System of equations
Y=-1/2x+4 3x-4y=12

The value of equation is 1041 according to the commutative property.

According to the statement

We have to solve the given statement

So, For this purpose, We know that the

Commutative property is a binary operation is commutative if changing the order of the operands does not change the result.

From the given information, the equation is:

(2 x 105) + (3 x 104) + (5 x 103) + 4

Now, multiply this with the help of above written property

(210) + (312) + (515) + 4

522+515+4

Now, add the terms

1037+4

Then the solution is

1041.

Then to the commutative property, the solution become

1041.

So, The value of equation is 1041 according to the commutative property.

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The length of AC in triangle BAC is equal 10.7 units

In trigonometry, the cosine rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

The formula is given as

AC² = AB² + BC² - 2(AB)(BC) cos AC

AC² = 6² + 7² - 2(6)(7)cos110

AC = 10.7

Using cosine rule, the length of AC is 10.7 unit.

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The numbers arranged in increasing order are: 7.204, 7.24, 7.243, 72.4, 72.43 To arrange the given numbers in increasing order, we compare the digits from left to right.

Starting with the tenth place, we compare 7.204, 7.24, and 7.243. Since 7.204 has the smallest value in the tenths place, it comes first. Among the remaining numbers, 7.24 has the next smallest value in the tenths place, followed by 7.243.

Next, we compare the whole numbers. The value 72.4 comes before 72.43 since 72.4 has a smaller value in the whole number part.

Therefore, the numbers arranged in increasing order are: 7.204, 7.24, 7.243, 72.4, 72.43.

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Answer:

0,5(3x+12+8x)

0,5(11x+12)

5,5x+6

Answer:

5.5x + 6

Step-by-step explanation:

0.5{3x + 4(3 + 2x)}

Apply the distributive property, multiply 4 by 3 and 4 by 2x.

0.5(3x + 12 + 8x)

Add 3x and 8x

0.5(11x + 12)

Apply the distribdistributive proproperty again and multiply 0.5 by 11x and 0.5 by 12.

The product would be 5.5x + 6.

Answer:

309.82??

Step-by-step explanation:

I did the times they worked multiplied by how much they were being paid. and then I Mulitipled by the number of employees.

Therefore, 27/72 simplified to lowest terms is 3/8.

Answer:

The correct statements are: B and D.

Step-by-step explanation:

Standard deviation is one of the measure of dispersion or spread of a dataset from the average value of the dataset. The standard deviation measures the variability of the distribution of values.

The higher the spread or variability in the data set, the greater is the standard deviation value and thus greater will be the magnitude of the deviance of the value from their average.

Then the standard deviation (S.D.) is given by,

\(S.D.=\sqrt{\frac{1}{n-1}\sum\limits^{n}_{i=1} {(x_{i}-\bar x)^{2} }}\)

The correct statements are:

B. It is a measure of variability.

D. It is calculated using the mean.

Arithmetic Sequence

rows ---------32-n

first term ------------26-----------a

d---------------------------4

Sn = n/2( 2a+(n-1)d)

=32/2 (2*26+(31)4)

=16(52+124)

=16(176)

=2816 seats

If theater has 30 rows of seats, then the number of people that the theater will hold is 2400 people.

To find out how many people the theater will hold, we need to calculate the total number of seats across all 30 rows. Since the number of seats increases by 4 for each successive row, we can treat this as an arithmetic sequence.

The formula to find the sum of an arithmetic sequence is = (n/2) × (first term + last term),

where n = number of terms and the first and last terms are given,

In this case : First term = 22,

Last term = 22 + (30 - 1) × 4 = 22 + 116 = 138,

Number of terms (rows) = 30,

Sum = (30/2) × (22 + 138) = 15 × 160 = 2400;

Therefore, The theater will hold 2400 people.

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The recommended rule to sequence the jobs for minimum flow time is the EDD (Earliest Due Date) rule.

The EDD rule prioritizes jobs based on their due dates, where jobs with earlier due dates are given higher priority. By sequencing the jobs in order of their due dates, the goal is to minimize the total flow time, which is the sum of the time it takes to complete each job.

In this case, applying the EDD rule, the sequence of jobs would be as follows:

D (Due on Friday 10th June)

F (Due on Tuesday 14th June)

E (Due on Wednesday 15th June)

C (Due on Friday 17th June)

G (Due on Thursday 16th June)

H (Due on Saturday 18th June)

A (Due on Monday 13th June)

B (Due on Monday 20th June)

By following the EDD rule, we aim to complete the jobs with earlier due dates first, minimizing the flow time and ensuring timely delivery of the orders.

Therefore, the recommended rule for sequencing the jobs in this scenario is the EDD (Earliest Due Date) rule.

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This tells us that the matrices are linearly dependent.

If a, b is a multiple of c, d, and abcd is 0, then we can write this as a matrix equation:

[a b] [c] [0]

[c d] [d] = [0]

This tells us that the matrix [a b] is a left-multiple of the matrix [c d]. In other words, there exists some scalar k such that [a b] = k[c d].

From this, we can see that a, c is a multiple of b, d. This is because a = kc and b = kd. Therefore, a is a multiple of c, and b is a multiple of d.

This tells us that the matrices are linearly dependent. In general, whether a matrix is a multiple of another matrix or not depends on the specific elements of the matrices. In order to determine if a matrix is a multiple of another, one can use matrix algebra and linear algebra techniques to simplify the matrices and look for patterns.

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1.-2x+y=12 is Neither parallel nor perpendicular to the line.

2. 3x+2y=-2 is lines are perpendicular.

3. y=2/3x-1 is lines are parallel.

4. -2x+3y=11 is lines are parallel.

Given that,

Is each line in relation to the line 2x+3y=12 parallel, perpendicular, or neither parallel nor perpendicular.

We are given first equation: −2x+3y=12.

Converting it in slope-intercept form

3y=2x + 12

y= 2/3 x + 12/3

y= 2/3 x + 4.

Slope of the given equation is 2/3.

1) First option : -2x+y=12.

In slope-intercept form y = 2x +12.

Slope is 2 there.

neither parallel to the line nor perpendicular to it −2x+3y=12.

2) 3x+2y=-2

y = -3/2 x - 1

Slope = -3/2.

Slope are negative reciprocal of −2x+3y=12 equation.

Therefore, lines are perpendicular.

3) y=2/3x-1

Slope = 2/3.

Slopes are same therefore lines are parallel.

4) -2x+3y=11

y = 2/3 x + 11/3.

Slopes are same therefore lines are parallel.

Therefore, 1.-2x+y=12 is Neither parallel nor perpendicular to the line.

2. 3x+2y=-2 is lines are perpendicular.

3. y=2/3x-1 is lines are parallel.

4. -2x+3y=11 is lines are parallel.

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Answer:

x = 2 ; y= 4

Step-by-step explanation:

3x -2y = -2

y = -3x+10

3x + 6x -20 = -2

9x = 18

x = 2

y = -6 + 10

y = 4

Answer:

x = 2

y = 4

Steps:

given:

3x – 2y = -2

3x + y = 10

2y = 3x+2

y = (3x+2)/2

3x + y = 10

3x + (3x+2)/2 = 10

(6x+3x+2)/2 = 10

(9x + 2)/2 = 10

9x + 2 = 20

9x = 18

x = 2

y = 4

To find the average quarterly loads for the rest of the years, you can use the formula below:

Average Quarterly Load = Total Annual Load  4 For example, let's say the total annual load for Year 1 is 800.

To find the average quarterly loads for Year 1, we would divide 800 by 4 to get an average quarterly load of 200. Then, you can use this average quarterly load to find the seasonal indices for each quarter of each year.To find the seasonal index for a given quarter and year, you would divide the actual quarterly load by the average quarterly load for that year.

For example, let's say the actual load for Quarter 1, Year 1 is 240. To find the seasonal index for this quarter and year, we would divide 240 by 200 to get a seasonal index of 1.2. You would repeat this process for each quarter and year to find the seasonal indices for all quarters and years.

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The value of the logarithmic expression is (b) 0

From the question, we have the following parameters that can be used in our computation:

log₉(1ˣ)

The logarithmic rule log(1^b) = 0 can be used to evaluate log(1^x) base 9:

log₉(1ˣ)

This is true because

Since 1^x = 1, no matter what the value of x is,

Then log(1^x) base 9 = x = 0.

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Answer:

Cubic polynomial has zeros at x=−1x=−1 and 22, is tangent to x−x−axis at x=−1x=−1, and passes through the point (0,−6)(0,−6).

So cubic polynomial has double zero at x=−1x=−1, and single zero at x=2x=2

f(x)=a(x+1)2(x−2)f(x)=a(x+1)2(x−2)

f(0)=−6f(0)=−6

a(1)(−2)=−6a(1)(−2)=−6

a=3a=3

f(x)=3(x+1)2(x−2)f(x)=3(x+1)2(x−2)

f(x)=3x3−9x−6

Answer:

First, put a multiplications sign in between the brackets:

(5x - 2) * (3x + 4)

Then using distributive property:

5x(3x + 4) - 2(3x + 4)

Then using distributive proper once again:

15x^2 + 20x - 6x - 8

Finally, calculate:

15x^2 + 14x - 8

The answer is. \(15x^2-6x+12\)

The question is of the type in algebraic equations.

Here the first step is multiplying the two algebraic expressions.

5x is multiplied with 3x and 4

-2 should be multiplied by 3x and 4.

we will get. \(5x(3x+4)-2(3x+4)\)

Next, we get. \(15x^2+20-6x-8\) (calculating constants and variables)

Therefore, the final answer = \(15x^2-6x+12\).

This type of equation is called as quadratic equation with one variable as the degree of the equation is 2.

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Answer:

#1= 5x5=25

25x the amount of squares= 25x6= 150cm^2

#2=  1.5x2.6= 3.9ft.

3.9xamount of right angle triangles= 3.9x8=31.2ft^2

(^2 means squared)

The unit rate of commercials per hour is 12 commercials per hour

From the question, we have the following parameters that can be used in our computation:

Time = 1 1/2 hour

Commercials = 18

The unit rate of commercials per hour is calculated as

Unit rate = Commercials/Time

Substitute the known values in the above equation, so, we have the following representation

Unit rate = 18/(1 1/2)

Evaluate

Unit rate = 12

Hence, the unit rate is 12

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Answer: 12

Step-by-step explanation: The unit rate of commercials per hour is 12 commercials per hour

How to determine the unit rate of commercials per hour?

From the question, we have the following parameters that can be used in our computation:

Time = 1 1/2 hour

Commercials = 18

The unit rate of commercials per hour is calculated as

Unit rate = Commercials/Time

Substitute the known values in the above equation, so, we have the following representation

Unit rate = 18/(1 1/2)

Evaluate

Unit rate = 12

Hence, the unit rate is 12

According to Weber's law, two items must differ in weight by "5 percent"of weight in order to detect a difference.

We are given that Weber's law

For weight discrimination, Weber’s law states that the JND is proportional to the weight of the stimulus.

The JND is defined as the smallest difference between two weights that can be detected by an observer.

The proportionality constant is known as Weber’s fraction and varies depending on the type of stimulus and the sensory modality involved.

For weight discrimination, Weber’s fraction is typically around 2-3%.

This means that two items must differ in weight by approximately 2-3% of their weight in order to detect a difference.

The difference of weight in percent is 5%, the correct option is A.

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0.99999028444 is the probability that at most 22 heads occur.

What does the maths term "probability" mean?

The simple definition of probability is the likelihood that something will occur. We can discuss the probability of different outcomes if we are unclear of how an event will turn out. Probability is a measure of how likely or likely-possible something is to happen.

                               For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of flipping a coin and receiving heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.

probability of getting head,  P = 1/2 = 0.5

        q = 1 - p  = 1 - 0.5 = 0.5   and n = 25

 P(X ≤ 22)

 P(X = x ) = ⁿCₓ (q)ⁿ⁻ˣ (p)ˣ

      = 1 - P(x = 23) - P(24) - P(25)

  = 1 - ²⁵C₂₃(0.5)²⁵⁻²³ (0.5)²³ - ²⁵C₂₄ (0.5)²⁵⁻²⁴ (0.5)²⁴ - ²⁵C²⁵ (0.5)²⁵⁻²⁵ (0.5)²⁵

        = 0.99999028444

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1. The minimum sum of their squares is achieved when the two integers are 8 and 9, resulting in a sum of 793.

2.  The greatest possible area for the rectangle is 625 square centimeters, which occurs when the length is 25 cm and the width is also 25 cm.

The sum of two positive integers is 35. To find the minimum sum of their squares, let's assume the two integers are x and y.

Given: x + y = 35

We want to minimize the sum of their squares, which can be represented as:

S = x^2 + y^2

To solve this problem using quadratic functions, we need to express one variable in terms of the other and then substitute it into the equation for S.

From the given information, we have:

x = 35 - y

Substituting this into the equation for S, we get:

S = (35 - y)^2 + y^2

Expanding and simplifying, we have:

S = 1225 - 70y + y^2 + y^2

S = 2y^2 - 70y + 1225

Now, we have a quadratic function for S in terms of y. To find the minimum value of S, we can use the vertex formula:

The x-coordinate of the vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by x = -b / (2a).

In our case, a = 2, b = -70. Substituting these values into the formula, we get:

y = -(-70) / (2 * 2)

y = 35 / 4

y = 8.75

Since the variables represent positive integers, we will consider the nearest integer values of y, which are 8 and 9.

Checking the values of S at y = 8 and y = 9:

For y = 8:

S = 2(8^2) - 70(8) + 1225

S = 128 - 560 + 1225

S = 793

For y = 9:

S = 2(9^2) - 70(9) + 1225

S = 162 - 630 + 1225

S = 757

Therefore, the minimum sum of their squares is achieved when the two integers are 8 and 9, resulting in a sum of 793.

A rectangle has a perimeter of 100 cm. To find the greatest possible area for the rectangle, let's assume the length of the rectangle is x and the width is y.

Given: 2x + 2y = 100

We want to maximize the area of the rectangle, which can be represented as:

A = xy

To solve this problem using quadratic functions, we need to express one variable in terms of the other and then substitute it into the equation for A.

From the given information, we have:

x = (100 - 2y) / 2

x = 50 - y

Substituting this into the equation for A, we get:

A = (50 - y) * y

A = 50y - y^2

Now, we have a quadratic function for A in terms of y. To find the maximum value of A, we can again use the vertex formula:

The x-coordinate of the vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by x = -b / (2a).

In our case, a = -1, b = 50. Substituting these values into the formula, we get:

y = -(50) / (2 * -1)

y = 25

Checking the value of A at y = 25:

A = 50(25) - (25)^2

A = 1250 - 625

A = 625

Therefore, the greatest possible area for the rectangle is 625 square centimeters, which occurs when the length is 25 cm and the width is also 25 cm.

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Answer:

A: y = -4/5x + 3/2 i believe is the correct answer

Step-by-step explanation:

Answer:

Nickels are equal to 5 cent and pennies are equal to 1 so:

5 times 100 = 500

1 times 60 = 60

500 + 60 = 560

560 converted to dollars would be $5.60!

Step-by-step explanation:

Hope it helps! =D

The scale factor of dilation is 1/40 and the coordinates of F" are (1440, 600)

The image of the label is attached

Given that

D'E' = 36 units

Then, we have

D"E" = 0.9 units

The scale factor is calculated as

Scale factor = D"E"/D'E'

So, we have

Scale factor = 0.9/36

Evaluate

Scale factor = 1/40

So, the scale factor of dilation is 1/40

This is calculated as

F = F'/Scale factor

So, we have

F = (36, 15)/(1/40)

F = (1440, 600)

The trigonometry ratios are calculated as

sin(D") = EF/DF

cos(D") = DE/DF

tan(D") = EF/DE

So, we have the following approximated values

sin(D") = 15/39 = 0.36

cos(D") = 36/39 = 0.92

tan(D") = 0.36/0.92 = 0.39

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The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

Answer:

A = 2b² + 15b + 7

Step-by-step explanation:

Assuming the figure is a trapezium , then

the area (A) is calculated as

A = \(\frac{1}{2}\) h (b₁ + b₂)

where h is the perpendicular height between the parallel bases b₁ and b₂

here h = b + 7 , b₁ = 3b - 5 , b₂ = b + 7 , then

A = \(\frac{1}{2}\) (b + 7)(3b - 5 + b + 7)

   = \(\frac{1}{2}\) (b + 7)(4b + 2) ← expand factors using FOIL

   = \(\frac{1}{2}\) (4b² + 30b + 14) ← distribute parenthesis by \(\frac{1}{2}\)

   = 2b² + 15b + 7

Answer:

28

Step-by-step explanation:

Because by adding 28 to -28,you are adding to a negative number to same positive number,you get 0 each time

The employee's total earnings on $81,500 in Sales is $3,797.50.

The employee's total earnings on $81,500 in sales, we need to consider the graduated commission rates for the different portions of the sales.

For the first $50,000 in sales, the employee earns a 3.5% interest. So the earnings on the first $50,000 would be:

(0.035)(50,000) = $1,750

For the remaining sales over $50,000, the employee earns a 6.5% interest. So the earnings on the sales over $50,000 would be:

(0.065)(81,500 - 50,000) = (0.065)(31,500) = $2,047.50

The total earnings, we add the earnings from the first $50,000 to the earnings on the sales over $50,000:

$1,750 + $2,047.50 = $3,797.50

Therefore, the correct expression that represents the employee's total earnings on $81,500 in sales is option b:

(0.035)(50,000) + (0.065)(31,500)

Calculating this expression, we get:

$1,750 + $2,047.50 = $3,797.50

Hence, the employee's total earnings on $81,500 in sales is $3,797.50.

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