Find the sum of the following using the column method a^2+2*ab+b^2, a^2-2*ab-b^2, a^2+b^2

The percentage change from 92 to 108 is 13.4% approx

What is Percentage?

A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. The term per cent refers to one hundred percent.

Solution:

Percentage = Change / Original * 100

Change = 108 - 92 = 16

Original/Initial Value = 92

Percentage Change = 16/92 * 100 = 17.39% = 17.4% (approx)

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Answer:

i rly hate graph them but what ever heres the graph

(8,9)

Hope This Helps!!!

Answer:

13 sessions

The cost for either plan: $675

Step-by-step explanation:

48x + 51 = 49x + 38

51 - 38 = 49x - 48x

13 = x

The center of the given circle is (-3,-3) and the radius is 9 units

Given that the equation of the circle is `x² + y² + 6x + 6y = 63`.

We have to determine the center and the length of the radius of the circle.

Step-by-step explanation:

The given equation is `x² + y² + 6x + 6y = 63`.

We have to write this equation in the standard form of the circle i.e (x - a)² + (y - b)² = r² by completing the square method.

Here, the values of a, b and r can be determined by comparing the given equation with the standard form of the circle.   x² + y² + 6x + 6y = 63 [Rearrange the terms by grouping the variables of x and y]

x² + 6x + y² + 6y = 63  [Add 9 (6/2)^2 to complete the square for x]

x² + 6x + 9 + y² + 6y + 9 = 63 + 9 + 9 [Add 9 (6/2)^2 to complete the square for y]

(x + 3)² + (y + 3)² = 81  [Rearrange the terms by comparing with the standard form of circle i.e (x-a)² + (y-b)² = r²]

Therefore, the center of the circle is (-3,-3) and the radius is 9 units.

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The interest earned by Mrs Grey over the 7 years is R5670. The cost of the television set 5 years ago was R20,600.

4.1.1 To calculate the interest earned by Mrs Grey over 7 years, we use the formula for simple interest: Interest = Principal x Rate x Time. Mrs Grey's principal is R18,000 and the rate is 4.5% per annum. The time is 7 years. Using the formula, we can calculate the interest as follows:

Interest = R18,000 x 0.045 x 7 = R5670. Therefore, Mrs Grey has earned R5670 in interest over the 7 years.

4.1.2 To calculate the cost of the television set 5 years ago, we need to account for the inflation rate. The cost of the television set now is R27,660. The average rate of inflation over the last 5 years is 6.7% per annum. We can use the formula for compound interest to calculate the original cost of the television set:

Cost 5 years ago = Cost now / (1 + Inflation rate)^Time

Cost 5 years ago = R27,660 / (1 + 0.067)^5 = R20,600. Therefore, the cost of the television set 5 years ago was R20,600.

4.1.3 To determine the rate of simple interest Mrs Grey should have invested her money at 7 years ago, we can use the formula for interest: Interest = Principal x Rate x Time. We know the principal is R18,000, the time is 7 years, and the interest earned is R5670. Rearranging the formula, we can solve for the rate:

Rate = Interest / (Principal x Time)

Rate = R5670 / (R18,000 x 7) ≈ 0.0448 or 4.48% per annum. Therefore, Mrs Grey should have invested her money at a rate of approximately 4.48% per annum to have earned enough interest to purchase the television set using only her original investment and the interest earned over the 7 years.

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Answer:

The height of the window is 150 centimeters.

Step-by-step explanation:

Use ratio and proportion to find the height of the window.

\(\frac{h}{60cm} = \frac{210cm}{84cm}\)

Cross multiply

\(h = \frac{210cm(60cm)}{84cm} \\h = \frac{12600cm^2}{84cm} \\h = 150 cm\)

a)the ratio of the heights of the pyramids is 5:3. b)the volume of the larger pyramid is 23.04 cm³.

what is volume  ?

Volume is a measure of the amount of space that a three-dimensional object occupies. It is usually measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³). The volume of an object can be calculated using different formulas depending on its shape.

In the given question,

a. Let the height of the smaller pyramid be h₁ and the height of the larger pyramid be h₂. Since the two pyramids are similar, their corresponding linear dimensions are in the same ratio as the areas of their bases. Therefore, we have:

(base area of smaller pyramid)/(base area of larger pyramid) = (linear dimension of smaller pyramid)² / (linear dimension of larger pyramid)²

Since the linear dimension is the height in this case, we can substitute the given ratio of the base areas to obtain:

25/9 = (h₁/h₂)²

Taking the square root of both sides, we get:

h₁/h₂ = 5/3

Therefore, the ratio of the heights of the pyramids is 5:3.

b. Since the volume of a pyramid is proportional to the cube of its height, we have:

(volume of smaller pyramid) / (volume of larger pyramid) = (h₁/h₂)³ = (5/3)³ = 125/27

Substituting the given volume of the smaller pyramid, we get:

108 / (volume of larger pyramid) = 125/27

Solving for the volume of the larger pyramid, we obtain:

volume of larger pyramid = (27/125) * 108 = 23.04 cm³ (rounded to two decimal places)

Therefore, the volume of the larger pyramid is 23.04 cm³.

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Answer:

Step-by-step explanation:Rearrange terms

3x-5+({5+6x})

Solution

9x     will that help?

Answer:

Step-by-step explanation:

(3x-5)+(5+6x)

3x-5+5+6x

3x+6x+5-5

3x+6x

9x

i think this is the right answer

Answer:

30 ft

Step-by-step explanation:

h/(40 + 8) = 5/8

h = 30

Answer:

c

Step-by-step explanation:

100%

Answer:

C

Step-by-step explanation:

Nya!!

A. The value of x coordinate for each coin are:xA = 5.0 cmxB = -5.0 cmxC = 0 cm

Let’s say, coin A lies on the right corner of the square, coin B lies on the left corner of the square and coin C lies on the bottom corner of the square. The distance from the center of the square to each corner is 5.0 cm.The x coordinate of the center is calculated as follows:For coin A: 10.0/2 = 5.0 cmFor coin B: -10.0/2 = -5.0 cmFor coin C: 0B. The value of y coordinate for each coin are:yA = -5.0 cmyB = -5.0 cmyC = 5.0 cm.For coin A: The distance from the center of the square to coin A is 5.0 cm in the downward direction, hence yA = -5.0 cmFor coin B: The distance from the center of the square to coin B is 5.0 cm in the upward direction, hence yB = -5.0 cmFor coin C: The distance from the center of the square to coin C is 5.0 cm in the upward direction, hence yC = 5.0 cmC. The x and y coordinates of the center of gravity of the three coins described in Part A are:xcg = 0ycg = -5.0/3 = -1.6667 cmExplanation:The center of gravity of the coins lies at the point of intersection of the median lines of the triangle formed by joining the centers of the three coins.

Therefore, the center of gravity is at the point of intersection of the line joining the midpoints of the lines connecting A and B and C and the midpoint of the line connecting A and C and B and C. The midpoint of AB and C is (0, -5/2) and the midpoint of AC and B is (5/2, -5/2). The line joining these two points is y = -x - 5/2. This line will intersect with the line passing through the center of coin C and perpendicular to AB at (0, -5/3). Hence, the center of gravity of the system lies at the point (0, -5/3) = (0, -1.6667 cm).The explanation is more than 100 words, explaining the solution to the problem by using proper formulas and steps.

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Answer:0.375

Step-by-step explanation:

3/4=0.75

0.75/2=0.375

(3/4)/2=0.375

Answer:

87.8

Step-by-step explanation:

I assume you know how to do this so I didn't show any steps. Have a nice night. :)

Answer

Quiz: Measures of Center

I got one wrong, so use at discretion

Step-by-step explanation: I took the test

1. 87.8

2. 6,060

3. 36

4. 312

5. 4.41 and 45.6

6. no mode

7. 0.236

8. 1,136

9. no mode

10. 33,745

Answer:

17/3

Step-by-step explanation:

x +  y +  z   = 47

y - x  = 10   x =  y - 10

z - y = 10     z = 10 + y      

y-10    +     y    +   10 + y    = 47

3 y = 47

 y = 47/3       x = 17/3     z = 77/3  

Answer:

5

Step-by-step explanation:

Answer: No, they are not inverses of one another.

=======================================================

Explanation:

There are at least 3 methods we can use to prove the functions aren't inverses of each other.

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

Method 1

Let's say we plugged x = 0 into f(x).

\(f(\text{x}) = 2\text{x}+1\\\\f(0) = 2*0+1\\\\f(0) = 1\\\\\)

The input x = 0 leads to the output y = 1.

Then let's treat y = 1 as the input of the g(x) function, so we'll plug x = 1 into here.

\(g(\text{x}) = -2\text{x}-1\\\\g(1) = -2*1-1\\\\g(1) = -3\\\\\)

If g(x) was the inverse of f(x), then the g(1) output value should be 0 to get us back where we started. However, we get an output of -3 instead.

This is sufficient evidence to conclude that f(x) and g(x) are not inverses of each other. We only need one counter-example to disprove this claim.

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

Method 2

Recall that if f(x) and g(x) are inverses of each other, then we have the following two properties

The left hand side of each equation involves the concept of "function composition".

Let's see what f(g(x)) is equal to in this case.

\(f(\text{x}) = 2\text{x}+1\\\\f(g(\text{x})) = 2(g(\text{x}))+1\\\\f(g(\text{x})) = 2(-2\text{x}-1)+1\\\\f(g(\text{x})) = -4\text{x}-2+1\\\\f(g(\text{x})) = -4\text{x}-1\\\\\)

We do not get an output of simply x only, so this is another way to see how we don't have inverses.

Through similar steps, you should find that \(g(f(\text{x})) = -4\text{x}-3\) which is further confirmation that f(x) and g(x) are not inverses of each other.

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

Method 3

Let's ignore g(x) for now. We'll start with f(x) and find the inverse of it.

The process involves this basic outline:

So,

\(f(\text{x}) = 2\text{x}+1\\\\\text{y} = 2\text{x}+1\\\\\text{x} = 2\text{y}+1\\\\\text{x}-1 = 2\text{y}\\\\\text{y} = \frac{\text{x}-1}{2}\\\\f^{-1}(x) = \frac{\text{x}-1}{2}\\\\\)

Unfortunately we do not end up with -2x-1 as the actual inverse.

So if \(g(\text{x}) = \frac{\text{x}-1}{2}\) was the case, then f(x) and g(x) would be inverses of each other.

Through similar steps, the inverse of \(g(\text{x}) = -2\text{x}-1\\\\\) is \(g^{-1}(\text{x}) = -\frac{\text{x}+1}{2}\\\\\)

The Kutta-Joukowski theorem, which is represented by equation (3.140), was originally derived for the case of a lifting cylinder. However, it can also be applied to a two-dimensional body of arbitrary shape, as stated in section 3.16.

A more detailed explanation of the answer.
To make a physical argument for this generalization, we can draw a closed curve around the body.

The key is to draw the curve far enough away from the body such that the body appears as a very small speck in the middle of the domain enclosed by the closed curve.

By doing this, we are essentially treating the body as a point object at the center of the curve. Since the body is now a very small speck in comparison to the large domain, its specific shape becomes insignificant to the overall flow around it.

Therefore, the lifting force calculations derived from the Kutta-Joukowski theorem for the lifting cylinder should also apply to the two-dimensional body of arbitrary shape, as long as the body is small in comparison to the domain enclosed by the closed curve.

This physical argument allows us to accept that equation (3.140) can be applied in general to a two-dimensional body of arbitrary shape without requiring a mathematical proof.

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=========================================================

Explanation:

If we tried the x coordinate of choice A, then,

y = -3x-7

y = -3*2-7

y = -6-7

y = -13

This shows that the point (2,-13) is on the line and not (2,-1). This rules out choice A, and also choice E.

Let's try x = -2

y = -3x-7

y = -3*(-2)-7

y = 6-7

y = -1

This shows that (-2,-1) is a point on the line, and it points us to choice C being the final answer. This rules out choice B.

If we tried x = 1, then,

y = -3x-7

y = -3*1-7

y = -3-7

y = -10

Which shows that (1,-10) is a point on this line, which rules out choice D.

The visual summary is shown below as a graph. Only point C is on the red line.

The total cost of each utility eliminating 450 tons of pollution is $180,000.

To calculate the total cost for each utility to eliminate 450 tons of pollution, we need to multiply the cost per ton of pollution elimination by the number of tons each utility needs to eliminate.

For People's Electric, the cost of eliminating one ton of pollution is $400. So, to eliminate 450 tons, the total cost would be 450 tons * $400/ton = $180,000.

For Municipal Energy, the cost of eliminating one ton of pollution is $350. Again, to eliminate 450 tons, the total cost would be 450 tons * $350/ton = $157,500.

Therefore, the total cost for each utility to eliminate 450 tons of pollution is $180,000 for People's Electric and $157,500 for Municipal Energy.

The cost calculation is based on the given information that each utility is provided with 450 pollution permits by the government. These permits allow them to legally produce a ton of pollution. By setting a limit on the number of permits, the government aims to reduce pollution by half. The utilities have the option to trade permits with each other.

In this scenario, People's Electric has a higher cost of eliminating pollution per ton compared to Municipal Energy ($400 vs. $350). It means that People's Electric would find it more expensive to reduce pollution through internal measures like investing in cleaner technology or implementing environmental initiatives. On the other hand, Municipal Energy has a lower cost, indicating that they have relatively more cost-effective methods for pollution reduction.

Given these costs, it is more beneficial for People's Electric to purchase permits from Municipal Energy rather than eliminating the pollution themselves. By purchasing permits, People's Electric can meet the pollution reduction target at a lower cost. Conversely, Municipal Energy can generate additional revenue by selling their permits.

This permit trading mechanism allows for cost efficiency in achieving the government's pollution reduction goal. The total cost for each utility is determined by multiplying the cost per ton of pollution elimination with the number of tons they need to eliminate.

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Step-by-step explanation:

To find the X value corresponding to z = -0.25, we can use the formula:

z = (X - M) / s

where z is the standardized score, X is the raw score we want to find, M is the population mean, and s is the population standard deviation.

Rearranging this formula, we get:

X = z * s + M

Substituting the given values, we get:

X = -0.25 * 12 + 50

X = 47

Therefore, the X value corresponding to z = -0.25 is 47.

Hence, the answer is option B.

The X value corresponding to z = -0.25 is 47 (option b).

To answer this question, we need to use the formula for calculating z-scores, which is:
z = (X - M) / (s)
where z is the z-score, X is the raw score, M is the population mean, and s is the population standard deviation.
In this case, we are given the population mean (M = 50) and the z-score (z = -0.25). We also know that the population standard deviation (s) is 12.
We can rearrange the formula to solve for X:
X = z * s + M
Plugging in the values we have:
X = -0.25 * 12 + 50
X = 47
Therefore, the X value corresponding to z = -0.25 is 47. The answer is (b).
It's important to note that z-scores are a way of standardizing data so that we can compare different sets of data that may have different scales or units. In this case, we are using the z-score to find the corresponding raw score.

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Answer: 1/4 and 0.25

Step-by-step explanation:

Answer:

0.25m & 1/4

This question is incomplete, it is very signficant that the questions are complete.

Step-by-step explanation:

Answer:

(9,4) right

Step-by-step explanation:

From the calculation done below, it can be seen that the cost of one orange is 85 cents.

The cost of one orange can be determined as follows:

One dime = 10 cents

2 dollars = 200 cents

Total amount given by Sue to the store clerk = One dime + 2 dollars = 10 cents + 200 cents = 210 cents

Cost of two oranges = Total amount given by Sue to the store clerk –

Change = 210 cents – 40 cents = 170 cents

Cost of one orange = Cost of two oranges / 2 = 170 cents / 2 = 85 cents

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The number of model of cars Eleni has in terms of R is E = R / 2 - 3.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

Let us suppose the model of cars with Ridhi = R.

Andrea thus has:

A = R / 2

Eleni has three fewer model cars that Andrei. Thus,

E = R / 2 - 3

Hence, the number of model of cars Eleni has in terms of R is E = R / 2 - 3.

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The area of the triangle is 19.5 square units.

To find the area of the triangle, we can use the formula:

Area = (1/2) * base * height

where the base and height are the distance between two of the vertices of the triangle. We can choose any two vertices to use as the base and height, as long as we use the same units for both. Let's choose (-3,2) and (6,-2) as our base.

The distance between (-3,2) and (6,-2) can be found using the distance formula:

d = \(\sqrt((6 - (-3))^2 + (-2 - 2)^2)\)
d = \(\sqrt(81 + 16)\)
d = \(\sqrt(97)\)

Now we need to find the height of the triangle. The height is the perpendicular distance from the third vertex (3,5) to the line containing the base (-3,2) and (6,-2). We can use the formula:

height = \(|Ax + By + C| / \sqrt(A^2 + B^2)\)

where A, B, and C are the coefficients of the line in the standard form Ax + By + C = 0, and x and y are the coordinates of the third vertex. We can find the coefficients of the line by using the two points (-3,2) and (6,-2):

A = 2 - (-2) = 4
B = (-3) - 6 = -9
C = 6*(-2) - (-3)*2 = -18

Now we can plug in the values to find the height:

height = \(|4*3 - 9*5 - 18| / \sqrt(4^2 + (-9)^2)\)
height = \(39 / \sqrt(97)\)

Finally, we can plug in the base and height to find the area:

Area = \((1/2) * \sqrt(97) * (39 / \sqrt(97))\)
Area = 19.5

Therefore, the area of the triangle is 19.5 square units.

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The vertex B' of the dilated triangle is B′(7.5, −5). So, the correct option is (D).

To find the vertex B' of the dilated triangle, we need to apply the scale factor of 2.5 to the coordinates of point B(3,-2) and find the new coordinates of B'.

The formula for dilation with a scale factor k centred at the origin is:

(x', y') = (kx, ky)

Using this formula with k = 2.5 and the coordinates of B(3,-2), we get:

(x', y') = (2.53, 2.5(-2)) = (7.5, -5)

Therefore, the vertex B' of the dilated triangle is B′(7.5, −5). So, the correct option is (D).

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Answer:

I believe C, 8 feet

Step-by-step explanation:

10/16  5/8

The answer is that the given set of numbers is represented by a Venn Diagram which has two overlapping groups, Multiple of 3, 5, and Multiple of 4, 2.

The set of numbers given is 44, and the question is based on the Venn Diagram which has two overlapping groups, Multiple of 3, 5, and Multiple of 4, 2. The area shared by both groups contains 4 and the area not included in any group contains the number 5.

Venn Diagram is a graphical representation of sets of elements. It is a set of overlapping circles in which the positions of the circles and their overlapping parts represent the relationship between the sets.

The given set of numbers is 44, so it can be represented by drawing a rectangle. The given rectangle is drawn, and it is divided into three parts. In the first part, numbers which are multiples of 3 and 5 are represented.

In the second part, numbers which are multiples of 4 and 2 are represented. In the third part, numbers which are not a multiple of 3, 5, 4, or 2 are represented.

It is given that the overlapping area shared by both groups contains 4, and the area not included in any group contains the number 5, so this can be represented as follows:

The Venn Diagram representation is as follows:In the diagram, the region which represents the numbers that are multiples of both 3 and 5 is shaded with the pink color, and the region that represents the numbers that are multiples of both 4 and 2 is shaded with the blue color.

The area shared by both groups contains 4, and it is shown with the overlapping region of the pink and blue color. The area not included in any group contains the number 5, and it is shown with the white space in the middle of the diagram.

 The overlapping area shared by both groups contains 4. The area not included in any group contains the number 5.

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Answer:

He is about 6 years old (5 years 11 months)

Step-by-step explanation:

13 - 7 and 3 - 2

The correct answer is (a) response, or dependent, variable

In regression analysis, the variable that is being predicted is the response variable, which is also known as the dependent variable. The dependent variable is the variable that is being explained or predicted by the regression model.

The independent variable(s), on the other hand, are the variable(s) that are used to explain or predict the variation in the dependent variable. These variables are also called predictor variables or explanatory variables.

Intervening variables are variables that come between the independent variable(s) and the dependent variable and affect the relationship between them. These variables are also known as mediator variables or intermediate variables.

Therefore, the correct answer is (a) response, or dependent, variable.

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