the sum of three consecutive even integers is 216. find the intergents

The polynomial with the given zeros is [tex]x^3 - (25/4)x^2 + (19/4)ix + (30/4)i.[/tex]

To find the factors corresponding to the given zeros, we can use the fact that if a number is a zero of a polynomial, then (x - zero) is a factor of the polynomial.

Given zeros: 5, -3/4, 2i

For the zero 5, the corresponding factor is (x - 5).

For the zero -3/4, the corresponding factor is (x + 3/4).

For the zero 2i, the corresponding factor is (x - 2i).

To find the complete polynomial, we can multiply these factors together:

[tex](x - 5)(x + 3/4)(x - 2i)[/tex]

To simplify the polynomial, we can multiply the factors using the distributive property:

[tex](x^2 - 5x + (3/4)x - 15/4)(x - 2i)[/tex]

Combining like terms:

[tex](x^2 - (17/4)x - 15/4)(x - 2i)[/tex]

Expanding further:

[tex]x^3 - (17/4)x^2 - (15/4)x - 2ix^2 + (34/4)ix + (30/4)i[/tex]

Simplifying and combining like terms, we have the final polynomial:

[tex]x^3 - (25/4)x^2 + (19/4)ix + (30/4)i[/tex]

Therefore , the polynomial with the given zeros is [tex]x^3 - (25/4)x^2 + (19/4)ix + (30/4)i.[/tex]

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Answer:

sorry

Step-by-step explanation:

One way to answer this is to expand the function:

    f(x) = (2x+6)(x-7)

          = 2x^2 - 14x + 6x - 42

          = 2x^2 - 8x - 42

And then use the formula [tex]x=\dfrac{-b}{2a}[/tex] to find the x-value of the vertex and then use that to find the y-value of the vertex, while is the minimum value.

x = -(-8) / 2(2)

   = 8/4

   = 2

f(2) = 2(2)^2 - 8(2) - 42

     = 2(4) - 16 - 42

     = 8 - 16 - 42

     = - 50

So the minimum value is -50, since (2,-50) is the lowest point on the parabola.

Answer:

Hi

Please mark brainliest

Step-by-step explanation:

First man walks in one hour =  6 miles

Second man walks in one hour =  10 miles

Since they are walking in opposite direction so distance between them after 1 hour   =  6 + 10 = 16 miles

Since after one hour they are 16 miles apart from each other

Therefore, they will be 200 miles apart  from their starting point

= 200 ÷ 16 = 12.5 hours.

Answer:

Answer:I believe the answer is 12.5 hours

Answer:I believe the answer is 12.5 hoursExplanation: one men walked 6 hours

the second men walked 10 hours

6+10=16 so they were 16 miles apart

200÷16=12.5 so the answer would be 12.5 hours

Answer:

a four-sided plane rectilinear figure with opposite sides parallel.

Step-by-step explanation:

Answer:

Parallelograms are a type of quadrilateral, which is a polygon with four sides. A parallelogram is a specific type of quadrilateral that has two pairs of parallel sides. This means that the opposite sides of a parallelogram are parallel and equal in length.

In addition to having parallel sides, parallelograms also have some other notable properties:

Opposite angles are congruent: The opposite angles of a parallelogram are equal in measure. This means that if you label the angles A, B, C, and D, then angle A is congruent to angle C, and angle B is congruent to angle D.

Step-by-step explanation:

Answer:

Step-by-step explanation:

do the parenthesis first (2+2)=4

then 8/2= 4

4(4)=16

Step-by-step explanation:

3pi / 10 * 180 / pi = 54 degrees.

The circumference of the circle would be 10 pi. Multiply this by 54/360 to get 1.5pi or 3 pi /2

Area of the circle would be 25 pi. Multiply this by 54/360 to get 3.75 pi or 15pi /4

I'm confused on part (c), is it not just the same question as part (b)?

All these answers are assuming that 3pi/10 is the central angle. If it is an inscribed angle, then the central angle would be 6pi/10 or 3pi/5.

Edit: if part (c) is talking about inscribed angle, then the degrees would be 108. Then you just multiply 25pi by 108/360 for your answer

Answer:

Step-by-step explanation:

a.

l=rθ (θ in radians)

l=5×3π/10=3π/2≈3/2×3.14≈3×1.57≈4.71 cm

area of sector=π×5²×3π/10×1/2π=15/4 π=15π/4 cm²

≈15/4 ×3.14

≈15×1.57/4

≈5.8875

≈5.89 cm²

Given statement solution is :- 9086 is a multiple of 4 because it can be divided by 4 without leaving a remainder.

Sum is a way of putting all things together. The sum brings two or more numbers together to make a new total.

A multiple of a number is the product obtained when the number is multiplied by another number (integer; not a fraction).

To complete the expression so that the results are multiples of 4, we can add multiples of 4 into each of the blank spaces. Here's an option:

1.0000 + 250 + 7836

By adding these numbers, we will get a result that is a multiple of 4:

1.0000 + 250 + 7836 = 9086

9086 is a multiple of 4 because it can be divided by 4 without leaving a remainder.

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The algebraic expression for √(4+x)(10-x), which is 121.

To find the value of √(4+x)(10-x) algebraically, we start by simplifying the given equation:

√(4+x) + √(10-x) = 6

To eliminate the square roots, we can square both sides of the equation:

(√(4+x) + √(10-x)[tex])^2 = 6^2[/tex]

Expanding the left side using the binomial formula, we get:

(4+x) + 2√[(4+x)(10-x)] + (10-x) = 36

Simplifying further:

14 + 2√[(4+x)(10-x)] = 36

Subtracting 14 from both sides:

2√[(4+x)(10-x)] = 22

Dividing both sides by 2:

√[(4+x)(10-x)] = 11

Now we can square both sides again to get rid of the square root:

[(4+x)(10-x)] = [tex]11^2[/tex]

Simplifying further:

(4+x)(10-x) = 121

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Answer:

An ordinary annuity has payments made at the end of each period, while an annuity due has payments made at the beginning of each period.

Now, let's calculate the future value of the annuity due, given that the future value of the ordinary annuity is $100,000 and the interest rate is 5 per cent.

Step 1: Determine the future value factor of the ordinary annuity.

Future Value of Ordinary Annuity (FVOA) = $100,000

Interest Rate (r) = 5% = 0.05

Number of Periods (n) = 5 years

Step 2: Use the FVOA formula to find the annuity payment (PMT).

FVOA = PMT * [(1 + r)ⁿ - 1] / r

$100,000 = PMT * [(1 + 0.05)⁵ - 1] / 0.05

PMT = $18,039.37 (approx.)

Step 3: Calculate the future value of the annuity due (FVAD).

FVAD = PMT * [(1 + r)ⁿ - 1] / r * (1 + r)

FVAD = $18,039.37 * [(1 + 0.05)⁵ - 1] / 0.05 * (1 + 0.05)

FVAD = $105,000 (approx.)

Step-by-step explanation:

This equation is not valid, as it leads to an inconsistency.

In Aaron's grade 7 class, the ratio of students with a brother is 1 in every 3 students. This means that for every 3 students in the class, there is 1 student who has a brother.

On the other hand, for the school overall, including Aaron's class, the ratio of grade 7 students with a brother is 5 out of every 12 students. This means that for every 12 grade 7 students, there are 5 students who have a brother.

Let's assume there are a total of N grade 7 students in the school.

In Aaron's class, the ratio of students with a brother is 1 in every 3 students. So, the number of students in Aaron's class with a brother can be calculated as N/3.

For the school overall, the ratio of grade 7 students with a brother is 5 out of every 12 students. So, the number of grade 7 students in the school with a brother can be calculated as (5/12) * N.

Since Aaron's class is part of the school overall, we can equate these two values:

N/3 = (5/12) * N

To solve for N, we can cross multiply:

12 * N = 3 * (5/12) * N

12 * N = 15 * N/12

144 * N = 15 * N

144 = 15

This equation is not valid, as it leads to an inconsistency.

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Given statement solution is :- Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

3.1 Activity: Procedural and Conceptual Understanding in Action

Content Area: Fractions

Problem: Comparing Fractions

Objective: Students will demonstrate both procedural and conceptual understanding of comparing fractions.

Activity Steps:

Begin by introducing the concept of fractions and reviewing the basic procedures for comparing fractions (e.g., finding a common denominator, cross-multiplying).

Provide students with a set of fraction comparison problems (e.g., 2/3 vs. 3/4, 5/8 vs. 7/12) and ask them to solve the problems using the traditional procedural approach.

After students have solved the problems procedurally, engage them in a group discussion to explore the underlying concepts and relationships between fractions. Ask questions such as:

What does it mean for one fraction to be greater than or less than another?

Can you explain why we need a common denominator when comparing fractions?

How can you visually represent and compare fractions to better understand their relative sizes?

Introduce visual aids, such as fraction bars or manipulatives, to help students visualize the fractions and compare them conceptually. Encourage students to reason and explain their thinking.

Have students revisit the fraction comparison problems and solve them again, this time using the conceptual understanding gained from the group discussion and visual aids.

Compare the students' procedural solutions with their conceptual solutions, and discuss the similarities and differences.

Conclude the activity by emphasizing the importance of both procedural and conceptual understanding in solving fraction comparison problems effectively.

By incorporating both procedural and conceptual approaches, this activity allows students to develop a deeper understanding of comparing fractions. The procedural approach provides them with the necessary steps to solve problems efficiently, while the conceptual approach helps them grasp the underlying principles and relationships involved in fraction comparison.

3.2 Example: Conceptual Knowledge vs. Procedural Knowledge

Conceptual knowledge refers to the understanding of underlying concepts, principles, and relationships within a domain, whereas procedural knowledge focuses on knowing the specific steps or procedures to perform a task without necessarily understanding the underlying concepts.

Example: Division of Fractions

Conceptual Knowledge: Understanding the concept of division as the inverse operation of multiplication, and recognizing that dividing fractions is equivalent to multiplying by the reciprocal of the divisor. This understanding allows for generalization and application of division concepts to various fractions.

Procedural Knowledge: Following the specific steps to divide fractions, such as "invert the divisor and multiply" or "keep-change-flip" method. This knowledge involves applying the procedure without necessarily grasping the underlying concept or reasoning behind it.

In this example, Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

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If x decreases by 8 units, then the variable y is increased by 8a/b units.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The parameters of the definition of the linear function are given as follows:

The function for this problem is given as follows:

ax + by = c.

In slope intercept form, we have that:

by = -ax + c

y = -ax/b + c/b.

Hence the slope is:

m = -a/b.

The slope is negative, hence if x decreases by 8 units, then the variable y is increased by 8a/b units.

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The cumulative probability 0.68 from the z-score for the cumulative probability 0.236, we find that 'c' is approximately 0.0686.

To determine the value of 'c' in the expression P(0.68 <= Z <= c) = 0.236, where Z is a standard normal random variable, we need to use the standard normal distribution table.

The standard normal distribution table provides the cumulative probability for values up to a given z-score. In this case, we are given the cumulative probability of 0.236.

To find the value of 'c', we need to look up the corresponding z-score in the table.

Look up the z-score for the cumulative probability 0.68 in the standard normal distribution table. The closest value in the table is 0.7486.

Subtract the z-score for the cumulative probability 0.68 from the z-score for the cumulative probability 0.236:

c = 0.7486 - 0.68 = 0.0686

In summary, to find the value of 'c' in the expression P(0.68 <= Z <= c) = 0.236, we use the standard normal distribution table to find the corresponding z-score. Therefore, the value of 'c' is approximately 0.0686.

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To refund and stop your subscription for Brainly.

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"A0" typically refers to a paper size under the ISO 216 standard, commonly known as the International Organization for Standardization (ISO) paper size system.

An "Interest Only" loan means that you only pay the interest on the loan for a specific period, typically a fixed number of years. During this period, your payments are applied only to cover the interest charges, and the principal amount of the loan remains unchanged.

An "Interest Only" loan means that you only pay the interest on the loan for a specific period, typically a fixed number of years. During this period, your payments are applied only to cover the interest charges, and the principal amount of the loan remains unchanged. As a result, the loan balance does not decrease, and you do not make progress in paying off the principal.

Once the interest-only period ends, you may have to start making payments that include both the principal and the interest, or you may need to refinance the loan. It's important to note that during the interest-only period, you are not making any progress in reducing the overall loan amount.

Regarding your second question, "A0" typically refers to a paper size under the ISO 216 standard, commonly known as the International Organization for Standardization (ISO) paper size system. However, the A0 paper size specifically refers to the largest commonly used paper size, measuring approximately 841 mm by 1189 mm (33.1 inches by 46.8 inches). It is often used for large posters, architectural plans, and other similar applications.

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Answer:

  319

Step-by-step explanation:

You want to know the 45th term of the arithmetic sequence that begins -33, -25, -17, ...

The general term of an arithmetic sequence with first term a1 and common difference d is ...

  an = a1 +d(n -1)

For a1 = -33 and d = (-25 -(-33)) = 8, the n-th term is ...

  an = -33 +8(n -1)

Then the 45th term is ...

  a45 = -33 +8(45 -1) = -33 +352 = 319

The 45th term of the sequence is 319.

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Trevor’s total investment is $2850.30.(Option-c)

Trevor buys 80 shares of Upton Group and 70 shares of TJH Small-Cap. The offer price for Upton Group is $18.96 and the offer price for TJH Small-Cap is $19.05. Therefore, Trevor's total investment is:

80 shares * $18.96 + 70 shares * $19.05 = $1516.80 + $1333.50 = $2850.30

The offer price is the price at which a mutual fund is sold to investors. It is calculated by adding the net asset value (NAV) of the fund to the sales charge. The NAV is the value of the fund's assets minus its liabilities. The sales charge is a fee that is paid to the fund's distributor.

Trevor's total investment of $2,850.30 is the sum of the offer prices of the two funds he purchased. The offer price of Upton Group is $18.96 per share, and the offer price of TJH Small-Cap is $19.05 per share. Trevor purchased 80 shares of Upton Group and 70 shares of TJH Small-Cap, so his total investment is 80 shares * $18.96 + 70 shares * $19.05 = $1516.80 + $1333.50 = $2850.30.(Option-c)

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Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

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The simplification of the expression ab³/a⁴b  +  (c²)³ is determined as b²/a³  +  c⁶.

The given expression is simplified as follows;

The given expression is written as;

ab³/a⁴b  +  (c²)³

To simplify the expression given above, we will divide the fraction with the common factor as follows;

From the numerator; ab³, we will factor out "ab"

From denominator; a⁴b, we will factor out "ab"

The resulting expression becomes;

ab³/a⁴b  +  (c²)³

= b²/a³  +  c⁶

Note: for the power of c, we simplify by multiplying 2 and 3 = 6

Thus, the simplification of the expression ab³/a⁴b  +  (c²)³ is determined as b²/a³  +  c⁶.

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The equation of the line in slope-intercept form is y = 3x + 4.

We can use the combination formula to determine how many different packages can be created from a set of 24 crayons with 36 different colours.

The formula for the mixture is provided by:

n C r equals n!/r! (n-r)!

where r is the number of items we want to choose, n is the total number of items, and! stands for the factorial of a number, which is the sum of all positive integers up to that number.

In this instance, we are trying to determine how many various methods there are to choose 24 crayons from a set of 36 colours, regardless of the sequence in which they are chosen. Consequently, we can apply the following combination formula:

36 C 24 = 36! / (24! * 12!)

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The multiplicative rate of change for the exponential function is

The multiplicative rate of change for an exponential function is determined by the base of the exponent.

In this case, the function is f(x) = 2(5/2)⁻ˣ,

where the base of the exponent is (5/2).

The multiplicative rate of change for an exponential function with a base greater than 1 is greater than 1, indicating exponential growth. Conversely, if the base is between 0 and 1, the multiplicative rate of change is less than 1, representing exponential decay.

In this function, the base (5/2) is greater than 1.

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The cost for 5 t-shirts, including Sales tax, is $53.

The cost of 5 t-shirts with a price of $10 each and a sales tax of 6%, we need to multiply the total price of the t-shirts by the sales tax rate and add it to the original price.

The original price of one t-shirt is $10. Therefore, the total price of 5 t-shirts is:

$10 * 5 = $50

To calculate the sales tax, we need to multiply the total price by the sales tax rate of 6%:

$50 * 6% = $50 * 0.06 = $3

Adding the sales tax to the total price:

$50 + $3 = $53

Therefore, the cost for 5 t-shirts, including sales tax, is $53.

The correct answer is: $53.

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The brother currently has $34. Let's assume the amount of money you currently have is represented by the variable "x" (in dollars).

According to the given information, two scenarios are presented:

Scenario 1: If you give your brother $5, then you both will have the same amount of money. This can be expressed as:

x - 5 = x + 5

Simplifying the equation:

-5 = 5

The equation is contradictory, which means this scenario is not possible.

Scenario 2: If your brother gives you $17, then you will have twice as much money as he will have. This can be expressed as:

x + 17 = 2(x - 17)

Expanding and simplifying the equation:

x + 17 = 2x - 34

x = 51

Therefore, you currently have $51. To find out how much money your brother currently has, we substitute this value back into the equation:

51 + 17 = 2(x - 17)

68 = 2(x - 17)

34 = x - 17

x = 51.

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Solution:

Let x be the number of dollars my brother has. Since we will have the same amount of money if I give him 5 dollars, I must have x + 10 dollars. (Make sure you see why I don't have x + 5 dollars. If I give him 5 dollars of my x + 10 dollars, then we will both have x + 5 dollars.)

If he gives me 17 dollars, then he will have x - 17 dollars and I will have x + 10 + 17 = x + 27 dollars. I'll then have twice as much money as he has, so

x + 27 = 2(x - 17) Expanding the right-hand side gives x + 27 = 2x - 34, so x = 61. So, my brother has $61, and I have $71

The divisor in the division problem is 21, given the values of dividend, quotient, and remainder as 1830, 87, and 3 respectively.

To find the divisor in a division problem with the given values of dividend, quotient, and remainder, we can use the formula:

Dividend = Divisor * Quotient + Remainder

Substituting the given values:

1830 = Divisor * 87 + 3

Rearranging the equation:

Divisor * 87 = 1830 - 3

Divisor * 87 = 1827

Divisor = 1827 / 87

Divisor = 21

Therefore, the divisor in the division problem is 21, given the values of dividend, quotient, and remainder as 1830, 87, and 3 respectively.

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Both calculations from part (1) and part (2) yield the same result of $0.86 for the new cost of the candy bar after 11 years.

Part 1 of 2:

The new cost of the candy bar after 11 years can be calculated by applying a 3% price increase each year to the original cost of $0.60.

To calculate the new cost after 11 years, we can use the formula:

New Cost = Original Cost * (1 + Percentage Increase)^Number of Years

Plugging in the values:

New Cost = $0.60 * (1 + 3%)^11

        ≈ $0.60 * (1 + 0.03)^11

        ≈ $0.60 * (1.03)^11

        ≈ $0.60 * 1.432364654

Rounding to the nearest cent, the new cost of the candy bar after 11 years is $0.86.

Part 2 of 2:

If the cost of the candy bar increased by 3% of the original cost each year for 11 years, we can calculate the final cost by multiplying the original cost by (1 + 3%) for each year.

Using the formula:

Final Cost = Original Cost * (1 + Percentage Increase)^Number of Years

Plugging in the values:

Final Cost = $0.60 * (1 + 3%)^11

          ≈ $0.60 * (1 + 0.03)^11

          ≈ $0.60 * (1.03)^11

          ≈ $0.60 * 1.432364654

Rounding to the nearest cent, the final cost would also be $0.86.

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Note: The complete question is - What will be the cost of the candy bar after a specific number of years if it originally sold for $.60 and undergoes a 3% price increase each year?

1. Using multiplication, the number of students from Mr. Murray's primary drama class going to the theatre for the show is 30.

2. The mass of the bus is measured in kilograms because 1,900 cannot represent the mass of a bus that can carry 10 students and the standard unit of mass in the International System (SI) is the kilogram (kg).

3. The number of Mr. Murray's students who should sit in each row, using division operation, is 6.

4. Using multiplication, the number of high school students in the theater for the show is 60, since they are two times as many high students as in Mr. Murray's class.

5. Using division, the number of high school students in each row is 12.

6. The total number of students seated in the theater is 90 with 6 primary school student and 12 high school student sitting (18 students) in each of the 5 rows of the theater.

The basic mathematical operations are addition, subtraction, multiplication, and division.

1. Mr. Murray's primary drama class:

The number of buses the class is traveling in = 3

The capacity for each bus = 10 stuents

The total number of students going to the show = 30 (3 x 10)

2. Mass of the Buses:

The mass of one bus = 1,900 kg

The masses of the three buses = 5,700 (1,900 x 3)

3. Theater Rows:

The number of rows in the theater = 5

The average number of students that can sit in each row = 6 (30 ÷ 5)

4. Mrs. Stewart's High School Class:

The number of high school students from Mrs. Stewart's class = 60 (30 x 2)

5.  The total number of high school students = 60

The number of rows in the theater = 5

The number of high school students in each row = 12 (60 ÷ 5)

6. The Theater Manager:

The total number of primary school students = 30

The total number of high school students = 60

The total number of students attending the show = 90 (30 + 60)

The number of students in each row = 18 (90 ÷ 5) or (12 + 6)

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Based on the information given, we can conclude that RM = 2, but we cannot determine the lengths of the other sides of the quadrilaterals without further information.

Given that quadrilateral YFGT can be mapped onto quadrilateral MKNR by a translation, we can use the information to determine the length of RM.

A translation is a transformation that moves every point of a figure by the same distance and in the same direction. In this case, the translation is such that the corresponding sides of the quadrilaterals are parallel.

Since TY = 2, and the translation moves every point by the same distance, we can conclude that the distance between the corresponding points R and M is also 2 units.

Therefore, RM = 2.

By the properties of a translation, corresponding sides of the two quadrilaterals are congruent. Hence, side YG of quadrilateral YFGT is congruent to side MK of quadrilateral MKNR, and side GT is congruent to NR. However, the given information does not provide any additional details or measurements to determine the lengths of these sides.

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