the sum of
44+45+46+47+...+131

Answer: 9x^2y

the gcf of -63 , 9 and 90 is 9

And the gcf of the variables is x^2 and y

So, 9x^2y

By answering the question using the information provided, we can conclude that in order to arrive at the general solution, we must take into account the scenario in which [tex]y-1\neq 0 , y \neq 1[/tex], by constructing equations.

Two equations are said to be equivalent when their bases and solutions line up. To create an equivalent equation, the same quantity, symbol, or expression must be added to or removed from both of the equation's two sides.

We can also create an analogous equation by multiplying or dividing both sides of an equation by a nonzero integer.

Solving differntial calculus

[tex](1+x)y'=( x+2) (y-1)[/tex]

We will first employ varying separation. The variables y and x will be placed on the opposite sides of the equation, and both sides will be integrated.

[tex](1+x)y'/(y-1) = (x+2)dx[/tex]

We will integrate both sides using the substitution[tex]u= y-1,\frac{du}{dy} =y'[/tex]

∫[tex](x+2)dx[/tex] =∫[tex](1+x)\frac{du}{u}[/tex]

㏑l[tex]u[/tex]l +[tex]x[/tex]㏑l[tex]u[/tex]l= [tex]\frac{1}{2} x^{2}+2x+c[/tex]

Substituting [tex]u= y-1[/tex]

㏑l[tex]y-1[/tex]l+ [tex]x[/tex]㏑l[tex]y-1[/tex]l= [tex]\frac{1}{2x^{2} } +2x+c[/tex]

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The complete question is: Find the general solution to the differential equation (1+x)y' = (x + 2)(y − 1).

Answer:

x = -6

Step-by-step explanation:

2-3(x+4) = 8

2 - 3x - 12 = 8

-3x - 10 = 8

-3x = 18

x = -6

Answer:

x = -6

Step-by-step explanation:

2 - 3 (x + 4) = 8

2 - 3x - 12 = 8

- 10 - 3x = 8

- 3x = 8 + 10

- 3x = 18

x = -18/3

x = -6

___________

hope this helps!

Answer:

Step-by-step explanation:

To calculate the amount of money Nathaniel needs to deposit today to fund this gift for his descendants, we can use the present value formula for a perpetuity:

Present Value = Annual Payment / Discount Rate

In this case, the annual payment is R380 000 and the discount rate (expected rate of return) is 6.45% in decimals, or 0.0645 as a fraction. So we can plug these values into the formula:

Present Value = R380 000 / 0.0645

This gives us a present value of approximately R5,899,225.68. Therefore, Nathaniel would need to deposit R5,899,225.68 today into the trust fund to provide R380 000 a year forever for his descendants, assuming a 6.45% expected rate of return.

Frequency Distribution Table is down below.

Class Count Cumulative Frequency Table

160 - 180 3 3

181 - 201 5 8

202 - 222 14 22

223 - 243 14 36

244 - 264 10 46

265 - 285 2 48

286 - 306 1 49

307 - 327 1 50

Total 50     100

Here its peak is in between 202 to 243 frequency range. There are three extreme values that are 270, 295 and 325 pounds weight.

Median lies in the interval 223-243 and mean also lies in that interval. Maximum values lies in between 200 - 225 interval.

The distribution is left skewed.

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The intercepts of the line are:

x-intercept: (3, 0)

y-intercept: (0, 1)

What are the intercepts?

To find the x-intercept, we need to find the point where the line intersects the x-axis. This occurs when the y-coordinate of the point is zero. From the given information, we know that the line passes through the point (3, 0), so this point must be the x-intercept.

Therefore, the x-intercept is (3, 0).

To find the y-intercept, we need to find the point where the line intersects the y-axis. This occurs when the x-coordinate of the point is zero. We can find the equation of the line using the two given points (0, y) and (3, 0):

Slope of the line = (y2 - y1) / (x2 - x1)

= (0 - y) / (3 - 0)

= -y / 3

Using the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can write:

y - 0 = (-y/3)(x - 3)

Simplifying this equation, we get:

y = (-y/3)x + 1

Multiplying both sides by 3, we get:

3y = -yx + 3

Adding yx to both sides, we get:

yx + 3y = 3

This is the equation of the line in standard form. To find the y-intercept, we set x = 0:

0 + 3y = 3

Solving for y, we get:

y = 1

Therefore, the y-intercept is (0, 1).

Hence, the intercepts of the line are:

x-intercept: (3, 0)

y-intercept: (0, 1)

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The domain is all real numbers, The range is all real numbers and There is one y-intercept is true from the given option in context of all linear functions. option B. The domain is all real numbers, C. The range is all real numbers , and E. There is one y-intercept is right choice.

All linear functions have a domain that includes all real numbers, a range that includes all real numbers, and exactly

one y-intercept.

The rate of change of a linear function is non-zero only if the function is not constant (i.e. its slope is not zero).

However, there are linear functions that have a slope of zero, such as the function f(x) = 2, which is a horizontal line.

This means that statement A is not true of all linear functions.

Furthermore, there are linear functions that have no x-intercept (if the line is parallel to the x-axis) or that have more

than one x-intercept (if the line intersects the x-axis more than once).

Therefore, statement D is also not true of all linear functions.

The correct answers to this question are B. The domain is all real numbers, C. The range is all real numbers , and E. There is one y-intercept.

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Step-by-step explanation:

given quadratic equation is

simplification,

by using,

[tex]y^\frac{1}{2} -6y^\frac{1}{4} +8=0

\\ y^\frac{1}{2} -6y^\frac{1}{4} = - 8 \\

[/tex]

[tex]square[/tex]

[tex] \\ {(y^\frac{1}{2} -6y^\frac{1}{4})}^{2} = {(- 8)}^{2}[/tex]

[tex]y + 36 {y}^{ \frac{1}{2}} \: [/tex]

Answer:

Option (C)

-0.46 brother

Answer:

Option (C)

-0.46

Step-by-step explanation:

Answer:

[tex]k = - 3[/tex]

Step-by-step explanation:

[tex]y = kx[/tex]

[tex]k \times ( - 1) = 3[/tex]

[tex] - k = 3[/tex]

[tex]k = - 3[/tex]

Answer:

[tex]k = -3[/tex]

Step-by-step explanation:

Step 1: Substitute

To solve this problem you are going to need to substitute the values of y and x into the problem y=kx.  Which would give you the problem of 3=-1k or 3 = -k to make things easier.

Step 2: Using properties of equality

In order to isolate the value of k you would need to divide both sides by -1 because division cancels out multiplication. You would get [tex]\frac{3}{-1} = \frac{-k}{-1}[/tex] or [tex]-3 = k[/tex]

Step 3: Check

In order to check this problem you would need to insert the values back into the original equation and solve. So that would be 3= -1*-3 which does equal 3. So the answer is correct

Fionna and Anuar each had 349 cards, bringing the total to 417. Fionna alone had 145 cards.

A mathematical concept known as the unitary approach entails calculating the value of a single unit in order to calculate the value of a given quantity. Finding the value of one unit and utilising that value to determine the value of a given quantity is an approach for solving problems. For instance, you can use the unitary technique to determine the price of 10 apples if you know that 5 apples cost $10. Now, divide $10 by 5, which equals $2, to determine the price of one apple. The cost of 10 apples is then determined by multiplying the price of one apple ($2) by 10, giving you a final cost of $20.

given

145 total cards with Fionna

349 total cards with Fionna and Aura

Card count with Anuar: 349 - 145

= 204

Rizza's number of cards equals 1/3 of 204.

= 204 / 3

= 68

Total number of cards: 68, 204, and 145

= 417

Fionna and Anuar each had 349 cards, bringing the total to 417. Fionna alone had 145 cards.

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Reflections, rotations, and translations are all transformations that change the position and/or orientation of a geometric figure.

In mathematics, reflection is a transformation that flips a figure over a line called the line of reflection. This line acts like a mirror, reflecting the original figure onto the opposite side of the line.

Reflections, rotations, and translations are all transformations that change the position and/or orientation of a geometric figure.

Reflections (also known as flips) change the orientation of a figure by flipping it across a line of reflection, which acts like a mirror.

Rotations change the orientation of a figure by rotating it around a fixed point. The figure stays the same shape and size, but its position and orientation in space changes.

Translations (also known as slides) change the position of a figure by sliding it along a straight line without changing its orientation or shape.

All of these transformations are important in geometry and other fields, such as physics and computer graphics, and can be used to describe the motion and properties of geometric objects.

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Answer:

0.167

Step-by-step explanation:

if you divide 30/180 it will get you a decimal of 0.166666667 but if you were to divide 180 by 30 you will get 6

technecaly your answer would be 0.166666667 but you only take the first number in the decimal which is 0.1 then take six 0.16 then add the 7 0.167

that should end up being your answer if i did the math right

Answer:

Step-by-step explanation:

5/12 * 6/15 =30/180

1/6=1/6

which is true, Right-hand side is equal to left-hand side

The measures οf the three angIes are x = 51.43 degrees, y = 92.85 degrees, and z = 118.85 degrees.

A Iinear equatiοn is a mathematicaI equatiοn that describes a straight Iine in a twο-dimensiοnaI pIane.

We can use the infοrmatiοn given in the prοbIem tο fοrm a system οf three equatiοns with three variabIes. Let x, y, and z represent the measures οf the first, secοnd, and third angIes, respectiveIy.

Frοm the first piece οf infοrmatiοn, we knοw that: x + y + z = 180

Frοm the secοnd piece οf infοrmatiοn, we knοw that: y + z = 5x

Frοm the third piece οf infοrmatiοn, we knοw that: z = y + 26

We can substitute the third equatiοn intο the secοnd equatiοn tο eIiminate z:

y + (y + 26) = 5x

2y + 26 = 5x

2y = 5x - 26

y = (5x - 26)/2

We can substitute this expressiοn fοr y intο the first equatiοn tο eIiminate y and z:

x + (5x - 26)/2 + (5x - 26)/2 + 26 = 180

2x + 5x - 26 + 26 = 360

7x = 360

x = 51.43

We can substitute this vaIue οf x back intο the expressiοn fοr y tο find y:

y = (5x - 26)/2

y = (5(51.43) - 26)/2

y = 92.85

FinaIIy, we can use the equatiοn z = y + 26 tο find z:

z = y + 26

z = 92.85 + 26

z = 118.85

Therefοre, the measures οf the three angIes are x = 51.43 degrees, y = 92.85 degrees, and z = 118.85 degrees.

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Answer: 41

Step-by-step explanation:

-26+z =1 5

       z= 15+26

       z= 41

Answer:

z = 41

Step-by-step explanation:

-26 + z = 15.                      | + 26
-26 + z + 26 = 15 + 26
z = 41

We can claim that after answering the above question, the As a result, angles the regular polygon has ten sides.

An angle is a shape in Euclidean geometry that is made up of two rays, known as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays may combine to generate an angle in the plane in which they are located. An angle is formed when two planes collide. They are known as dihedral angles. In plane geometry, an angle is a potential configuration of two rays or lines that share a termination. The English term "angle" derives from the Latin word "angulus," which means "horn." The vertex is the point at where the two rays, also known as the angle's sides, converge.

The interior angle of a regular polygon with n sides is calculated as follows:

(n-2) * 180° / n = interior angle

The internal angle of the polygon is presented to us as 144°. When we plug this into the formula, we get:

144° = (n - 2) * 180° / n

144° * n = (n - 2) * 180°

144° * n = 180° * n - 360°

144° * n + 360° = 180° * n

360° = 36° * n

n = 10

As a result, the regular polygon has ten sides.

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The true statement about the parallelogram is (c) Yes, because adjacent sides are congruent.

Given that

Figure ABCD is a parallelogram

Such that

Side lengths = 5 cm

This means that

The figure is a square

As a general rule

All squares can be classified as rhombus

This is because a rhombus is a quadrilateral with all four sides of equal length and square is a type of rhombus in which all four sides are equal in length

Hence, the true statement is (c)

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Answer:

Step-by-step explanation:

Let x be the original price of the television set.

The sale price is 28% off the original price, which means that the sale price is equal to 100% - 28% = 72% of the original price.

So we can write an equation based on this information:

0.72x = 435.60

Solving for x, we get:

x = 435.60 / 0.72

x ≈ $605

Therefore, the original price of the television set was approximately $605.

Answer: James' age now is 12 years old.

Answer: 5kg

Step-by-step explanation:

If Ms. Walker has 15 kilograms of clay that she wants to distribute evenly among 3 students, all you need to do is divide 15 by 3. Doing so, we get:

15 kg / 3 = 5 kg

Therefore, each student will receive 5 kilograms of clay.

The mass of clay that each student will get is 5kg.

Here, the given questions ask for a solution that deals with the concept of  the basic principle of division. hence implementing the principle we can see that,

The given total amount of clay by Ms. walker is 15 kilograms(kg).

Furthermore, this total amount of clay needs to be divided equally between the  3 students.

Then, let the mass of clay given to each student equally be denoted by M in  the equation to find out the solution can be written as

M = Total amount of clay ÷ Total number of students

Then,

M = 15 ÷ 3

M = 5 kg

Therefore, The mass of clay that each student will get is 5kg.

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The missing values that make this statement true are as

x² + 9x + 14,  x² - 3x - 10

x² - 2x - 15,   x² + 10x + 21

What is the quadratic equation?

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. The term "quadratic" comes from the Latin word "quadratus," which means "square."

First, let Xa, Xb, Xc, Xd = each factor

Xd = each factor which shows In the graph

Then, we can know that

Xa, Xb are the roots of x² + ___x + 14

Xb, Xd are the roots of x²= 3x - __

Xc, Xd are the roots of x² - __x - 15

Xa, Xc are the roots of x² + 10x + __

Xa * Xb = 14           Xd = 15/10 +Xa

Xb+ Xd = 3            14/Xa + 15/10 +Xa = 3

Xc* Xd = - 15          140 + 29Xa/Xa(10+Xa)

Xa + Xc = -10x        140 + 29Xa = 30Xₐ + 3Xₐ²

Xb = 14/Xa             3Xₐ² + Xₐ² - 140 = 0

14/Xa + Xd = 3       Xa1 = -7   Xa2 = 20/3

Xd = -15/-3             Xb1 = -2   Xb2 = 21/10

Xc = -10 -X1            Xc1 = -3    Xc2 = -30/3

Xc1 = -3     Xc2 = -30/3

Xd1 = 5         Xd2=9/10

There are two kinds of answers.

1) x² + 9x + 1x           Xa1 + Xb1 = -9

x² - 3x + 10           Xb1 * Xd1 = -10

x² - 2x - 15           Xc1 + Xd1 = 2

x² + 10x + 21           Xa1 * Xc1 = 21

2)

x² - (263/30)x + 14           Xa2 * Xb2 = 263/30

x² - 3x - (-189/100)           Xb2 * Xd2 = 189/100

x² - (413/30)x - 15           Xc2 + Xd2 = 413/30

x² + 10x + (1000/9)           Xa2 * Xc2 = 1000/9

Hence, the missing values that make this statement true are as

x² + 9x + 14,  x² - 3x - 10

x² - 2x - 15,   x² + 10x + 21

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Texas' location and climate led to the development of the aviation industry.

What is the significance of Texas in the development of the aviation industry?

The development of the aviation industry in Texas can be attributed to its favorable geographical location and climate. Texas is located in the southern part of the United States, making it a strategic location for air travel between the east and west coasts of the country. Additionally, its warm and dry climate provided ideal conditions for flight testing and training.

Reason what led to the development of the aviation industry :

Texas has a long history of aviation, with the Wright brothers conducting one of their earliest flight demonstrations in the state in 1910. The establishment of military bases during World War II and the subsequent development of aircraft training facilities in Texas further fueled the growth of the aviation industry in the state. Additionally, the placement of the Johnson Space Center in Houston helped to establish Texas as a hub for aerospace research and development. However, it is Texas' favorable location and climate that truly made it a prime location for the aviation industry. Its central location made it a strategic location for air travel and logistics, while its warm and dry climate provided ideal conditions for flight testing and training. Today, Texas remains one of the top states for aviation and aerospace industries, with major airports, aircraft manufacturers, and research institutions located throughout the state.

Therefore, option (d) is correct.

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Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

A value or combination of values that satisfy an equation, inequality, system of equations, or system of inequalities are known as solutions in mathematics. Take the equation x2 - 3x + 2 = 0, for instance. This equation has a solution in the form of an x value that makes the equation true. The quadratic formula allows us to determine that this equation has two solutions, x = 1 and x = 2. According to this, a solution for a system of equations is a set of values that simultaneously satisfy every equation in the system. Mathematical problem-solving, which has many applications in areas like engineering, physics, economics, and more, is a crucial component of the subject.

given

We must identify the point(s) at where the two lines intersect in order to obtain the solution(s) to the system of equations depicted by the graph. The graph demonstrates that the lines cross at the location (-3, 3).

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

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To determine the profit earned from selling 250 shares worth $4.50 each with a 7% fee charged by the stock broker, we need to calculate the total revenue earned and the total cost incurred.

Total revenue earned from selling 250 shares at $4.50 per share:

Revenue = 250 x $4.50 = $1,125

Total cost incurred for buying and selling the shares, including the 7% fee charged by the broker:

Cost = 2 x 250 x $4.50 x 0.07 = $157.50

Here, we are multiplying the number of shares (250) by the price per share ($4.50) to get the total value of the shares. Then we multiply this by 2, since we need to account for both the buying and selling transactions, and then multiply by the broker fee rate of 7% (0.07) to get the total cost incurred.

Therefore, the profit earned from the sale of 250 shares is:

Profit = Revenue - Cost

Profit = $1,125 - $157.50

Profit = $967.50

Hence, the profit earned from selling 250 shares worth $4.50 each with a 7% fee charged by the stock broker is $967.50.

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Answer:

The answer would be 14 miles!

Answer:

Let x be the cost of 1 kg of mushrooms and y be the cost of 1 kg of turnips.

From the given information, we can form two equations:

2x + 2.5y = 8.55 (Equation 1)

3x + 4y = 13.10 (Equation 2)

To solve for x and y, we can use the method of elimination. Multiplying Equation 1 by 4 and Equation 2 by -2, we get:

8x + 10y = 34.20 (Equation 3)

-6x - 8y = -26.20 (Equation 4)

Adding Equation 3 and Equation 4, we get:

2x + 2y = 8

Simplifying this equation, we get:

x + y = 4 (Equation 5)

Now we have two equations: Equation 2 and Equation 5. We can solve for x and y using substitution or elimination. Here, we will use substitution.

From Equation 5, we can express x in terms of y as:

x = 4 - y

Substituting this expression for x into Equation 2, we get:

3(4 - y) + 4y = 13.10

Simplifying and solving for y, we get:

y = £1.50

Substituting this value for y into Equation 5, we can solve for x:

x + £1.50 = 4

x = £2.50

Therefore, the cost of 1 kg of mushrooms is £2.50 and the cost of 1 kg of turnips is £1.50.

a) The cost of 1 kg of turnips is £1.50.

b) The cost of 1 kg of mushrooms is £2.50.

Answer:

1st -pentagon -regular

2nd -hexagon -irregular

3rd -octagon -irregular

Answer:

The correct equation that represents the relationship between b and f is:

Ob = (3/2)f

Explanation:

We know that Priya uses 4 cups of flour to make 3 loaves of banana bread.

So, the amount of flour required per loaf of bread is 4/3 cups.

Now, if Andre makes b loaves of bread using f cups of flour, then the amount of flour required per loaf of bread is f/b cups.

We can set up a proportion as follows:

4/3 = f/b

Cross multiplying, we get:

4b = 3f

Dividing both sides by 3, we get:

b = (3/4)f

This means that Andre can make (3/4) loaves of bread per cup of flour.

But the question asks for the relationship between b and f, so we need to rearrange the equation:

b = (3/4)f

Multiplying both sides by (2/3), we get:

(2/3)b = (1/2)f

Simplifying, we get:

Ob = (3/2)f

Therefore, the correct equation that represents the relationship between b and f is Ob = (3/2)f.

The equivalent fraction for 2/3 is 8/12.

Equivalent fraction of a given fraction is got by multiplying or dividing its numerator and denominator by the same whole number. For example, if we multiply the numerator and denominator of 2/3 by 4 we get. 2/3 = 2×4 / 3×4 = 8/12 which is an equivalent fraction of 2/3.