Integration by partial fraction but im unsure how to proceed

The greatest common factor of the given polynomial is 2, so we can factor it out to get: 2(x³ - 5)

We have to factories 2x³ - 10

So, 2x³ = 2 . x . x . x

10 = 2 . 5

Then, 2x³ - 10

= 2. x . x . x - 2.  5

= 2( x . x .x - 5)

= 2 (x³ - 5)

The greatest common factor of the given polynomial is 2, so we can factor it out to get: 2(x³ - 5)

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The fountain will occupy a fraction of 50/173 of the Total area of the courtyard.

Let A be the area of the courtyard and F be the area of the fountain.

We know that the area of the stone-covered part of the courtyard is 246 square feet.

So, the area of the whole courtyard is A = 246 + F square feet.

The fraction of the area of the courtyard occupied by the fountain is given by:

F / A = F / (246 + F)

We can simplify this expression by multiplying the numerator and denominator by the reciprocal of the denominator:

F / A = F / (246 + F) * (1 / (246 + F))

F / A = F / (246 * (246 + F))

F / A = 1 / (246 / F + 1)

We don't know F yet, but we can use the fact that the fountain is rectangular to set up an equation relating the length and width of the fountain:

F = L * W

where L is the length of the fountain and W is the width of the fountain.

We also know that the perimeter of the fountain is 50 feet:

2L + 2W = 50

Simplifying this equation, we get:

L + W = 25

Solving for one variable in terms of the other, we get:

L = 25 - W

Substituting this expression for L into the equation for F, we get:

F = (25 - W) * W

Expanding this expression, we get:

F = 25W - W^2

We also know that the cost of the fountain is $600, which includes installation. So, we can set up another equation relating the cost of the fountain to its dimensions:

1.5LW = 600

Substituting 25 - W for L, we get:

1.5(25 - W)W = 600

Expanding and simplifying this equation, we get:

W^2 - 25W + 400 = 0

Solving this quadratic equation, we get:

W = 20 or W = 5

We reject the solution W = 5 because it implies a negative length for the fountain, which is not physically possible. Therefore, the width of the fountain is W = 20 feet and its length is L = 25 - W = 5 feet.

The area of the fountain is therefore:

F = L * W = 5 * 20 = 100 square feet

The fraction of the area of the courtyard occupied by the fountain is

F / A = 100 / (246 + 100) = 100 / 346 = 50 / 173

So, the fountain will occupy a fraction of 50/173 of the total area of the courtyard.

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The average gas mileage of the cars traded is 15.8 miles per gallon round to the nearest.

Let's assume that the average gas mileage of the cars traded in is x miles per gallon. According to the problem, the average increase in gas mileage for the new car purchased versus the car traded in was 61%. This means that the new car gets 61% more miles per gallon than the car traded in. We can express this relationship mathematically as:

25.4 = x + 0.61x

Simplifying the right-hand side of the equation, we get:

25.4 = 1.61x15.78

Dividing both sides by 1.61, we get:

x = 15.78

Therefore, the average gas mileage of the cars traded in was approximately 15.8 miles per gallon, rounded to the nearest tenth.

To understand this result, we can interpret it as follows: for the first week of the "Cash for Clunkers" program, the average gas mileage of the new cars purchased was 25.4 miles per gallon, which is 61% higher than the average gas mileage of the cars traded in. This suggests that the program was successful in incentivizing people to trade in their old, less fuel-efficient cars for new, more fuel-efficient cars.

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the x coordinates are matched as follows

For y = √110/11  x = ± 1/√(11)

For y = 7/11  x = ± 6√(2) /11

For y = 5/11   x = ±4√(6) /11

For y = 9/11:   x = ±2√(10) /11

Using the equation of the unit circle

x² + y² = 1

For y = √110 / 11

x² + (√110/11)² = 1

x² + 110/121 = 1

x² = 1 - 110/121

x² = 11/121

x = ±√(11)/11

x = ± 1/√(11)

For y = 7/11

x² + (7/11)² = 1

x² + 49/121 = 1

x² = 1 - 49/121

x² = 72/121

x = ±√72/11

x = ± 6√(2) /11

For y = 5/11

x² + (5/11)² = 1

x² = 1 - 25/121

x² = 96/121

x = ±4√(6) /11

For y = 9/11

x² + (9/11)² = 1

x² = 1 - 81/121

x² = 40/121

x = ±√40/11

x = ±2√(10) /11

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The probability of drawing a red or green M&M is 29/74.

The probability of drawing an M&M that is not blue or green is 36/74.

the probability of drawing an M&M that is not brown is 69/74.

The probability of drawing a red or green M&M is the sum of their probabilities, since they are mutually exclusive events (meaning that an M&M can't be both red and green at the same time):

P(red or green) = P(red) + P(green) = 8/74 + 21/74 = 29/74

The probability of drawing an M&M that is not blue or green is the complement of the probability of drawing a blue or green M&M:

P(not blue or green) = 1 - P(blue or green) = 1 - (P(blue) + P(green)) = 1 - (17/74 + 21/74) = 36/74

The probability of drawing an M&M that is not brown is the complement of the probability of drawing a brown M&M:

P(not brown) = 1 - P(brown) = 1 - 5/74 = 69/74

To determine which is more likely, drawing a red M&M or drawing an orange M&M, we need to compare their probabilities:

P(red) = 8/74

P(orange) = 12/74

Since 12/74 is greater than 8/74, it is more likely to draw an orange M&M than a red M&M.

The color with the highest chance of being drawn is the one with the highest probability, which is green with a probability of 21/74.

The probability of drawing any M&M is 1, since there is a 100% chance of drawing an M&M when you draw from the bag.

Probability is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

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Answer:

Step-by-step explanation:

Pneumonoultramicroscopicsilicovolcanoconiosis

Answer: Supercalafragilisticexpialadocious

Step-by-step explanation:

Answer:

       0      1      2      3      4      5      6      7

       |      |      |      |      |      |      |      |

     2/3   1     2.7    3.4         7      |

                         |_____________|

                               |

                             3 3/4

The two answers that describe the unit rate at which Darrell walks are 1.5 seconds per meter and 1.5 meters per second

To find the unit rate at which Darrell walks, we need to determine how many meters he walks per second. We are given that he walks 90 meters in 60 seconds.
Step 1: Divide the total distance by the total time to find the unit rate.
Unit rate = (total distance) / (total time)
Step 2: Plug in the given values and calculate.
Unit rate = 90 meters / 60 seconds
Step 3: Simplify the fraction.
Unit rate = 1.5 meters per second
The two answers that describe the unit rate at which Darrell walks are:
1. 1.5 meters per second
2. 30 seconds per meter (the reciprocal of the unit rate)

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Answer: $28.00 (C)

Step-by-step explanation:

The total is 28 (based on the equation).

No matter how many blueberries or raspberries Amit buys, the toal must equal 28 dollars.

Georgia will need [tex]\(\boxed{333}\)[/tex] square inches of cardboard to construct the square pyramid.

To calculate the amount of cardboard needed to construct the square pyramid, we need to find the surface area of each individual face and then add them together.

Given that the base of the pyramid is a square with side length [tex]\(b = 9\) inches[/tex] and the height of the triangular sides is [tex]\(a = 14\) inches[/tex], we can proceed as follows:

The surface area of the square base is [tex]\(b^2 = 9^2 = 81\)[/tex] square inches.

Each triangular face has a base equal to the side length of the square base, [tex]\(b = 9\) inches[/tex], and a height of [tex]\(a = 14\) inches[/tex]. Therefore, the surface area of each triangular face is [tex]\(\frac{1}{2} \times b \times a = \frac{1}{2} \times 9 \times 14 = 63\)[/tex] square inches.

Since there are four triangular faces in a square pyramid, the total surface area of the triangular faces is [tex]\(4 \times 63 = 252\)[/tex] square inches.

Adding the surface area of the square base and the total surface area of the triangular faces, we get [tex]\(81 + 252 = 333\)[/tex] square inches.

Therefore, Georgia will need [tex]\(\boxed{333}\)[/tex] square inches of cardboard to construct the square pyramid.

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There is a bias because the question suggests a particular answer. Option B

A systematic inaccuracy or departure from the true value that causes inaccurate conclusions to be drawn about a population or topic under study is referred to as bias in research. Any step of the research process, including study design, data collecting, analysis, and interpretation, is susceptible to bias.

It may be caused by a number of variables, including the sample strategy, participant selection, measuring methods, the researcher's own ideas and preconceptions, or the influence of outside variables like funding sources or political motivations.

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if we will divide 137 with 100 and then multiply it with 680 you will gett your answer

the answer is 931.6

Answer:

931.6

Step-by-step explanation:

We need to change the percent to decimal form.

137%  = 1.37

Multiply this by 680.

1.37 * 680

931.6

Answer

I think it's acute scalene triangle

Step-by-step explanation:

All the angles are less than 90 degrees, which is acute.

Step-by-step explanation:

[tex]f'(x)=[(3x^2-4x+1)^4]'=4(3x^2-4x+1)^3*(3x^2-4x+1)'=4(3x^2-4x+1)^3*(6x-4)=8(3x^2-4x+1)^3(3x-2);[/tex]

The required derivative of f(x) = (3x² - 4x + 1)⁴ is f'(x) = 4(3x² - 4x + 1)³ * (6x - 4)

We can use the chain rule and power rule of differentiation to find the derivative of f(x).

Let u = 3x² - 4x + 1, then we have:

f(x) = u⁴

Using the chain rule, we get:

f'(x) = 4u³ * u'

To find u', we can differentiate u with respect to x using the power rule:

u' = d/dx (3x² - 4x + 1) = 6x - 4

Substituting u' and u into f'(x), we get:

f'(x) = 4(3x² - 4x + 1)³ * (6x - 4)

Therefore, the derivative of f(x) = (3x² - 4x + 1)⁴ is f'(x) = 4(3x² - 4x + 1)³ * (6x - 4)

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Answer: We can use both formulas to calculate the interest on an investment of $3500 at 2.75% for 3 years.

Using the formula A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate as a decimal, n is the number of times interest is compounded per year, and t is the time in years, we have:

A = 3500(1+0.0275/1)^(1*3) ≈ $3843.84

Therefore, the interest earned is:

Interest = A - P = $3843.84 - $3500 = $343.84

Using the formula A = Pe^(rt), where A is the final amount, P is the principal amount, r is the annual interest rate as a decimal, t is the time in years, and e is the mathematical constant approximately equal to 2.71828, we have:

A = 3500e^(0.0275*3) ≈ $3843.84

Therefore, the interest earned is:

Interest = A - P = $3843.84 - $3500 = $343.84

The interest earned is $343.84 in both cases.

Answer: 5(x - 12) = 3x

Step-by-step explanation:

       We can cross-multiply to answer this question.

[tex]\frac{5}{x} =\frac{3}{x-12}[/tex]

5 * (x - 12) = 3 * x

5(x - 12) = 3x

Answer:

b) 5(x - 12) = 3x

Step-by-step explanation:

Given expression,

→ 5/x = 3/(x - 12)

Now we have to,

→ Find the equivalent expression.

Let's find the required answer,

→ 5/x = 3/(x - 12)

Cross multiplying both sides:

→ 5(x - 12) = 3(x)

→ 5(x - 12) = 3x

Applying Distributive property:

→ 5(x) - 5(12) = 3x

→ 5x - 60 = 3x

Solving for the value of x:

→ 5x - 3x = 60

→ 2x = 60

→ x = 60/2

→ [ x = 30 ]

Hence, the value of x is 30.

Answer:

The domain of a function is the set of all possible input values for the function. In this case, the function is a graph, so the domain is the set of all possible x-values that correspond to points on the graph.

To find the domain, we need to consider all of the points on the graph. We can see that the graph extends infinitely to the left and right, so all real numbers are possible input values. Therefore, the domain of the function is all real numbers, or R.

Here is a more formal definition of the domain of a function:

The domain of a function is the set of all real numbers x for which the function f(x) is defined.

In other words, the domain is the set of all input values for which the function produces a valid output value.

Step-by-step explanation:

Answer:

-----------------------

Tangent is perpendicular to radius, hence ΔAOB is right triangle.

Given that OA = AB, and we know OA = OC as two radius. Therefore OAC is equilateral triangle, hence all its angles are same:

It means ΔOAB is a specific 30x60x90 right triangle.

The ratio of its sides is:

It gives us that:

The area of the pentagon using the composite area formula is 37 in².

A pentagon is one of the many types of polygon having five sides and five angles.

To calculate the area of the pentagon, we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1

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The quotient evaluated in 7 is equal to the quotient of the two functions evaluated in 7, thus:

(f/g)(7) = f(7)/g(7) = 3

Here we know the functions:

f(x) = 2x + 1

g(x) = x - 2

The quotient evaluated in 7 is equal to the quotient between the two functions evaluated in x = 7, then here we will get:

f(7) = 2*7 + 1 = 14 + 1 = 15

g(7) = 7 - 2 = 5

Then the quotient gives:

(f/g)(7) = f(7)/g(7) = 15/5 = 3

That is the value.

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The solutions of the given equations are x = 0 and x = -36.

We have,

To solve these equations:

9x - 7 = -7

We can add 7 to both sides to isolate the variable:

9x - 7 + 7 = -7 + 7

Simplifying the left-hand side and the right-hand side, we get:

9x = 0

Finally, dividing both sides by 9, we get:

x = 0

Next, to solve:

-1 = 5 + x/6

We can begin by subtracting 5 from both sides:

-1 - 5 = 5 + x/6 - 5

Simplifying the left-hand side and the right-hand side, we get:

-6 = x/6

Finally, multiplying both sides by 6, we get:

-36 = x

Thus,

The solutions of the given equations are x = 0 and x = -36.

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The complete question.

9x - 7 = -7

-1 = 5  + x/6

Answer:

Squaring positive and negative numbers always yields a positive number; the product of two negative numbers is always a positve number.  Using √4 as an example, we know the positive answer is 2 since 2 * 2 = 4.  However, the negative answer is -2 since -2 * -2 = 4 also.

[tex]\cos(40^o )=\cfrac{\stackrel{adjacent}{32}}{\underset{hypotenuse}{x}} \implies x=\cfrac{32}{\cos(40^o)}\implies x\approx 41.77[/tex]

Make sure your calculator is in Degree mode.

Answer:b

Step-by-step explanation:b

Answer:

i'm pretty sure it is "the graph forms a parabola"

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to know the amounts invested in stocks, bonds, and CDs when the total investment is $145000, $10000 more is invested in bonds than CDs, earnings are $6977.50, and rates of return are 6.7% for stocks, 2.5% for bonds, and 5.75% for CDs.

We can write three equations in 3 unknowns for this problem. Let s, b, c represent amounts invested in stocks, bonds, and CDs, respectively. Then the problem statement tells us the relations are ...

These equations can be solved using any of several methods. The second equation offers a nice relation between b and c, so substitution for one or the other of those will reduce the equations to two equations in two unknowns.

We prefer a calculator solution using an augmented matrix of the coefficients. That is shown in the attachment. It tells us the investment amounts are ...

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Additional comment

Using b = c +10000, the two remaining equations are ...

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