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Only matrices of the same size can be added or subtracted.

A matrix is a rectangular array of numbers and is composed of rows and columns. In order to add or subtract matrices, the matrices must have the same number of rows and columns. If the matrices do not have the same size, they cannot be added or subtracted.

For example, if one matrix is a 2x3 matrix, the other matrix must also be a 2x3 matrix. Similarly, if one matrix is a 3x2 matrix, the other matrix must also be a 3x2 matrix. The numbers in each matrix may vary, but the size of the matrices must be the same for the operation to be valid.

When adding or subtracting matrices, the numbers in the same position (row and column) are added or subtracted. For example, if one matrix is [[1,2,3], [4,5,6], [7,8,9]] and the other matrix is [[2,4,6], [8,10,12], [14,16,18]], the resulting matrix would be [[3,6,9], [12,15,18], [21,24,27]].

Adding and subtracting matrices is a useful tool in mathematics and is often used to solve equations and simplify complex problems. It is important to remember that only matrices of the same size can be added or subtracted.

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The sides n and s of the given similar triangles are 12 and 10 respectively.

What are similar triangles?

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are similar. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

The polygon with three sides is a triangle. The prerequisites for a triangle's similarity are that the corresponding angles on both triangles must be equal, and the corresponding sides must be proportional to one another.

In the given figure both triangles are similar triangles.

So according to the properties of similar triangles,

[tex]\frac{15}{s} = \frac{9}{6}=\frac{n}{8}[/tex]

Solving the above equations,

15/s = 9/6

s = 10

n/8 = 9/6

n = 12

Therefore the sides n and s of the given similar triangles are 12 and 10 respectively.

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For the trigonometric function -0.575 = cos c the value is obtained as c = 2.18340 + 2πn and c = 2.18340 - 2πn.

What is trigonometric function?

Simply put, trigonometric functions also referred to as circular functions are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle.

The trigonometric function is -

-0.575 = cos c

The value for c is -

cos c = -0.575

c = arccos (-0.575)

c = 2.18340 + 2πn

In radians the value of c is -

c = 2.18340 + 2πn and c = 2.18340 - 2πn

In degrees the value of c is -

c = 125.1° + 360° and c = 125.1° - 360°

Therefore, the value of c is c = 2.18340 + 2πn.

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Erika has 6.53 kilograms of apples, which is more than the 6 kilograms she needed for the recipe. Therefore, she has enough apples to make the recipe.

To determine if Erika has at least 6 kilograms of apples, we need to add the weight of all three bags of apples. The total weight of the apples is:

It is given that:

There is 2.56 kg of red apples.

There is 1.18 kg of green apples.

And, 2.79 kg of yellow Apples.

Therefore,

2.56 kg + 1.18 kg + 2.79 kg = 6.53 kg

Erica needs a certain number of apples for her recipe, i.e. 6 kg. She goes to her store and chooses three different bags of apples: a 2.56 kg bag of red apples, a 1.18 kg bag of green apples, and a 2.79 kg bag of yellow apples.

To determine if you have enough apples, you must add up the weight of all three bags. The total weight of the apples is 6.53 kg. This means that Erika has more than 6 kg of apples she needs and has enough for the recipe. It's important to note that Erica has a surplus of apples that can come in handy if she needs more apples for recipes or later.

Combining different types of apples can also add variety and flavor to your recipe.

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The correct way to solve for the answer is to divide the quantity of potatoes the store bought by the quantity of each bag of potatoes.

Quantity of potatoes the store bought = 250 kilograms

Quantity of each bag of potatoes= 10 pounds

Convert kilograms to pounds:

1 kilogram = 2.20462 pounds

25 kilograms= 551.156 pounds

Number of bags of potatoes= Quantity of potatoes the store bought / Quantity of each bag of potatoes

= 551.156 pounds ÷ 10 pounds

= 55.1156 bags

Approximately,

55 bags

Therefore, the store will pack an approximate number of 55 bags of potatoes.

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Answer:

$141.30

Step-by-step explanation:

180 - 38.70 = 141.30

Answer:

D. 12x = -8

Step-by-step explanation:

D. 12(-2/3) = -8

-24/3 = -8

-8 = -8

The completed table is given below

Sr. No. Mortgage Amount Interest Rate First Monthly Payment Amount of Interest Amount of Principal New Principal

a b c d e f

(given) (a*b/12) (c-d) (a-e)

1 86,000 8.00% 663.92 573.33 90.59 85,909.41

2 1,65,000 5.00% 886.05 687.50 198.55 1,64,801.45

3 42,500 6.50% 286.88 230.21 56.67 42,443.33

Answer to Question 4

Investment in house 96,400.00

Down Payment 25% 24,100.00 (96,400*25%)

Mortgage Amount 72,300.00 (96,400-24,100)

Mortgage Amount Interest Rate First Monthly Payment Amount of Interest Amount of Principal New Principal

a b c d e f

(given) (a*b/12) (c-d) (a-e)

72,300 5.50% 410.66 331.38 79.29 72,220.72

Thus First Monthly Payment used to reduce Principal is $79.29

5.

Investment in house 1,37,400.00

Down Payment 17,400.00

Mortgage Amount 1,20,000.00 (1,37,400-17,400)

Mortgage Amount Interest Rate First Monthly Payment Amount of Interest Amount of Principal New Principal

a b c d e f

(given) (a*b/12) (c-d) (a-e)

1,20,000 6.00% 772.80 600.00 172.80 1,19,827.20

New Principal will be $119,827.20.

6. Investment in house 2,87,000.00

Down Payment 31,000.00

Mortgage Amount 2,56,000.00 (287,000-31,000)

Mortgage Amount Interest Rate First Monthly Payment Amount of Interest Amount of Principal New Principal

a b c d e f

(given) (a*b/12) (c-d) (a-e)

2,56,000 6.00% 1,536.00 1,280.00 256.00 2,55,744.00

The first Monthly Payment used to reduce the Principal is $256 and New Principal after first monthly payment is $255,744.

7 Investment in house 87,500.00

Down Payment 17,500.00

Mortgage Amount 70,000.00 87,500-17,500)

Month Mortgage Amount Interest Rate Monthly Payment Amount of Interest Amount of Principal New Principal

a b c d e f

(given) (a*b/12) (c-d) (a-e)

1 70,000 6.00% 409.50 350.00 59.50 69,940.50

2 69,941 6.00% 409.50 349.70 59.80 69,880.70

3 69,881 6.00% 409.50 349.40 60.10 69,820.61

4 69,821 6.00% 409.50 349.10 60.40 69,760.21

5 69,760 6.00% 409.50 348.80 60.70 69,699.51

6 69,700 6.00% 409.50 348.50 61.00 69,638.51

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Answer:

  3.  · (times)

Step-by-step explanation:

You want to know the operation that will give a binomial result from the expressions (3y^6 +4) and (9y^12 -12y^6 +16).

The like terms in the two expressions are 3y^6 and -12y^6, or +4 and +16. Combining these terms by addition or subtraction will not result in the elimination of either the y^6 term or the constant term. Hence addition or subtraction cannot result in a binomial.

We know that the sum of cubes is factored into the product of a binomial and a trinomial:

  a³ +b³ = (a +b)(a² -ab +b²)

Comparing this form to the given binomial and trinomial, we see that we can choose ...

  a = 3y^6

  b = 4

to make the given factors match exactly. That tells us their product will be a binomial sum:

  (3y^6 +4) × (9y^12 -12y^6 +16) = (3y^6)^3 +(4)^3 = 27y^18 +64

The operation "times" (·) will result in a binomial.

The triangle ABC is equal to triangle ADE by Angle-Angle-Side theorem.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

In triangle ABC and ADE -

It can be seen that ∠B = ∠E.

Also the line segment AB is equal to line segment AE.

AB = AE

The angles ∠BAC and ∠DAE are vertically opposite to each other.

So, they are also equal.

∠BAC = ∠DAE

Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

Therefore, Δ ABC ≅ Δ ADE according to AAS theorem.

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Show A is 90 minutes long, and Show B is 45 minutes long.

Let's say Show A is x minutes long. Then Show B is x/2 minutes long since Show A is twice as long as Show B. The total duration of Show A and Show B is 2 hours and 15 minutes, or 135 minutes.

So, x + x/2 = 135

Multiplying both sides by 2, we get 2x + x = 270

Combining like terms, we get 3x = 270

Dividing both sides by 3, we get x = 90

So Show A is 90 minutes long, and Show B is 45 minutes long.

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Answer:

Step-by-step explanation:

Given, the sides of triangle ABC are 12, 16 and 20, which form a right triangle (as 20 is the hypotenuse).

Let us assume that the sides of triangle XYZ are x, y and 24 (XZ=24).

Since ABC ~ XYZ, we can use ratios of corresponding sides to find the lengths of the sides of triangle XYZ:

x/12 = y/16 = 24/20

Solving for x and y, we get:

x = 9 and y = 12

So, the perimeter of triangle AXYZ = 9 + 12 + 12 + 24 = 57.

254 degrees is the coterminal to 614°

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side.

To find coterminal angles when given a positive angle, subtract 360 degrees to the given angle until you get an angle between 0 and 360.

614-360=254

254 lies between 0 and 360 degrees.

Hence, 254 degrees is the coterminal to 614°

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It is important to check that the number of successes and number of failures in each sample is at least 10 because this helps ensure that the normal approximation of the binomial distribution is accurate.

When constructing a confidence interval for the difference between two population proportions, it is important to check that the number of successes and the number of failures in each sample is at least 10 because this helps ensure that the normal approximation of the binomial distribution is accurate. The normal approximation is often used in constructing confidence intervals for proportions because it simplifies the calculations, but it is only accurate if the sample size is large enough.

A common rule of thumb is that each sample should have at least 10 successes and 10 failures in order to ensure that the normal approximation is reasonable. This is because the Central Limit Theorem states that the sum of many independent and identically distributed random variables will approximately follow a normal distribution. When the sample size is large enough, the distribution of the sample proportions will be approximately normal, even if the individual observations are not.

If the number of successes and failures in each sample is less.

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The cost of a restricted pass is equals to £35 and the cost of a full pass is equals to £20.

We have, Brian and Bob visit a ski resort.

In case of Brain,

Number of full passes = 3

Number of restricted passes = 4

In case of Bob,

Number of full passes = 2

Number of restricted passes = 3

Let " £r" and " £p" be the cost of each full pass and restricted pass. Then, on basis of problem,

Total cost of passes in case of brain = £185

=> 3p + 4r = 185 --(1)

Similarly, Total cost of passes in case of bob

= £130

=> 2p + 3r = 130 --(2)

Now, equation (1) and (2) formed a system of two linear equations. We have to calculate the value of "r" and "p" . So, using the Elimination method,

Multiplying the equation (1) and equation (2) by 2 and 3 respectively and then equation (2) from (1) to eliminate the variable "p".

=> 2(3p + 4r) - 3(2p + 3r) = 2× 185 - 3× 130

=> 6p + 8r - 6p - 9r = 370 - 390

=> -r = - 20

=> r = 20

then from equation (1) , 3p + 4(20) = 185

=> 3p = 185 - 80 = 105

=> p = 105/3 = 35

Hence, the required values of r = £20 and p = £35.

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Answer:

12 houses

Step-by-step explanation:

First you need to figure out how many were sold the first month. You need to figure out how much 1/3 of 48 is, so you need to divide 48 by 3, equaling 16. You then multiply 16 by two, because they didnt sell 1/3, but 2/3. 16 times 2 is 32, so 32 houses were sold in the first month, by doing 48-32, you can say that there were 16 houses left to sell. Then if 1/4 of those houses were sold the next month, then you need to figure out what 1/4 of 16 is. In the same way as before, you divide 16 by 4, which equals 4. If they sold 4 of 16 the next month, you then need to subtract 16 by 4, equaling 12. This means there are 12 houses remaining to be sold.

The difference between the sample standard deviation (s) and the population standard deviation (σ) will generally be greater for the data set with fewer data values.

This is because the sample standard deviation is an estimate of the population standard deviation, and with a smaller sample size, the estimate is likely to be less accurate.
In this case, the data set with 20 data values has a smaller sample size, so the difference between s and σ will be greater for this data set compared to the data set with 50 data values. The larger the sample size, the more representative the sample is of the population and the more accurate the estimate of the population standard deviation is likely to be.
It's worth noting that while the sample standard deviation is a useful measure of variability in the sample, it is not the same as the population standard deviation, which is a true measure of the variability in the population. The sample standard deviation can be used to make inferences about the population standard deviation, but it is important to consider the sample size and other factors that may affect the accuracy of the estimate

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Sum of angles,

∠6 +∠2 +∠5 = 180°

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. There are two different types of alternate angles, alternate interior angles and alternate exterior angles.

Given,

y || x

To prove,

∠5 +∠2 +∠6 = 180°

∠1, ∠2, ∠3 are on straight line,

∠1 +∠2 +∠3 = 180°

∠1 = ∠5    (alternate angles on transversal AC)

∠3 = ∠6    (alternate angles on transversal AB)

∠5 +∠2 +∠6 = 180°

Hence, ∠5 +∠2 +∠6 = 180° is proved.

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The measure of {x} in the figure is 14.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Given is a parallelogram as shown in the image.

Opposite angles of a parallelogram are equal. So, we can write -

x + 50 = y

y - x = 50                                                                  .... Eq { 1 }

Sum of the angles of a quadrilateral are 360°. We can write -

2(x - 30) + (x + 50) + y = 360                                          .... Eq { 2 }

2x - 60 + x + 50 + y = 360

3x + y = 370

3x + 50 + x = 370

4x = 320

x = 80

y = 130

Therefore, the measure of {x} and {y} are 80 and 130 respectively.

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{Question in english -

Help please, I need to find the values, well, I'll settle for one...}

If Bill does not really know if the concept will be viable, so he develops a limited menu and has friends and family fill out a questionnaire to gather information. Bill is using creation in action.

What is questionnaire?

A questionnaire is a type of research tool used to collect data from respondents for a survey or statistical analysis. It consists of a set of questions (or other forms of prompts). Typically, a research questionnaire will have both closed-ended and open-ended questions. Long-term, open-ended inquiries provide the respondent the chance to go into more detail. The Statistical Society of London created the research questionnaire in 1838. Although statistical analysis of the replies is frequently the goal of questionnaire design, this is not always the case.

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By understanding stratified random sampling concept, it can be concluded that the problem is a type of stratified random sampling.

Stratified random sampling is a structured random sampling technique that is carried out by dividing members of the population into several strata (levels), then a sample is selected from each level.

Population elements are divided into several levels based on the characters attached to them.

With this method, it is expected that the sampling will be evenly distributed at all levels and the sample represents the character of all heterogeneous population elements.

By understanding this concept, it can be concluded that the problem is stratified random sampling.

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Answer:

The general form of a quadratic equation is ax^2 + bx + c = y.  From the equation for c, our a is -2, our b is -7 and our c is 5.  

When a < 0, the function opens downward and has a maximum for its vertex.

When a quadratic function has maximum, its x values will always be increasing from negative infinity to the x-coordinate of the maximum (You can also simply write x < x coordinate of the maximum as you've already done).

We can find the x-coordinate of the maximum using the equation

[tex]-b/2a[/tex]

Thus, since b is -7 and a is -2, we have

[tex]-(-7)/2(-2)\\7/-4\\-7/4=-1.75[/tex]

This is how you get that the function is increasing from x < -1.75.

The green line in the attached picture also highlights the same idea.

Answer:

1. -23

2. -20

3. 20

4. 23

Step-by-step explanation:

In the Fixed deposit account, you will not be able to withdraw your money before time without a penalty fee from the bank and you will receive a fixed amount of interest on your original deposit.

In a Fixed-Term Deposit account, an account is opened with a bank wherein, the bank pays a guaranteed interest rate on the sums deposited for a fixed period or tenure.

This type of account allows you to earn higher returns (interest) on funds lying idle in your Savings Account.

Banks are free to charge their own penalty fee in the case of premature withdrawal of Fixed Deposit.

At the end of the stipulated period, the deposit will automatically be renewed unless you update your maturity instructions.

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Answer:

x²+y²+2xy

Step-by-step explanation:

Hope it helps! If it did, please thank, rate and mark brainliest!

Answer:

O x² + 2xy + y². The result of squaring a binomial is the sum of the square of the first term in the binomial, the product of twice the first term and the second term and the square of the second term: (x + y)² = x² + 2xy + y².

The coordinates of R are (2,3) which represents an intersecting point of the given lines.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

The lines are given in the question, as follows:

y = x+1 ...(i)

x+2y = 8  ...(ii)

Since both lines intersect at R.

Substitute the value of equation (i), in (ii), and we get

x+2(x+1) = 8

x + 2x + 2 = 8

3x = 8 - 2

3x = 6

x = 2

Substitute the value of x = 2 in equation (i),

y = 2 + 1

y = 3

Thus, the coordinates of R are (2,3).

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The question seems incomplete, the correct question would be as:

If the lines y=x+1 and x+2y=8 intersect at R, find the coordinates of R. Show this the coordinate plan.

When we want to find all the points on a surface where the tangent plane is horizontal, we are essentially looking for the points where the surface has a horizontal slope. The points on the surface where the tangent plane is horizontal are the points (0, 0, 0).

To find these points, we can use the partial derivative test. First, we calculate the partial derivatives of the surface function with respect to x and y, and set them equal to zero. These equations will give us the x and y values of the points where the slope is zero.

Next, we plug these values back into the original surface function to obtain the z-coordinate of the points. These are the points on the surface where the tangent plane is horizontal.

For example, let's consider the surface function z = x^2 + y^2. To find the points on this surface where the tangent plane is horizontal, we need to find the x and y values where the partial derivatives of z with respect to x and y are equal to zero.

Taking the partial derivative of z with respect to x, we get:

∂z/∂x = 2x

Setting this equal to zero, we get: 2x = 0

Solving for x, we get x = 0.

Taking the partial derivative of z with respect to y, we get:

∂z/∂y = 2y

Setting this equal to zero, we get: 2y = 0

Solving for y, we get y = 0.

Therefore, the points on the surface where the tangent plane is horizontal are the points (0, 0, 0).

In summary, when we want to find all the points on a surface where the tangent plane is horizontal, we can use the partial derivative test and set the partial derivatives of the surface function with respect to x and y equal to zero. We can then plug these values back into the original surface function to obtain the z-coordinate of the points.

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