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Solve the simultaneous equations
4x + 3y = 21
and
4x + 2y = 16

Answer:

As a fraction: \(\mathbf{\dfrac{363}{2}}\)

As a colon,  363:2

By using the word to; we have: 363 to 2

Step-by-step explanation:

A ratio is a comparison of two quantities. We can write a ratio as a fraction, using the word “to,” or using a colon.

A rate is a ratio that compares two different units, such as distance and time, or a ratio that compares two different things measured with the same unit, such as cups of water and litres of petrol.

We can use a ratio to compare the number of days regardless of employing any professional sports events each year with the total number of days in a year.

The ratio with which we can write, that compares days with games in a year with two days without them can be written in three ways.

Suppose there are 365 days in a year and it appears that two days in that year exist without a game.

i.e.

365 - 2(days without game) = 363 days with a game

Then:

As a fraction: \(\mathbf{\dfrac{363}{2}}\)

As a colon,  363:2

By using the word to; we have: 363 to 2

Answer:

a to b        a:b         a/b

Ratio that compare days with games to days without them:

1- 363 to 2

2- 363 : 2

3- 363 / 2

Step-by-step explanation:

Ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

A ratio compares two quantities by division, with the dividend.

We can write a ratio to compare the number of days without any professional sports events each year with the total number of days in a year.

There are three ways to write a ratio to express the relationship between two quantities.

a to b        a:b         a/b

Ratio that compare days with games to days without them:

1- 363 to 2

2- 363 : 2

3- 363 / 2

These are the three ways to describe a ratio.

The total width of each piece of paper:

Yousef cuts the piece of paper into two pieces of paper of equal widths:

Let each of the smaller pieces have a width of w

W = 2w (since the smaller pieces have equal widths)

Using Maxwell's equations, we can determine the magnetic flux density. One of the Maxwell's equations is:

\(\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}\),

where \(\displaystyle \nabla \times \mathbf{H}\) is the curl of the magnetic field intensity \(\displaystyle \mathbf{H}\), \(\displaystyle \mathbf{J}\) is the current density, and \(\displaystyle \frac{\partial \mathbf{D}}{\partial t}\) is the time derivative of the electric displacement \(\displaystyle \mathbf{D}\).

In this problem, there is no current density (\(\displaystyle \mathbf{J} =0\)) and no time-varying electric displacement (\(\displaystyle \frac{\partial \mathbf{D}}{\partial t} =0\)). Therefore, the equation simplifies to:

\(\displaystyle \nabla \times \mathbf{H} =0\).

Taking the curl of the given magnetic field intensity \(\displaystyle \mathbf{R} =2\cos( 10^{10} t-600x)\hat{a}_{z}\, \text{Am}\):

\(\displaystyle \nabla \times \mathbf{R} =\nabla \times ( 2\cos( 10^{10} t-600x)\hat{a}_{z}) \, \text{Am}\).

Using the curl identity and applying the chain rule, we can expand the expression:

\(\displaystyle \nabla \times \mathbf{R} =\left( \frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial y} -\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial z}\right) \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Since the magnetic field intensity \(\displaystyle \mathbf{R}\) is not dependent on \(\displaystyle y\) or \(\displaystyle z\), the partial derivatives with respect to \(\displaystyle y\) and \(\displaystyle z\) are zero. Therefore, the expression further simplifies to:

\(\displaystyle \nabla \times \mathbf{R} =-\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial x} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Differentiating the cosine function with respect to \(\displaystyle x\):

\(\displaystyle \nabla \times \mathbf{R} =-2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Setting this expression equal to zero according to \(\displaystyle \nabla \times \mathbf{H} =0\):

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z =0\).

Since the equation should hold for any arbitrary values of \(\displaystyle \mathrm{d} x\), \(\displaystyle \mathrm{d} y\), and \(\displaystyle \mathrm{d} z\), we can equate the coefficient of each term to zero:

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x) =0\).

Simplifying the equation:

\(\displaystyle \sin( 10^{10} t-600x) =0\).

The sine function is equal to zero at certain values of \(\displaystyle ( 10^{10} t-600x) \):

\(\displaystyle 10^{10} t-600x =n\pi\),

where \(\displaystyle n\) is an integer. Rearranging the equation:

\(\displaystyle x =\frac{ 10^{10} t-n\pi }{600}\).

The equation provides a relationship between \(\displaystyle x\) and \(\displaystyle t\), indicating that the magnetic field intensity is constant along lines of constant \(\displaystyle x\) and \(\displaystyle t\). Therefore, the magnetic field intensity is uniform in the given medium.

Since the magnetic flux density \(\displaystyle B\) is related to the magnetic field intensity \(\displaystyle H\) through the equation \(\displaystyle B =\mu H\), where \(\displaystyle \mu\) is the permeability of the medium, we can conclude that the magnetic flux density is also uniform in the medium.

Thus, the correct expression for the magnetic flux density in the given medium is:

\(\displaystyle B =6\cos( 10^{10} t-600x)\hat{a}_{z}\).

Answer:

d

Step-by-step explanation:

Answer: 2 (p+ 2(

Step-by-step explanation:

Answer:

310

Step-by-step explanation:

189+122=311

(311 rounded to the nearest ten is 310.)

The set of ordered pairs above: is a function.

The mapping diagram above: is a function.

y = x²: is a function.

The table above: is not a function.

In Mathematics and Geometry, a function is a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

Based on the set of ordered pairs, mapping diagram, and the equation above, we can reasonably infer and logically deduce that it represent a function because the input values (domain, x-value, or independent values) are uniquely mapped to the output values (range, y-value or dependent values).

In this context, we can reasonably infer and logically deduce that the table does not represent a function because the input value (-1) has more than output values (2 and 4 respectively).

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Answer:

Your answer is 40%

Hope that this is helpful. Tap the crown button, Like & Follow me

Answer:ok

Step-by-step explanation: 2+2 =4 - 1 = 3 quick maths!

The sine equation for the object's height is given as follows:

d = -5sin(0.24t).

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

The amplitude for this problem is of 5 inches, hence:

A = 5.

The period is of 1.5 seconds, hence the coefficient B is given as follows:

2π/B = 1.5

B = 1.5/2π

B = 0.24.

The function starts moving down, hence it is negative, so:

d = -5sin(0.24t).

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Answer

z = -201

Explanation

26 equals the total of 227 and z.

In mathematical terms, this means

26 = 227 + z

To solve for z, we will subtract 227 from both sides

26 = 227 + z

26 - 227 = 227 + z - 227

-201 = z

z = -201

Hope this Helps!!!

Answer:

B

Step-by-step explanation:

Answer:

Question number 2 is A

And so is question number 3

Step-by-step explanation:

It says for 15 minus a number (meaning a variable like x or y) divided by 2 equals eleven

so 15 - y/2 = 11

For question number 3 it says the insurance company wants 100 dollars in deduction fee and then it will pay 80 percent or 0.8 of the medical costs.  so we get

0.8(960- 100)

The reason why we subtract 100 is because we paid the insurance company 100 dollars, so that is our own money going to the medical bills.

then we multiply 0.8 by 860

The values of the constants m and c include the following:

m = -1.3

c = 7.1

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Since the point P(-7, 2) is mapped onto P' (3, -11) by the reflection y = mx + c, we can write the following system of equations;

2 = -7m + c    ...equation 1.

-11 = 3m + c    ...equation 2.

By solving the system of equations simultaneously, we have:

2 = -7m - 3m - 11

11 + 2 = -10m

13 = -10m

m = -1.3

c = 7m + 2

c = 7(-1.3) + 2

c = -7.1

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Answer: f(n+1) =f(n)+2

Step-by-step explanation:

I did the test

Given parameters:

Dimension of the flowerbed  = 4ft by 7ft

Unknown:

Number of feet to build the flowerbed = ?

Since the flowerbed will be surrounding the flows, we should simply find the perimeter of the bed.

 This is a rectangular area;

  Perimeter = 2(L + B)

Input the parameters and solve;

   Perimeter  = 2 (4 + 7)

    Perimeter = 2 x 11 = 22cm

The perimeter of the board is 22cm

Step-by-step explanation:

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The function is increasing from (–∞, 0). Then the correct option is A.

If the value of y increases as the value of x increases, then increasing function.

And if the value of y decreases as the value of x increases, then decreasing function.

From the graph, the function is increasing from (–∞, 0).

Then the correct option is A.

The complete question is attached below.

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The mean of the test is 20.

To determine the mean of the test, we need to use the information provided about the scores falling above the mean in terms of standard deviations.

Let's denote the mean of the test as μ, and the standard deviation as σ.

We are given that a score of 29 falls three standard deviations above the mean, so we can write this as:

29 = μ + 3σ

Similarly, we are told that a score of 23 falls one standard deviation above the mean, which can be expressed as:

23 = μ + σ

Now we have a system of two equations with two variables (μ and σ). We can solve this system of equations to find the values of μ and σ.

From the second equation, we can isolate μ:

μ = 23 - σ

Substituting this value into the first equation, we have:

29 = (23 - σ) + 3σ

Simplifying the equation, we get:

29 = 23 + 2σ

2σ = 29 - 23

2σ = 6

σ = 3

Substituting the value of σ back into the second equation, we find:

μ = 23 - 3

μ = 20

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9514 1404 393

Answer:

  sin(D) = cos(E) = (√3)/2

  cos(D) = sin(E) = 1/2

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships between trig functions and right triangle sides.

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

For this diagram, this means ...

  sin(D) = cos(E) = (13√3)/26 = (√3)/2

  cos(D) = sin(E) = 13/26 = 1/2

Answer:

The range of the following set of points is {4, -2, -8}

Step-by-step explanation:

∵ The set of points is {(3, 4), (7, -2), (11, -8)}

∵ The range is the y-coordinates of these points

∵ The y-coordinates of the points are 4, -2, -8

∴ The range is {4, -2, -8}

∴ The range of the following set of points is {4, -2, -8}

Answer/Step-by-step explanation:

Given:

Data set for sandwich calories=> 242, 290, 290, 280, 390, 350

Mean: the mean is given as sum of all values in the data set ÷ total no. of data set given

\( \frac{242 + 290 + 290 + 280 + 390 + 350}{6} = \frac{1,842}{6} = 307 \)

Mean Absolute Value:

Step 1: find the absolute value of the difference between each value and the mean

|242 - 307| = 65

|290 - 307| = 17

|290 - 307| = 17

|280 - 307| = 27

|390 - 307| = 83

|350 - 307| = 43

Step 2: find the sum of all values gotten in step 1

65 + 17 + 17 + 27 + 83 + 43 = 252

Step 3: divide the result you get in step 2 by 6 to get the M.A.D

\( M.A.D = \frac{252}{6} = 42 \)

The Mean Absolute Value represents or gives us an idea how spread the data set for the number of sandwich calories are.

Thus, averagely, the number of calories of sandwich at the restaurant are far from the mean caloric value by 42 calories.

Answer:

the shoes

Step-by-step explanation:

the shoes never changed, and the amount money sarah has remaining will depend on the shoes.

Answer:

Step-by-step explanation:

Answer:

C.   AB=10.56, BC=7.68

Step-by-step explanation:

AB) 8.8x7.32÷6.1=10.56

BC) 6.4x7.32÷6.1=7.68

Answer:

Jada should use the tank of golf balls

Step-by-step explanation:

Jada should choose the tank that has a higher probability of choosing a ball with even number from.

Tank of tennis balls has two even numbers out of the ten balls (2, 4)

Tank of golf balls has seven even numbers out of the ten balls.

Tank of golf balls would give Jada more chance to pick an even number to win the game

Therefore, Jada should use the tank of golf balls

Answer:

6 is 56.25

7 is 97.50

Step-by-step explanation:

Answer:

To find the total number of beads Naina used to complete the ornament, we need to sum the number of beads in each layer.

Total number of beads = 45 + 42 + 39 + ... (continue the pattern until the 10th layer)

Notice that the number of beads in each layer decreases by 3. We can use arithmetic series formula to find the sum of the beads in all 10 layers:

S = (n/2) x (a + l)

where S is the sum, n is the number of terms, a is the first term, and l is the last term.

Here, a = 45, l = 18 (since the 10th layer will have 18 beads), and n = 10 (since there are 10 layers). Thus, we have:

S = (10/2) x (45 + 18) = 5 x 63 = 315

Therefore, Naina used a total of 315 beads to complete the ornament.

Answer:

The answer to your problem is, 1260

Step-by-step explanation:

Well we know she made 10 “ strand ornaments “ for each layers we would need to add;

45 + 42 + 39

= 126

We would actually then need to multiply it by 10. Shown:

126 × 10

= 1260

Thus the answer to your problem is, 1260

Option of the matrices a, b, and d are non symmetric.

Symmetric matrices are those matrices that have equal dimensions, i.e. the number of rows is same as the number of columns. They are also known as square matrices.

It is provided that A and B are symmetric n × n matrices.

To multiply two matrices of different order, the number of rows of the first matrix must be same as the number of columns of the second matrix.

Suppose X is a 2 × 3 matrix and Y is a 3 × 2.

Then the product AB will be a n × n matrix.

(a) A= C+CT

Thus the sum of matrix A and B will be a n × n matrix.

Thus, the matrix A is non symmetric.

(b) B = C-CT

So, matrix D will also be a n × n matrix.

Thus, the matrix D is non symmetric.

(c) D = CTC = (CT) × C

Then the product CT will be a n × n matrix.

The next step would be to multiply CT and C.

Both are n × n matrices.

Thus, the matrix D is symmetric.

(d) E = CTC - CCT

Then he product CT will be a n × n matrix.

Similarly, the product CT will be a n × n matrix.

Thus, the matrix E is non symmetric.

Similalry,

(e) F = (I +C)(I + CT

Thus, the matrix F is symmetric.

(f) G = (I +C)(I -CT)

Thus, the matrix G is symmetric.

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Answer:

1. y-intercept(s):

(0,−53)

x-intercept(s):  

(−5,0)

2. x-intercept(s):

(13,0)

y-intercept(s):

(0,1)

Step-by-step explanation:

Answer:

scale factor 9

Step-by-step explanation:

Scale factor is whatever u multiply your area by so it would be 9 cause it 9 times greater

Answer:

the answer is 9:1 because it means that for every 1 area of the original picture, the photograph is 9 times larger

The measure of angle A is 63°, the measure of side b is 22.34 feet and the measure of side a is 37.57 feet.

From the given triangle ABC,

∠A+∠B+∠C=180° (Angle sum property of a triangle)

∠A+32°+85°=180°

∠A+117°=180°

∠A=180°-117°

∠A=63°

We know that, the formula for sine rule is sinA/a=sinB/b=sinC/c

Here, sin63°/a = sin32°/b = sin85°/42

sin63°/a = sin32°/b = 0.9961/42

sin32°/b = 0.9961/42 and sin63°/a = 0.9961/42

0.5299/b = 0.9961/42

0.9961b=22.2558

b=22.2558/0.9961

b=22.34 feet

sin63°/a = 0.9961/42

0.8910/a = 0.9961/42

0.9961a=37.422

a=37.422/0.9961

a=37.57 feet

Therefore, the measure of angle A is 63°, the measure of side b is 22.34 feet and the measure of side a is 37.57 feet.

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