A bicycle costs $175.
Salvadore has $55 and
plans to save $22 each
month. Describe the
numbers of months he
needs to save to
buy the bicycle.

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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To find the area of a parallelogram, you need to multiply the base by the height. In this case, the given dimensions are 60ft (base) and 67ft (height), and you need to subtract 52ft from the height.

New height = 67ft - 52ft = 15ft

Area of the parallelogram = Base * Height = 60ft * 15ft = 900 square feet.

Therefore, the area of the parallelogram is 900 square feet.

~~~Harsha~~~

The value of the angle x is 110 degrees

A transversal is described as a line that passes two lines of distinct points

Also, we need to know that pair of angles on a straight line sums up to 180 degrees.

Supplementary angles are described as angles that sum up to 180 degrees.

Corresponding angles are also equal, then, we have that;

70 + x = 180

collect the like terms, we get;

x = 180 - 70

subtract the values, we have;

x = 110 degrees

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we have to do alot for this

so first we gotta change 12.3 into a mixed fraction

n = 5 so 5 ÷ 12.3

Answer:A

Step-by-step explanation:

To find the rate of decay, we need to use the formula A(t) = P(0.82)^t, where A(t) is the amount after t years, P is the initial amount, and 0.82 is the decay factor.

The decay factor is equal to 1 minus the decay rate, so we can solve for the decay rate as follows:

0.82 = 1 - r

r = 1 - 0.82

r = 0.18

Therefore, the rate of decay is 18%, which corresponds to answer choice A.

Answer:

A

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

-3+7=4

The expression representing the perimeter of the polygon is given as follows:

7mn³/3 + 4m² + 3mn².

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

Hence the perimeter for the polygon in this problem is given as follows:

mn³(1/3 + 2) + m²(1 + 3) + mn²(1 + 2) = 7mn³/3 + 4m² + 3mn².

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The missing side in the similar figure below is 42.

We are given a diagrammatic expression of two triangles and we are asked to find the missing side in a similar triangle. To be able to solve this question, we need to understand what are triangles and the possible types of triangles.

A triangle is a plane figure that has three sides and three angles. The major types of triangles include:

The example of the triangle given is a right-angle triangle and can be solved by using the Pythagoras theorem.

The Pythagoras theorem states that the hypotenuse squared is equal to the sum of the opposite squared and the adjacent squared.

hyp² = opp² + adj²

48² = x² + 24²

2304 = x² + 576

x² = 2304 - 576

x² = 1728

x = √1728

x = 41.57

x ≅ 42

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135 as a product of its prime factors is written as  3 × 3 x 3 x 5

The prime factors are those prime digits that can divide a particular digit evenly and without leaving any remainder. To put it differently, these are the main digits that, when multiplied with one another, result in the initial number.

In mathematics and number theory, prime factors hold significant value as they enhance comprehension of number properties and interconnections. In addition, they are utilized in a range of mathematical calculations and algorithms.

From the information given, we have the value as;

135

The prime factors are  3 × 3 x 3 x 5

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Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

144ft^3

Step-by-step explanation:

To start, we have your formula: \(V=\frac{1}{2} (bh) (l)\)
b = base length of the triangle.
h = height of the triangle.
l = length of the prism

Fill in for each of those values:
\(V = \frac{1}{2} (6x6)(8)\)

\(V=\frac{1}{2} (36)(8)\)

\(V=(18)(8)\)

\(V=144\)

Your answer, because it is a 3D shape, should be cubed, so:
\(V=144ft^{3}\)

There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

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Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

To determine the average speed at which Sphenathi and the other matriculants must travel to reach Uptington by 09:45, we need to calculate the time available for the journey and the distance between the two locations.

The time available is from 07:25 to 09:45, which is a total of 2 hours and 20 minutes. We need to convert this time to hours by dividing by 60:

2 hours + 20 minutes / 60 = 2.33 hours

Now, let's calculate the distance between Bloemfontein and Uptington. Suppose the distance is 'd' kilometers.

We can use the formula for average speed: average speed = distance / time

In this case, the average speed should be such that the distance divided by the time is equal to the average speed.

d / 2.33 = average speed

Now, let's assume that Sphenathi and the other matriculants must travel a distance of 250 kilometers to reach Uptington. We'll substitute this value into the equation:

250 / 2.33 = average speed

To find the average speed to the nearest km/h, we'll calculate the result:

average speed ≈ 107.3 km/h

Therefore, Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

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Answer:

27.7% if I am correct, but I am confident I am

Answer:

x=8

Step-by-step explanation:

∠B=∠A

Base Angle Thm/ Def. of Iso.

72=9x

x=8

Here is your solution for the problem.

Thanks

Answer:

The z-score for the statistics test grade is of 1.11.

The z-score for the calculus test grade is 7.3.

Due to the higher z-score, the student performed better on the calculus test relative to the other students in each class

Step-by-step explanation:

Z-score:

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

The grade with the higher z-score is better relative to the other students in each class.

Statistics:

Mean of 79 and standard deviation of 4.5, so \(\mu = 79, \sigma = 4.5\)

Student got 84, so \(X = 84\)

The z-score is:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{84 - 79}{4.5}\)

\(Z = 1.11\)

The z-score for the statistics test grade is of 1.11.

Calculus:

Mean of 69, standard deviation of 3.7, so \(\mu = 69, \sigma = 3.7\)

Student got 96, so \(X = 96\)

The z-score is:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{96 - 69}{3.7}\)

\(Z = 7.3\)

The z-score for the calculus test grade is 7.3.

On which test did the student perform better relative to the other students in each class?

Due to the higher z-score, the student performed better on the calculus test relative to the other students in each class

Answer:

\(x=8, y=3\)

Step-by-step explanation:

Recall that if a matrix multiplication of two matrices is defined, then the number of columns of the first matrix is equivalent to the number of rows of the second matrix.

Since matrix M has (11-x) columns and matrix N has y rows, and MN is defined, so it follows:

\(y=11-x----(1)\)

Since matrix N has (y+5) columns and matrix M has x rows, and NM is defined, so it follows:

\(y+5=x----(2)\)

Substitute (1) into (2):

\(11-x+5=x\\2x=16\\\therefore x=8--(3)\)

Substitute (3) into (1):

\(y=11-8=3\)

Answer:

m = 5

Step-by-step explanation:

.........................

Answer:

B. 17°

Step-by-step explanation:

7x + 28° + 33° = 180°{ being linear pair }

7x = 180° - 33° - 28°

7x = 119°

x = 17°

Hope it will help :)✔

Answer:

1.  direct=hot, indirect=cool

2. wind systems

3. differences in air pressure

first diagram: density increases, pressure increases, tempature decreases

second diagram: temp. increases, density decreases, pressure decreases

Step-by-step explanation:

hope this helps

Answer:

x2 - 9x +20

Step-by-step explanation:

Of course, a businesswoman who is extremely wealthy. Martha has a lot of money thanks to her writing numerous best-selling books, publishing a magazine (shoutout to all the kids from the 1990s whose moms read Martha Stewart Living), appearing on various TV shows, and having her own brand of goods, which includes a CBD line.

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The domain and the range of its inverse function, h^-1( x) are x < 4 and y < 5

The domain and the range of the function are:

x < 5 and y < 4

When the function is inverted, the domain becomes the range and vice versa.

This means that the domain and the range of its inverse function, h^-1( x) are x < 4 and y < 5

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Harry has  90 mosquitoes on his uniform after the loop de loop.

An integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations

To find the number of mosquitoes that splat on Harry's uniform during the loop de loop, we need to integrate the mosquito density function M(x,y,z) over the curve given by the parametrization r(t):

\(\int _C\:M\left(x,y,z\right)\:ds\:=\:\int _{t_1}^{t_2}\:M\left(r\left(t\right)\right)\:||r'\left(t\right)||\:dt\:\)

where C is the curve defined by r(t), ||r'(t)|| is the magnitude of the tangent vector to the curve, and ds is the arc length element.

We can compute the tangent vector to the curve as:

\(r'\left(t\right)\:=\: < 7,\:3cos\left(t\right),\:-3sin\left(t\right) >\)

The magnitude of the tangent vector is:

\(||r'\left(t\right)||\:=\:\sqrt{7^2\:+\:3^2cos^2\left(t\right)\:+\:3^2sin^2\left(t\right)}\:=\:\sqrt{67}\)

Substituting these expressions into the integral, we get:

\(\int _C\:M\left(x,y,z\right)\:ds\:=\:\int _0^{5\pi }\:\frac{12+3cos\left(t\right)}{\pi \sqrt{58}}\sqrt{67}\:dt\:\)

\(\int _C\:M\left(x,y,z\right)\:ds\:\approx \:89.62\)

Hence, Harry has  90 mosquitoes on his uniform after the loop de loop.

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f(x) = -x^2 +1

g(x) = 2 / (x+1)

Find (f+g) (0)

We can find f(0) + g(0)

f(0) = -0^2 +1 = 1

g(0) = 2/(0+1) = 2/1 = 2

f(0) + g(0) = 1+2 = 3

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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Answer:

Step-by-step explanation:

y = mx + b

mx = slope

b = intercept

1. Simplify the equation

4y = -3x - 12

2. Divide both sides by 4

y = -3/4 x - 3

3. Make a graph

First start at the y-intercept, (0, -3)*

Then, use the pattern -3/4

It is called rise over run.

But, when the slope is negative you have to go down instead of up. So you have to go down 3 and 4 to the right.

Continue that pattern until you get your result.

But when you have to go to the upper part of the graph go up 3 and over 4 to the left.

Continue this pattern.

This also applies to other graphs.

* = remember a y-intercept always has a 0 as the x - coordinate.

Hope this helped,

Kavitha

Answer:

It's the first answer.

Step-by-step explanation:

As demonstrated through the image, the slope increases. Thus making it a positive slope.