of the answers too
Plz help this is khan and I don’t remember how to do this
Answers
it could be a I’m not sure
Explanation
A manufacturer of floor wax has developed two new brands, A and B, which she wishes to subject to homeowners' evaluation to determine which of the two is superior. Both waxes, A and B, are applied to floor surfaces in each of 15 homes. Assume that there is actually no difference in the quality of the brands.
Required:
What is the probability that ten or more homeowners would state a preference for either brand A or brand B?
Answers
Answer:
Probability that ten or more homeowners would state a preference for either brand A or brand B = 0.302
Step-by-step explanation:
Given - A manufacturer of floor wax has developed two new brands, A and B, which she wishes to subject to homeowners’ evaluation to determine which of the two is superior. Both waxes, A and B, are applied to floor surfaces in each of 15 homes. Assume that there is actually no difference in the quality of the brands.
To find - What is the probability that ten or more homeowners would state a preference for either brand A or brand B?
Proof -
Given that,
There is actually no difference in the quality of the brands.
⇒P(A) = \(\frac{1}{2}\) = 0.5
P(B) = \(\frac{1}{2}\) = 0.5
Now,
We know that,
Binomial distribution is equals to
B(n, x) = ⁿCₓ (p)ˣ (1 - p)ⁿ⁻ˣ
Now,
P(X(A) ≥ 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)
= ¹⁵C₁₀ (0.5)¹⁰ (0.5)⁵ + ¹⁵C₁₁ (0.5)¹¹ (0.5)⁴ + ¹⁵C₁₂ (0.5)¹² (0.5)³ + ¹⁵C₁₃ (0.5)¹³ (0.5)² + ¹⁵C₁₄ (0.5)¹⁴ (0.5)¹ + ¹⁵C₁₅ (0.5)¹⁵ (0.5)⁰
= 0.092 + 0.042 + 0.014 + 0.003 + 0.0005 + 0.00005
= 0.151
⇒P(X(A) ≥ 10) = 0.151
As given Quality of both brands are same ,
So, the probability of both the brands are equal
⇒P(X(B) ≥ 10) = 0.151
Now,
Probability that ten or more homeowners would state a preference for either brand A or brand B = P(X(A) ≥ 10) + P(X(A) ≥ 10)
= 0.151 + 0.151
= 0.302
∴ we get
Probability that ten or more homeowners would state a preference for either brand A or brand B = 0.302
The record high January temperature in Austin, Texas, is 90°F. The record low
January temperature is -2°F. Find the difference between the high and low
temperatures.
Answers
Answer:
92 degrees
Step-by-step explanation:
-2 is 2 degrees from 0. the high is 90. Add them together for 92 :)
Answer:
92 degrees
Step-by-step explanation:
90 - (-2) = 92
please help asap (answer only if you know the question)
Answers
The Equation of bisector 5x-7y+3=0 which is a straight line.
What is bisector?A straight line that divides an angle of a triangle in equal value.
What is perpendicular bisector?The line that lies perpendicular to a side and goes through the midpoint of its length.
Given, coordinate H (-7,2), K (3, -4) and L (5,4)
we plot a triangle HKL with this point.
midpoint of side HK is found by (-7+3)/2 and (2-4)/2
hence, midpoint of HK is (-2,-1) is denoted by P
the perpendicular bisector of side HK means a straight line from the midpoint of HK to the point L(5,4). The bisector line PL divide the angle HLK.
so, the equation of bisector is y-y₁ = (y₂-y₁)/(x₂-x₁)[x-x₁] because the bisector line passes through the point P(-2,-1) and L(5,4)
y-(-1) = [4-(-1)]/[5-(-2)]× [x-(-2)]
y+1 = 5/7×(x+2)
7y+7= 5x+10
5x-7y+3=0
hence, the equation of bisector is 5x-7y+3=0
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One plumber charges a flat fee of $50 to come to the house and then
$20 per hour. If h represents the number of hours that the plumber spent
fixing the problem and C represents the total charge, which of the following
equations shows how to determine the total fee charged?
C=50+20h
C=(50+20)h
C=h+50+20
C=20+50h
Answers
Answer:
C=50+20h
Step-by-step explanation:
Since 20 is going to be added every hour, that is the h value. Since 50 is the the initial payment, that is the other value
The equation for total fees charged, if One plumber charges a flat fee of $50, The per hour fees = $20, is C = 50 + 20h, so option A is correct.
What is equation?A formula known as an equation uses the equals sign to denote the equality of two expressions. Equation: A declaration that two expressions with variables or integers are equal.
Given:
One plumber charges a flat fee of $50,
The per hour fees = $20,
Write the equation for the total charged fees as shown below,
Total charge = One-time fees + per-hour fees × number of hours
Assume C represents the total charge, h represents the number of hours, then,
C = 50 + 20 × h
C = 50 + 20h
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What is the solution of p - 12 > -18
p> -30
p<-6
p> -6
p < -30
Answers
Answer:
p > -6
Step-by-step explanation:
1) Add 12 to both sides.
p > -18 + 12
2) Simplify -18 + 12 to -6.
p > -6
In a class of 25 students, there were 13 math majors, 10 were computer science majors, and 6 were dual majors in both.
How many were in math only?
How many were not majoring in computer science?
How many were not math or computer science?
Answers
Answer:
How many were in math only?7
How many were not majoring in computer science?9
How many were not math or computer science?2
Step-by-step explanation:
Total students 25
-math major 13
-Science major 10
_______________
2 not majoring in math or CS majors
math major 13 -6 dual majors = 7 major in math only
math major 7+ not math or CS 2 = 9 not majoring in CS
Write the fraction as a mixed number 10/20
Answers
Find to value of a if you knew the perimeter was 250 inches long
Answers
Answer:
To find the value of "a" when you know the perimeter of a shape, you need to know the specific shape you're referring to. Please provide more information about the shape in question, such as whether it's a rectangle, triangle, or another geometric figure. Additionally, if you have any specific measurements or relationships between the sides of the shape, please provide them as well.
what is the equivalent fraction of 13%
Answers
help help help help help
Answers
The equation of the line in slope-point form is:
y - 7 = -4/5(x + 6)
How to write an equation a line?The equation of a line in slope-point form is given by:
y - y₁ = m(x - x₁)
where:
(x₁, y₁) represents the coordinates of a point on the line.
m represents the slope of the line.
m = (y₂ - y₁)/(x₂ - x₁)
(x₁, y₁) represents the coordinates of the 1st point on the line
where (x₂, y₂) represents the coordinates of the 2nd point on the line
We have
(x₁, y₁) = (-6, 7)
(x₂, y₂) = (4, -1)
m = (y₂ - y₁)/(x₂ - x₁)
m = (-1 - 7) / (4 - (-6))
m = -8/10
m = -4/5
Using y - y₁ = m(x - x₁):
y - 7 = -4/5(x - (-6))
y - 7 = -4/5(x + 6)
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Idk anything about math please I need help
Answers
Answer:
21 boys
Step-by-step explanation:
2:3=14:x you cross multiply this to find the amount of boys
2x=42
x=21
There are 21 boys in the class.
Basically, solve what you have there with cross-multiplication.
2x = 14 x 3
2x = 42
Then divide both sides by 2. (edited it bc didn't say what you actually had to do)
2x ÷ 2 = 42 ÷ 2
x = 21.
There are 21 boys in the class.
4.) BLACK
Calculate the volume
of 500 g of salt
Density of Salt is 2.16
Answers
Answer: 2 170 kilograms [kg] of Salt fit into 1 cubic meter. 135.46867 pounds [lbs] of Salt fit into 1 cubic foot. Salt weighs 2.17 gram per cubic centimeter or 2 170 kilogram per cubic meter, i.e. density of salt is equal to 2 170 kg/m³; at 20°C (68°F or 293.15K) at standard atmospheric pressure . In Imperial or US customary measurement system, the density is equal to 135.469 pound per cubic foot [lb/ft³], or 1.254 ounce per cubic inch [oz/inch³] .
Step-by-step explanation:
Please help with my geometry homework.
Answers
Answer:
first option
Step-by-step explanation:
you multiply each coordinate per 4
For questions 3-4, use the graph of the polynomial function to find the factorization of the polynomial. Assume there is no constant term. 3
Answers
3. The factored polynomial is p(x) = (x - 1)(x - 5)
4. The factored polynomial is p(x) = (x + 3)²
What is a polynomial?A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.
3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.
This implies that its factors are (x - 1) and (x - 5)
So, the factored polynomial is p(x) = (x - 1)(x - 5)
4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots
This implies that its factors are (x - (-3)) = (x + 3) twice
So, the factored polynomial is p(x) = (x + 3)²
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There is one way that 100005 can be written as a sum of two prime numbers. Which two prime numbers add up to 100005?
Answers
The two prime numbers that add up to 100005, based on the properties of prime numbers would be 2 and 100003.
How to find the prime numbers ?To find the two prime numbers, the relevant relationship would be the Goldbach's Conjecture. This posits that every even number greater than 2 can be expressed as the sum of two prime numbers.
So, to write an odd number as the sum of two prime numbers, one of the prime numbers has to be 2 because we know that 2 is the only even prime number.
The other number would therefore be:
= 100005 - 2
= 100003
100003 is a prime number so the two prime numbers are 2 and 100003.
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