1
Select the correct answer.
The surface area of a cone is 250 square centimeters. The height of the cone is double the length of its radius.
What is the height of the cone to the nearest centimeter?
O A.
OB.
O C.
10 centimeters
15 centimeters
5 centimeters
OD. 20 centimeters
Reset
Next

Answer:

  A.  p(t) = 16 -5t +2t²

Step-by-step explanation:

You want the interpolating polynomial for points (1, 13), (2, 14), and (3, 19).

The given system of equations can be solved by your favorite method to find ...

The interpolating polynomial is p(t) = 16 -5t +2t².

__

Additional comment

The points and the polynomial are graphed in the second attachment.

<95141404393>

The interpolating polynomial  is (a) p(t) = 13 - 2.5t +1.5t²

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

Points =  (1, 13), (2, 14), and (3, 19).

Using the general form of the quadratic formula, we have

a + b + c = 12

4a + 2b + c = 14

9a + 3b + c = 19

Subtract the equations to eliminate c

So, we have

3a + b = 2

5a + b = 5

Subtract the equations to eliminate b

So, we have

2a = 3

So, we have

a = 1.5

Next, we have

3a + b = 2

3(1.5) + b = 2

Evaluate

b = -2.5

Lastly, we have

4a + 2b + c = 14

4(1.5) + 2(-2.5) + c = 14

Evaluate

c = 13

So, the equation is p(t) = 13 - 2.5t +1.5t²

Read more about polynomial at

https://brainly.com/question/30833611

#SPJ1

Answer:

x = 13

Step-by-step explanation:

Since [tex]\angle M\cong \angle Y[/tex], then we set the angles equal to each other:

[tex]m\angle M=m\angle Y\\52^\circ=(4x)^\circ\\52=4x\\13=x[/tex]

Therefore, x=13

Answer:

x = 23

Step-by-step explanation:

the angle 117° is the sum of the 2 angles 94 and x , then

x + 94 = 117 ( subtract 94 from both sides )

x = 23

then ∠ x = 23°

The cosine function graphed in this problem is given as follows:

D. y = 3cos(2(x + π/3)).

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

y = Asin(B(x - C)).

For which the parameters are given as follows:

The function varies between -3 and 3, hence the amplitude is given as follows:

A = 3.

The coefficient B is given as follows:

B = 2.

The vertical shift is given as follows:

C = -π/3.

Hence the function is:

D. y = 3cos(2(x + π/3)).

More can be learned about trigonometric functions at brainly.com/question/21558626

#SPJ1

The errors in the proposed statement to prove by contradiction that 3·√2 - 7 is an irrational number, is the option;

Proving by contradiction is an indirect method of proving a fact or a reductio ad absurdum, which is a method of proving a statement by the assumption that the opposite of the statement is true, then showing that a contradiction is obtained from the assumption.

The definition of rational numbers are numbers that can be expressed in the form a/b, where a and b are integers

The assumption that 3·√2 - 7 is a rational number indicates that we get;

3·√2 - 7 = a/b, where a and b are integers

Therefore, the error in the method used to prove that 3·√2 - 7 is an irrational number is the option; To apply the definition of rational, a and b must be integers. This is so as the value 3·√2 - 7 is a real number, which is also an irrational number, thereby contradicting the supposition.

Learn more on rational numbers here: https://brainly.com/question/31330500

#SPJ1

There is no unique output for the manufacturing sector that can satisfy the given final demand for transportation and manufacturing.

To determine the output for the manufacturing sector, we can set up a system of equations based on the given information. Let's denote the output for the transportation sector as T and the output for the manufacturing sector as M.

From the given information, we know that:

- Production of a dollar's worth of transportation requires an input of $0.20 from transportation and $0.15 from manufacturing.

- Production of a dollar's worth of manufacturing requires an input of $0.40 from transportation and $0.30 from manufacturing.

Using these statements, we can set up the following equations:

0.20T + 0.15M = $60 million (equation 1)

0.40T + 0.30M = $80 million (equation 2)

We can solve this system of equations to find the values of T and M

Multiplying equation 1 by 2, we have:

0.40T + 0.30M = $120 million (equation 3)

Now, subtracting equation 2 from equation 3, we get:

(0.40T + 0.30M) - (0.40T + 0.30M) = $120 million - $80 million

This simplifies to:

0 = $40 million

This means that the left-hand side of the equation is zero, and there is no valid solution that satisfies both equations simultaneously.

Therefore, there is no unique output for the manufacturing sector that can satisfy the given final demand for transportation and manufacturing. The given information seems to be inconsistent or incomplete.

It's important to note that the problem could be resolved by providing additional information or correcting any errors in the given data. Without further clarification, it is not possible to determine the output for the manufacturing sector.

for more such question on manufacturing visit

https://brainly.com/question/25158645

#SPJ8

Answer:

10[tex]\sqrt{2}[/tex]

Step-by-step explanation:

√200 = √(2 × 2 × 2 × 5 × 5)

√200 = (√2)2× (√5)2× √2

√200 = 10√2

Answer:

The square root of 200 in its simplest form is 10√2 is the answer.

This can be done if we know the prime factorization of a number we can right the radical form of the square root of that number.

As a result the prime factorization of 200 is 2×2×2×5×5 so in that way the simplest form of square root of 200 is 10√2.

Step-by-step explanation:

There is no solution in the system

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

The augmented matrix

In the augmented matrix, we have

Rows = 2

Columns = 4

This means that

there are 2 equations in the system and there are 3 variables

The general rule is that

The number of variables must be equal to or less than the number of equations

Hence, there is no solution in the system

Read more about augmented matrix at

https://brainly.com/question/17031675

#SPJ1

The two types of frequency distributions are Discrete Frequency Distribution and Grouped Frequency Distribution

The two types of frequency distributions are;

When the data consists of discrete, separate values, this sort of distribution is used. It displays the frequency or number of occurrences of each value.

The data is often expressed in a table with two columns: one for distinct values and another for the frequencies of those values.

This distribution is utilized when the data is continuous and has a wide range of values. It entails categorizing the data into intervals or classes and then calculating the frequency of values that fall within each interval.

Learn more about frequency distribution at: https://brainly.com/question/27820465

#SPJ1

The homeowner should put aside $375.30 each month in order to save up for these expenses. Rounded to the nearest cent, this is $375.31.

The question asks us to determine how much a homeowner should put aside each month in order to save up for property taxes, homeowner's insurance, and car insurance expenses that come up every six months and annually.

To solve this problem, we can add up the total cost of all these expenses and divide by the number of months in a year, then round to the nearest cent.
Let's begin by finding the total cost of all these expenses. The homeowner pays property taxes twice a year, so that's a total cost of $1470 x 2 = $2940. The homeowner's insurance is paid once per year, with a cost of $918. The car insurance is paid twice a year, with costs of $285.78 + $359.79 = $645.57.
Adding up all these costs, we get: $2940 + $918 + $645.57 = $4503.57.
To determine how much to put aside each month, we divide this total by 12 (the number of months in a year): $4503.57 ÷ 12 = $375.30.

For more such questions on expenses

https://brainly.com/question/28995167

#SPJ8

E} The simplified form of √(1/32) is 1/(4√2).  A) the simplified form of [tex]√18x^4y^6z^8 is 3xy^3z^4√2.[/tex]

1. To simplify √18x^4y^6z^8, we can break down the radicand into its prime factors:

[tex]√(18x^4y^6z^8) = √(2 × 3^2 × x^2 × y^3 × z^4 × z^4)[/tex]

Next, we can simplify the square roots of perfect squares within the radicand:

√(2 × 3^2 × x^2 × y^3 × z^4 × z^4) = 3xy^3z^4√2

Therefore, the simplified form of √18x^4y^6z^8 is 3xy^3z^4√2.

2. To simplify √(1/6), we can rationalize the denominator:

√(1/6) = √(1)/(√(6))

Multiplying the numerator and denominator by √(6), we get:

√(1/6) = √(1)√(6)/√(6)√(6)

Simplifying further, we have:

√(1/6) = √(6)/6

Therefore, the simplified form of √(1/6) is √(6)/6.

3. To simplify 12√(8x^6y^3), we can break down the radicand into its prime factors:

[tex]12√(8x^6y^3) = 12√(2 × 2 × 2 × x^2 × x^2 × x^2 × y)[/tex]

Next, we can simplify the square roots of perfect squares within the radicand:

12√(2 × 2 × 2 × x^2 × x^2 × x^2 × y) = 12(2x^3)√2y

Therefore, the simplified form of 12√(8x^6y^3) is 24x^3√(2y).

4. To simplify 3√(16m^5n^7), we can break down the radicand into its prime factors:

3√(16m^5n^7) = 3√(2 × 2 × 2 × 2 × m × m × m × m × m × n × n × n × n × n × n × n)

Next, we can simplify the cube roots of perfect cubes within the radicand:

3√(2 × 2 × 2 × 2 × m × m × m × m × m × n × n × n × n × n × n × n) = 3(2m^2n^2)√(2mn)

Therefore, the simplified form of 3√(16m^5n^7) is 6m^2n^2√(2mn).

5. To simplify √(1/32), we can rationalize the denominator:

√(1/32) = √(1)/(√(32))

Since 32 can be simplified to 16 × 2, we have:

√(1/32) = √(1)/(√(16 × 2))

Taking the square root of 16 and simplifying further, we get:

√(1/32) = 1/(4√2)

Therefore, the simplified form of √(1/32) is 1/(4√2).

for more such question on simplified visit

https://brainly.com/question/723406

#SPJ8

Answer:

X=20

Step-by-step explanation:

20 On one side and the other side are mirror so

is 40

120-40=80

Both the top and lower triangles are similar which will be half divided

40 each scare now divide again for 2 parts of x

x=20

The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.

The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.

The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.

The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).

Based on this information, we can draw the following conclusions:

The graph will be a U-shaped curve with the vertex at (1, -9).

The vertex represents the minimum point of the parabola since it opens upward.

The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.

The graph will extend indefinitely in both directions.

To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.

Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.

​for such more question on parabola

https://brainly.com/question/9201543

#SPJ8

The z-score for a student who earned a 75 on the history test is -5/6.

To calculate the z-score for a student who earned a 75 on the history test, we need to use the formula:

z = (x - μ) / σ

Where:

x is the individual score (75 in this case),

μ is the population mean (average) of the scores (80),

and σ is the standard deviation of the scores (6).

Plugging in the values, we have:

z = (75 - 80) / 6

Simplifying the equation:

z = -5 / 6

Therefore, the z-score for a student who earned a 75 on the history test is -5/6.

The z-score represents the number of standard deviations a particular data point is away from the mean.

In this case, since the z-score is negative (-5/6), it indicates that the student's score of 75 is below the mean score of 80. The magnitude of the z-score (5/6) suggests that the student's score is approximately 0.83 standard deviations below the mean.

Z-scores are useful in comparing individual scores to the distribution of scores.

They provide a standardized measure of how a data point relates to the mean and standard deviation of a dataset. In this case, the negative z-score indicates that the student's score is below average, and the magnitude of the z-score gives a sense of the deviation from the mean.

For more such questions on  z-score visit:

https://brainly.com/question/28000192

#SPJ8

The value of f(g(-2)) - 150 is -138.

To find the value of f(g(-2)), we first need to substitute -2 into the function g(x) and then use the result as the input for the function f(x).

Let's start with g(-2). Plugging -2 into the function g(x) gives us:

g(-2) = (-2)^2 + 2

= 4 + 2

= 6

Now, we have the value of g(-2) as 6. Next, we substitute this value into the function f(x):

f(g(-2)) = f(6) = -1/2(6)^2 + 5(6)

= -1/2(36) + 30

= -18 + 30

= 12

Finally, we have found that f(g(-2)) is equal to 12. To find the value of f(g(-2)) - 150, we subtract 150 from the value we obtained:

f(g(-2)) - 150 = 12 - 150

= -138

Therefore, the value of f(g(-2)) - 150 is -138.

To learn more about the function

https://brainly.com/question/11624077

#SPJ8

Answer:

Step-by-step explanation:

The matrix system has no solution.

option D is the correct answer.

A general solution of a system of linear equations is a formula which gives all solutions for different values of parameters.

The given linear expression;

x₂ - 4x₃  + 3x₄

x₁ - 3x₂  + 8x₃ - 4x₄

The given expression in matrix form;

x₂ - 4x₃  + 3x₄   =    [0    1     - 4     3 ]

x₁ - 3x₂  + 8x₃ - 4x₄ [1     -3     8    -4 ]

The solution of the matrix can be determined by applying row reduction or using a method Cramer's method.

However, the matrix expression has no equal entity and therefore will not have a any solution, as it does not meet the criteria of an equation.

Learn more about matrix equations here: https://brainly.com/question/11989522

#SPJ1

a) The particle is farthest to the left at t = 0.

b) The speed of the particle is decreasing at t = π.

c) The value of k is 2π.

a) To find the time at which the particle is farthest to the left, we need to determine when the particle's position is at its minimum on the x-axis. The position function x(t) = [tex]e^t^2 cos(t^2)[/tex] represents the particle's position at time t.

To find the minimum, we can take the derivative of x(t) with respect to t and set it equal to zero. Let's differentiate x(t) to find the velocity function v(t):

v(t) = [tex](1/2)e^t^2 (cos(t^2) - sin(t^2))[/tex]

Next, we solve the equation v(t) = 0 to find the critical points:

0 = [tex](1/2)e^t^2 (cos(t^2) - sin(t^2))[/tex]

Since [tex]e^t^2[/tex] is always positive, the critical points occur when cos([tex]t^2[/tex]) - sin([tex]t^2[/tex]) = 0. By solving this equation, we find that it is true for t = 0 and t = π/2.

Now, to determine which critical point corresponds to the particle being farthest to the left, we evaluate the positions at t = 0 and t = π/2:

x(0) = [tex]e^0^2 cos(0^2)[/tex]= 1 * 1 = 1

x(π/2) = e(π/[tex]2)^2[/tex] cos((π/[tex]2)^2[/tex]) = [tex]e^{(\pi ^{2/4)[/tex] * 0 = 0

The particle is farthest to the left when x(0) = 1. Therefore, the particle is farthest to the left at t = 0.

b) To determine if the speed of the particle is increasing or decreasing at t = π, we need to analyze the velocity function v(t).

Let's calculate the derivative of v(t) with respect to t to find the acceleration function a(t):

a(t) = [tex]d(v(t))/dt[/tex] = [tex]d^2x(t)/dt^2[/tex] = [tex]e^t^2 * (-2t^2[/tex] - 2) * [tex]sin(t^2)[/tex]

To determine if the speed is increasing or decreasing, we need to evaluate a(t) at t = π. Plugging in t = π into the acceleration function, we have:

a(π) = [tex]e^\pi ^2 * (-2\pi ^2[/tex] - 2) * si[tex]n(\pi ^2[/tex]) = [tex]e^\pi ^2 * (-2\pi ^2[/tex] - 2) * 0 = 0

Since the acceleration at t = π is zero, the speed of the particle is neither increasing nor decreasing at that time.

c) The total distance traveled by the particle can be calculated by integrating the absolute value of the velocity function v(t) with respect to t over the interval [0, 2π]. The expression given is:

∫ v(t) dt from 0 to k − ∫ v(t) dt from 0 to 2π

To find the value of k, we can evaluate the integral on the right side:

∫ v(t) dt from 0 to 2π = ∫ [(1/[tex]2)e^t^2[/tex] (co[tex]s(t^2[/tex]) - [tex]sin(t^2[/tex]))] dt from 0 to 2π

Evaluating this integral gives us the total distance traveled by the particle over the interval [0, 2π]. Since k represents a different upper limit, the integral from

0 to k will give us the distance traveled up to the time t = k.

To find the value of k, we need to find the total distance traveled. Since the integral from 0 to 2π represents the total distance, we have k = 2π.

Therefore, the value of k is 2π.

For more such questions on speed, click on:

https://brainly.com/question/553636

#SPJ8

My experience with problem-solving in mathematics education has demonstrated its immense value in fostering students' mathematical proficiency, critical thinking abilities, and transferable skills. It has been an enriching journey to witness students grow as problem solvers, embracing challenges, and applying their mathematical knowledge to solve complex problems in creative and innovative ways.

Overall Experience with Problem-Solving in Mathematics Education:

For more such questions on mathematics education, click on:

https://brainly.com/question/17394553

#SPJ8

For each z-score:

z = -0.40: X value corresponds to a score below the mean and within approximately 0.3446 standard deviations.

z = 0.75: X value corresponds to a score above the mean and within approximately 0.7734 standard deviations.

z = -0.50: X value corresponds to a score below the mean and within approximately 0.3085 standard deviations.

z = 1.50: X value corresponds to a score above the mean and within approximately 0.9332 standard deviations.

z = 1.80: X value corresponds to a score above the mean and within approximately 0.9641 standard deviations.

z = -1.25: X value corresponds to a score below the mean and within approximately 0.1056 standard deviations.

To find the corresponding score (X value) for each z-score, we need to use the standard normal distribution table or a calculator.

z = -0.40:

Looking up the z-score of -0.40 in the standard normal distribution table, we find the corresponding area under the curve to be 0.3446. This means that the score (X value) is below the mean but within 0.3446 standard deviations. The specific X value will depend on the mean and standard deviation of the distribution.

z = 0.75:

Looking up the z-score of 0.75 in the standard normal distribution table, we find the corresponding area under the curve to be 0.7734. This means that the score (X value) is above the mean and within 0.7734 standard deviations.

z = -0.50:

Looking up the z-score of -0.50 in the standard normal distribution table, we find the corresponding area under the curve to be 0.3085. This means that the score (X value) is below the mean but within 0.3085 standard deviations.

z = 1.50:

Looking up the z-score of 1.50 in the standard normal distribution table, we find the corresponding area under the curve to be 0.9332. This means that the score (X value) is above the mean and within 0.9332 standard deviations.

z = 1.80:

Looking up the z-score of 1.80 in the standard normal distribution table, we find the corresponding area under the curve to be 0.9641. This means that the score (X value) is above the mean and within 0.9641 standard deviations.

z = -1.25:

Looking up the z-score of -1.25 in the standard normal distribution table, we find the corresponding area under the curve to be 0.1056. This means that the score (X value) is below the mean but within 0.1056 standard deviations.

The specific X values will depend on the mean and standard deviation of the distribution.

for such more question on  z-score

https://brainly.com/question/15222372

#SPJ8

Answer:

B. Positive linear

Step-by-step explanation:

First, this graph is a linear graph because a linear graph is a straight line. The graph in the diagram is also a straight line, so it is linear.
Also, notice how as x increases, y increases. This means that the graph is positive

Answer:

169

Step-by-step explanation:

360-[36+160]-36

360-160-72

169

Answer:

  40.45°

Step-by-step explanation:

You want the angle opposite the side of length 13 ft in a triangle with the other sides being 16 ft and 20 ft.

The law of cosines tells you ...

  c² = a² +b² -2ab·cos(C)

Then angle C is ...

  C = arccos((a² +b² -c²)/(2ab))

In the given triangle, this is ...

  C = arccos((16² +20² -13²)/(2·16·20)) = arccos(487/640) ≈ 40.453°

The measure of angle θ is about 40.45°.

<95141404393>

Answer:

Step-by-step explanation:

The side ratio for the triangle is given as follows:

tan(50º) = 1.193.

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

For the angle of 50º, we have that:

Hence the side ratio is given as follows:

tan(50º) = 3.58/3 = 1.193.

A similar problem, also about trigonometric ratios, is given at brainly.com/question/24349828

#SPJ1

The output when the input is 8 in the given number machine is 1.

The given number machine input is - x5 - -2 - output. Now, we have to find the output when the input is 8. Let's understand how we can solve this problem.

What is a number machine? The numbering machine is an imaginary box or machine that takes in a number and does a specific task on it to produce an output.

This concept is usually taught to children in primary grades. It is a fun way to introduce basic mathematical operations such as addition, subtraction, multiplication, and division.

The machine we are dealing with here subtracts the input by 5 and then subtracts 2 from the result to get the output. We can write this as output = (input - 5) - 2 Now we have to find out what the output would be when the input is 8. We can substitute 8 into the formula to get: output = (8 - 5) - 2 Simplifying this, we get: output = 3 - 2output = 1

Therefore, the output when the input is 8 in the given number machine is 1.

For more such questions on output

https://brainly.com/question/27646651

#SPJ8

The solutions to the quadratics are;

10) Option C

11) Option C

12) Option C

13) Option A

14) Option B

15) Option B

16) Option C

17) Option A

18) Option A

A quadratic equation is a polynomial equation of degree 2

10) To factor [tex]20z^2 - 3z - 9[/tex]we would have;

(5z + 3) (4z - 3)

11) [tex]2x^2 - 11x = 0[/tex]

x(2x - 11) = 0

x = 0, 11/2

12)[tex]x^2 - 100 = 0[/tex]

[tex](x - 10)^2[/tex]= 0

x = ± 10

13)

[tex]x^2 - 7x + 12 = 0\\x^2 - 4x - 3x + 12 = 0[/tex]

x(x - 4) -3(x - 4) = 0

(x - 3) (x - 4) = 0

x = 3 , 4

14)

[tex]3x^2 + 12x - 15 = 0\\3x^2 + 15x - 3x - 15 = 0[/tex]

3x(x + 5) -3 (x + 5) = 0

(3x - 3) (x + 5) = 0

x = 5 or 1

15)

[tex]x^2 = 25[/tex]

x = ±5

16)[tex]x^2 = 7[/tex]

x = √7

17) [tex]x^2 + 4x - 3 = 0[/tex]

x = -4 ±√(4)^2 - 4(-3)(1)/2(1)

x = -4  ±√16 + 12/2

x = -4  ±√28/2

x = -2  ± √7/2

18)

x^2 + 7x + 2 = 0

x = (-7) ±√(7)^2 - 4(2)(1)/2(1)

x =  (-7) ±√49 - 8/2

x =  (-7) ±√41/2

Learn more about quadratic equation:https://brainly.com/question/29269455

#SPJ1

The transformation from f(x) to g(x) is (b) a rotation and a translation

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

f(x) = x

g(x) = 1/9x - 2

First f(x) = x is transformed to f'(x) = 1/9x

This transformation is a rotation

Next, f'(x) = 1/9x is transformed to g(x) = 1/9x - 2

This transformation is a translation

This means that the transformation from f(x) to g(x) is a rotation and a translation

Read more about transformation at

https://brainly.com/question/32430073

#SPJ1

Answer:

[tex]\text{Midpoint of $AC$}=\left(-2,2\right)[/tex]

[tex]\text{Midpoint of $AB$}=\left(\dfrac{5}{2},3\right)[/tex]

[tex]\text{Slope of midsegment}=\dfrac{2}{9}[/tex]

[tex]\text{Slope of $AC$}=3[/tex]

[tex]\text{Slope of $BC$}=\dfrac{2}{9}[/tex]

[tex]\text{Length of midsegment}=\dfrac{\sqrt{85}}2[/tex]

[tex]\text{Length of $BC$}=\sqrt{85}[/tex]

Step-by-step explanation:

Given points:

To determine the midpoints of AC and AB, substitute the given points into the midpoint formula.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]

[tex]\begin{aligned}\text{Midpoint of $AC$}&=\left(\dfrac{x_C+x_A}{2},\dfrac{y_C+y_A}{2}\right)\\\\&=\left(\dfrac{-3-1}{2},\dfrac{-1+5}{2}\right)\\\\&=\left(\dfrac{-4}{2},\dfrac{4}{2}\right)\\\\&=\left(-2,2\right)\end{aligned}[/tex]

[tex]\begin{aligned}\text{Midpoint of $AB$}&=\left(\dfrac{x_B+x_A}{2},\dfrac{y_B+y_A}{2}\right)\\\\&=\left(\dfrac{6-1}{2},\dfrac{1+5}{2}\right)\\\\&=\left(\dfrac{5}{2},\dfrac{6}{2}\right)\\\\&=\left(\dfrac{5}{2},3\right)\end{aligned}[/tex]

[tex]\hrulefill[/tex]

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

To determine the slope of the midsegment, substitute the midpoints of AC and AB into the slope formula:

[tex]\begin{aligned}\text{Slope of midsegment}&=\dfrac{y_{AB}-y_{AC}}{x_{AB}-x_{AC}}\\\\&=\dfrac{2-3}{-2-\frac{5}{2}}\\\\&=\dfrac{-1}{-\frac{9}{2}}\\\\&=\dfrac{2}{9}\end{aligned}[/tex]

Therefore, the slope of the midsegment is 2/9.

To find the slope of AC, substitute the points A and C into the slope formula:

[tex]\begin{aligned}\text{Slope of $AC$}&=\dfrac{y_{C}-y_{A}}{x_{C}-x_{A}}\\\\&=\dfrac{-1-5}{-3-(-1)}\\\\&=\dfrac{-6}{-2}\\\\&=3\end{aligned}[/tex]

Therefore, the slope of the AC is 3.

**Note** There may be an error in the question. I think you are supposed to find the slope of BC (not AC) since there is no relationship between the slopes of the midsegment and AC, but there is a relationship between the slopes of the midsegment and BC.  

[tex]\begin{aligned}\text{Slope of $BC$}&=\dfrac{y_{C}-y_{B}}{x_{C}-x_{B}}\\\\&=\dfrac{-1-1}{-3-6}\\\\&=\dfrac{-2}{-9}\\\\&=\dfrac{2}{9}\end{aligned}[/tex]

The slope of BC is 2/9, so the slopes of the midsegment and BC are the same. This implies that the midsegment and BC are parallel.

[tex]\hrulefill[/tex]

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where:\\ \phantom{ww}$\bullet$ $d$ is the distance between two points. \\\phantom{ww}$\bullet$ $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

To find the length of the midsegment, substitute the endpoints (-2, 2) and (5/2, 3) into the distance formula:

[tex]\begin{aligned}\text{Length of midsegment}&=\sqrt{\left(\frac{5}{2}-(-2)\right)^2+(3-2)^2}\\\\&=\sqrt{\left(\frac{9}{2}\right)^2+(1)^2}\\\\&=\sqrt{\frac{81}{4}+1}\\\\&=\sqrt{\frac{85}{4}}\\\\&=\dfrac{\sqrt{85}}2\end{aligned}[/tex]

To find the length of the BC, substitute points B and C into the distance formula:

[tex]\begin{aligned}\text{Length of $BC$}&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(-3-6)^2+(-1-1)^2}\\&=\sqrt{(-9)^2+(-2)^2}\\&=\sqrt{81+4}\\&=\sqrt{85}\end{aligned}[/tex]

Therefore, the length of BC is twice the length of the midsegment.

Using unit multipliers:

27 cubic feet per minute is equivalent to approximately 57.074 liters per hour.

To convert 27 cubic feet per minute to liters per hour, we can use unit multipliers and conversion factors.

Start with the given value: 27 cubic feet per minute.

Use the conversion factor for volume: 1 cubic foot = 28.3168466 liters. This conversion factor allows us to convert cubic feet to liters.

Set up the first unit multiplier to cancel out the cubic feet:

Multiply by (27 cubic feet / 1) to cancel out the cubic feet unit.

Use the conversion factor for time: 1 minute = 60 minutes. This conversion factor allows us to convert minutes to hours.

Set up the second unit multiplier to convert minutes to hours:

Multiply by (60 minutes / 1 hour) to convert minutes to hours.

Combine the unit multipliers and the conversion factors:

Multiply (27 cubic feet / 1) by (1 cubic foot / 28.3168466 liters) by (60 minutes / 1 hour).

Simplify the expression by canceling out the appropriate units:

The cubic feet units cancel out, and the minutes units cancel out.

Perform the calculation:

(27 / 1) x (1 / 28.3168466) x (60 / 1) = 27 x 60 / 28.3168466 = 57.074 liters per hour.

Therefore, 27 cubic feet per minute is equivalent to approximately 57.074 liters per hour.

For more such questions on unit multipliers, click on:

https://brainly.com/question/31876127

#SPJ8