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Launch realize. 8-2: Find Volume of Cylinders (LMS graded)
8.2.PS-13
The cylinder shown has a volume of 824 cubic inches.
a. What is the radius of the cylinder? Use 3.14 for .
b. If the height of the cylinder is changed, but the volume
stays the same, then how will the radius change? Explain.
a. The radius of the cylinder is about 8.2 in³.
(Type an integer or decimal rounded to the nearest tenth as needed.)
10.7 in.
Question Help
◇

The area of the triangle with side lengths 5, 6, and 7 is approximately 14.6969 square units.

To find the area of a triangle when the lengths of its three sides are given (5, 6, and 7), we can use Heron's formula. Heron's formula states that the area of a triangle with side lengths a, b, and c can be calculated as:

Area = √(s(s - a)(s - b)(s - c))

where s is the semi perimeter of the triangle, given by:

s = (a + b + c) / 2

Let's calculate the area step by step:

Determine the lengths of the sides.

a = 5

b = 6

c = 7

Calculate the semi perimeter.

s = (a + b + c) / 2

s = (5 + 6 + 7) / 2

s = 18 / 2

s = 9

Apply Heron's formula to find the area.

Area = √(s(s - a)(s - b)(s - c))

Area = √(9(9 - 5)(9 - 6)(9 - 7))

Area = √(9(4)(3)(2))

Area = √(216)

Area = 14.6969 (rounded to four decimal places)

Therefore, the area of the triangle with side lengths 5, 6, and 7 is approximately 14.6969 square units.

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The distance from the point (-2, 4) to the line y = 2x - 2 is approximately 4.47 units (rounded to the nearest hundredth).

Step 1: To find the equation of the line perpendicular to y = 2x - 2 that goes through (-2, 4), we need to determine the negative reciprocal of the slope of the given line. The slope of the given line is 2, so the negative reciprocal of 2 is -1/2.

We can use the point-slope form of a linear equation to find the equation of the line. Using the point (-2, 4) and the slope -1/2, the equation of the line can be written as:

y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Substituting the values, we have:

y - 4 = -1/2(x - (-2))

y - 4 = -1/2(x + 2)

y - 4 = -1/2x - 1

y = -1/2x + 3

Therefore, the equation of the line perpendicular to y = 2x - 2 that goes through (-2, 4) is y = -1/2x + 3.

Step 2: Now we need to solve the system of equations formed by y = 2x - 2 and y = -1/2x + 3. We can do this by setting the two equations equal to each other and solving for x:

2x - 2 = -1/2x + 3

Multiplying both sides by 2 to eliminate the fraction:

4x - 4 = -x + 6

Bringing like terms to one side:

4x + x = 6 + 4

5x = 10

Dividing both sides by 5:

x = 10/5

x = 2

Substituting the value of x back into one of the equations (let's use y = 2x - 2), we can find the value of y:

y = 2(2) - 2

y = 4 - 2

y = 2

Therefore, the coordinates of the point of intersection are (2, 2).

Step 3: To find the distance between (-2, 4) and the point (2, 2), we can use the distance formula:

d = √([tex](x2 - x1)^2 + (y2 - y1)^2)[/tex]

Substituting the coordinates, we have:

d = √((2 - [tex](-2))^2 + (2 - 4)^2)[/tex]

d = √([tex](4)^2 + (-2)^2)[/tex]

d = √(16 + 4)

d = √20

d ≈ 4.47

Therefore, the distance from the point (-2, 4) to the line y = 2x - 2 is approximately 4.47 units (rounded to the nearest hundredth).

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Answer:

My friend you have to send a picture, we can't see through the screen

Answer:

I hope this helps.

Step-by-step explanation:

In an isosceles trapezoid, the two non-parallel sides (legs) are congruent, and the base angles opposite each other are also congruent. Let's denote the measures of the angles as follows:

Angle A: The top left angle.

Angle B: The top right angle.

Angle C: The bottom left angle.

Angle D: The bottom right angle.

In an isosceles trapezoid, angles A and B are congruent, and angles C and D are congruent. The sum of the interior angles of any quadrilateral is 360 degrees. Therefore, we can set up the following equation:

Angle A + Angle B + Angle C + Angle D = 360 degrees

Since angles A and B are congruent, and angles C and D are congruent, we can rewrite the equation as:

2(A) + 2(C) = 360 degrees

Simplifying further:

2A + 2C = 360 degrees

Dividing both sides of the equation by 2:

A + C = 180 degrees

In an isosceles trapezoid, the base angles (C and D) are supplementary angles, meaning they add up to 180 degrees. Therefore, the measure of each base angle (C and D) is 180 degrees divided by 2:

Each base angle (C and D) = 90 degrees.

Since the sum of the interior angles in a quadrilateral is 360 degrees, and angles C and D (the base angles) each have a measure of 90 degrees, the sum of angles A and B (the top angles) must be:

Angle A + Angle B = 360 degrees - (Angle C + Angle D)

Angle A + Angle B = 360 degrees - (90 degrees + 90 degrees)

Angle A + Angle B = 360 degrees - 180 degrees

Angle A + Angle B = 180 degrees

Therefore, in an isosceles trapezoid, each top angle (A and B) has a measure of 180 degrees divided by 2:

Each top angle (A and B) = 90 degrees.

To summarize:

Each top angle (Angle A and Angle B) measures 90 degrees.

Each base angle (Angle C and Angle D) measures 90 degrees.

The cardinal number for the given set. A {20, 22, 24, 26, 34} sees; The given set has a cardinal number of 5.

This is further explained below.

Generally, cardinal numbers are an extension of the natural numbers that are used to assess the cardinality of sets. Cardinals are often referred to by their shorter form, cardinals. A finite set has a cardinality that is equal to a natural number, which is the number of items that are included inside the set.

A set of counting numbers is called its cardinal number. There is speculation that they are cardinals as well. Cardinal numbers are whole, non-fractional numerals, beginning with 1 and continuing in numerical order. Cardinal numbers include 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20.

To conclude it, The provided set A equals {20, 22, 24, 26, 34}

The number of unique components that make up a set is referred to as the cardinal number.

The given set has a cardinal number of 5, which is denoted by the notation n(A).

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Answer: The cardinal number for the given set is 5

Step-by-step explanation:

The cardinal number for a set is the quantity, or how many numbers are in the set. Since Set A has these numbers {20, 22, 24, 26, 34}, you can easily indicate how many numbers are in there. The n(a) quantity in the set would be the number five.

Since there is five numbers in this set, therefore, the cardinal number for the given set would be simply 5.

140

Step-by-step explanation:

Area of parallelogram=bxh

=14x10

=140

Answer:

140 square units

Step-by-step explanation:

The area of a parallelogram can be found by multiplying the length of its base by its height.

[tex]\boxed{\sf Area = base \times height}[/tex]

From inspection of the given parallelogram, its height is 10 units.

Since the lengths of opposite sides in a parallelogram are equal, the base of the given parallelogram is 14 units.

Therefore, the area of the parallelogram is:

[tex]\begin{aligned}\sf Area&=14 \times 10\\&=140\; \sf square\;units\end{aligned}[/tex]

The given algebraic expression is written as:

4b/n³ > 7b/4

Algebraic expressions are defined as the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra makes us to know how to express an unknown value with the aid of letters such as x, y, z, etc. These letters are referred to as variables. An algebraic expression can even be a combination of both variables as well as constants. Any value that is placed before and multiplied by a variable is a coefficient.

4b divided by n cubed more than 7b divided by 4, cubed can be expressed as:

4b/n³ > 7b/4

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The percent of the original price you end up paying is 42%.

Let's assume that the original price of an item is $100

The first discount of 25% off would reduce the price by:

25% of $100 = $25

So the sale price after the first discount is:

$100 - $25 = $75

Then, the store is offering an additional discount of 45% off on the clearance items.

The discount is removed from the sale price after the first discount:

45% of $75 = $33

So the final sale price after both discounts is:

$75 - $33 = $42

Therefore, you end up paying $42 for an item that originally cost $100. This is equivalent to paying:

($42 / $100) x 100% = 42% of the original price.

Hence, the percent of the original price you end up paying is 42%.

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Step-by-step explanation:

For angles outside circle    angle = 1/2 ( large arc - small arc)

46 = 1/2 [  21x-5  - (x + blank) ]

92 =   21x -5 - x -blank

97 = 20x - blank

97 = 20x - 23

120 = 20 x

x = 6

Answer: The angulier expression

Step-by-step explanation:

The parametric equations representing the same path as the given equations are: x = 1

y = 4sin(1)

To identify the parametric equations that represent the same path as the given equations x = 2 + 1 and y = 4 sin(theta), we can eliminate the parameter theta to express x and y in terms of a new parameter, let's call it t.

We know that [tex]cos^2(theta) + sin^2(theta)[/tex] = 1 (from the Pythagorean identity). Rearranging this equation, we have:

[tex]sin^2(theta) = 1 - cos^2(theta)[/tex]

Now, let's substitute the given equations into this identity:

[tex]sin^2(theta) = 1 - (2 + cos(theta))^2[/tex]

[tex]sin^2(theta) = 1 - (4 + 4cos(theta) + cos^2(theta))[/tex]

[tex]sin^2(theta) = 1 - 4 - 4cos(theta) - cos^2(theta)[/tex]

[tex]sin^2(theta) = -3 - 4cos(theta) - cos^2(theta)[/tex]

Next, let's substitute [tex]sin^2(theta) with (1 - cos^2(theta))[/tex]in the y equation:

[tex](1 - cos^2(theta)) = -3 - 4cos(theta) - cos^2(theta)[/tex]

Simplifying the equation, we get:

[tex]2cos^2(theta) + 4cos(theta)[/tex]+ 2 = 0

Dividing the equation by 2, we have:

[tex]cos^2(theta) + 2cos(theta[/tex]) + 1 = 0

This equation can be factored as:

[tex](cos(theta) + 1)^2[/tex]= 0

Taking the square root of both sides, we get:

cos(theta) + 1 = 0

cos(theta) = -1

Therefore, the value of cos(theta) is fixed at -1 for all values of theta.

Substituting cos(theta) = -1 into the given equations, we have:

x = 2 + (-1) = 1

y = 4sin(1)

Hence, the parametric equations representing the same path as the given equations are:

x = 1

y = 4sin(1)

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hello

the answer to the question is:

length A = 5 ft

length B = 4 ft

total volume = (8 × 3 × 2) + (4 × 5 × 2) = 88 ft³

The artist should buy the canvas with dimensions [tex]$10" \times 16"$[/tex]. This canvas has an aspect ratio of [tex]1.6[/tex], which is the closest among the available options to the Golden Ratio of [tex]1.618[/tex].

To determine which canvas size most closely matches the Golden Rectangle, we need to calculate the aspect ratio for each canvas and compare it to the Golden Ratio.

The Golden Ratio, also known as Phi [tex]($\varphi$)[/tex], is approximately [tex]1.618[/tex].

Let's calculate the aspect ratios for each canvas:

Canvas 1: [tex]$24" \times 36"$[/tex]

Aspect ratio = [tex]$\frac{36}{24} = 1.5$[/tex]

Canvas 2: [tex]$24" \times 40"$[/tex]

Aspect ratio = [tex]$\frac{40}{24} \approx 1.667$[/tex]

Canvas 3: [tex]$10" \times 16"$[/tex]

Aspect ratio = [tex]$\frac{16}{10} = 1.6$[/tex]

Canvas 4: [tex]$26" \times 16"$[/tex]

Aspect ratio = [tex]$\frac{16}{26} \approx 0.615$[/tex]

Canvas 5: [tex]$20" \times 12"$[/tex]

Aspect ratio = [tex]$\frac{12}{20} = 0.6$[/tex]

To find the canvas that most closely matches the Golden Ratio, we need to choose the canvas with an aspect ratio closest to [tex]1.618[/tex].

Calculating the differences between the aspect ratios and the Golden Ratio:

Canvas 1: [tex]$|1.5 - 1.618| \approx 0.118$[/tex]

Canvas 2: [tex]$|1.667 - 1.618| \approx 0.049$[/tex]

Canvas 3: [tex]$|1.6 - 1.618| \approx 0.018$[/tex]

Canvas 4: [tex]$|0.615 - 1.618| \approx 1.003$[/tex]

Canvas 5: [tex]$|0.6 - 1.618| \approx 1.018$[/tex]

The canvas with the aspect ratio closest to the Golden Ratio is Canvas 3: [tex]$10" \times 16"$[/tex], as it has the smallest difference of approximately [tex]0.018[/tex].

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To find out what percentage 25 is of 500, you can use the following formula:

percentage = (part / whole) x 100

In this case, 25 is the part and 500 is the whole. So, we can substitute these values into the formula:

percentage = (25 / 500) x 100

Simplifying the equation:

percentage = 0.05 x 100

percentage = 5%

Therefore, 25 is 5% of 500.

I hope it helps!

Answer:

5 % of 500 is 25

Step-by-step explanation:

500 * x% = 25

Divide each side by 500

x% = 25/500

x% = .05

Change to percent

x = 5

5 % of 500 is 25

The sequence of transformations includes translation, rotation, and reflection. The resulting image is congruent to the original if the transformations maintain the size, shape, and orientation of the object.

I need to know the specific transformations that you're referring to. However, I can provide you with a general explanation using the common types of transformations.

The sequence of transformations typically includes translation, rotation, and reflection. A translation involves moving an object from one location to another without changing its size or orientation. Rotation is the turning of an object around a fixed point, while reflection is flipping an object over a line, like a mirror image.

The resulting image is congruent to the original if the transformations preserve the size, shape, and orientation of the object. In the case of translation and rotation, the resulting image is always congruent to the original because the size and shape of the object do not change.

However, for reflection, the image remains congruent only if the reflection line is aligned with the symmetry axis of the object, preserving the shape and size.
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Answer:

Step-by-step explanation:

You want the domain and range of the function ...

  f(x) = 5·|x|

The domain of the function is the set of values of x for which it is defined. Here, the absolute value function is defined for all values of x.

The domain is all real numbers.

The range is the set of output values the function can produce. The absolute value function can produce any non-negative number.

The range is all real numbers greater than or equal to zero.

<95141404393>

Answer:

a) (1,4), b) -1 and 3, c) 3

Step-by-step explanation:

a) coordinates of turning point are the peak of the graph. this occurs at (1,4),

b) f(x) = 0 means where the graph meets x-axis. it meets x-axis at x = -1 and x =3,

c) f(0) means where the graph crosses the y-axis. it crosses at y = 3

Answer:

28.2 cm

Step-by-step explanation:

Circumference of circle = 2π r

Value of π = 3.14

Putting the required values,

Circumference = 2 × 3.14 × 4.5

= 6.28 × 4.5

= 28.2

Hence the circumference of the circle is 28.2 cm

Party A received the most votes with a total of 47 votes, while Party B received 38 votes.

To determine which party received the most votes, we need to calculate the number of votes for each party based on the given percentages and population distribution.

Let's assume the total population is 100 for easier calculations.

Based on the given information:

33% of the population (33 out of 100) said they would vote for Party A.

10% of the population (10 out of 100) said they would vote for Party B.

15% of the population (15 out of 100) said they would not vote.

So far, we have accounted for 33 + 10 + 15 = 58 people.

The remaining population is 100 - 58 = 42 people.

In the rest of the population:

1/3 (1/3 × 42) = 14 people voted for Party A.

2/3 (2/3 × 42) = 28 people voted for Party B.

Now let's calculate the total votes for each party:

Party A received 33 (from initial survey) + 14 (from the rest of the population) = 47 votes.

Party B received 10 (from initial survey) + 28 (from the rest of the population) = 38 votes.

Therefore, Party A received the most votes with a total of 47 votes, while Party B received 38 votes.

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2x² - 6x = -7 equation has  imaginary solutions

To determine if an equation has imaginary solutions, we can examine the discriminant of the quadratic equation

x² + 3x - 5 = 0

a = 1, b = 3, c = -5

Discriminant = (3)² - 4(1)(-5) = 9 + 20 = 29

The equation has two real solutions

x⁴ - 5x ^ 2 + 3 = 0

This equation is a quartic equation, not a quadratic equation. Quartic equations can have both real and imaginary solutions

2x² - 6x = -7

2x^2 - 6x + 7 = 0

a = 2, b = -6, c = 7

Discriminant = (-6)²- 4(2)(7) = 36 - 56 = -20

Since the discriminant (-20) is negative, the equation has two complex (imaginary) solutions.

-3x² = -5

Dividing both sides by -3, we get:

x²= 5

a = 1, b = 0, c = -5

Discriminant = 0² - 4(1)(-5) = 20

The equation has two real solutions.

Hence, 2x² - 6x = -7 equation has imaginary solutions

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Answer:

50:1

Step-by-step explanation:

There are 50 goats and 1 chicken

The GCD of 50 and 1 is 1 so you can't simplify

The measure of the angles are;

<1 = 109 degrees

<2 = 39 degrees

<3 = 71 degrees

We need to know the following about triangles, we have that;

From the information given, we have that;

For triangle UVT, we get;

35 + 36 + <1 = 180

add the like terms, we have;

<1 = 180 -71

<1 = 109 degrees

<2 + 80 + 71 = 180

collect terms

<2 = 180 - 151

<2 = 39 degrees

<3 = 71 degrees

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Answer: 0.14 cubic meters

To cover the rectangular yard with a concrete layer one tenth of a meter thick, we need to find the volume of concrete required, which can be calculated as:

Volume = area * thickness

The area is the product of the length and width of the rectangular yard, and the thickness is one tenth of a meter.

The length of the rectangular yard is given as 0.2 meters, the width is given as 7 meters, and the thickness is 0.1 meters.

So, the volume of concrete is:

Volume = 0.2 meters * 7 meters * 0.1 meters = 0.14 cubic meters

Hope this helps!

The statement is incorrect because a confidence interval provides a range where we are 90% confident that the population mean falls, not where 90% of the data lies.

The statement made by the classmate is incorrect.

A 90% confidence interval does not represent the range in which 90% of the data falls. Instead, it provides a range of values within which we can be 90% confident that the true population parameter lies. In this case, the interval is given as 22.5 < u < 32.0, where "u" represents the population mean.

To clarify, a 90% confidence interval implies that if we were to take multiple samples from the population and calculate the confidence interval for each sample, approximately 90% of those intervals would contain the true population mean.

It is important to understand that a confidence interval does not describe the distribution or range of the actual data points themselves. It is solely an estimate of where the population parameter (in this case, the mean) is likely to lie with a specified level of confidence.

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A Normal distribution has skewness and kurtosis values close to zero.

There are several methods that can be used to assess whether a variable follows a normal distribution.

1. Histogram: Creating a histogram of the variable's data can provide a visual representation of its distribution. If the histogram displays a bell-shaped curve with a symmetric pattern, it suggests the variable may follow a normal distribution. However, this method is subjective and depends on the chosen bin width.

2. Normal probability plot: Also known as a Q-Q plot (quantile-quantile plot), this graphical tool compares the quantiles of the variable's data against the expected quantiles of a normal distribution. If the points on the plot roughly fall along a straight line, it suggests that the variable approximates a normal distribution.

3. Shapiro-Wilk test: The Shapiro-Wilk test is a statistical test that assesses the normality of a variable. It produces a test statistic and a p-value. If the p-value is greater than the chosen significance level (e.g., 0.05), it indicates that there is not enough evidence to reject the null hypothesis of normality.

4. Kolmogorov-Smirnov test: The Kolmogorov-Smirnov test compares the cumulative distribution function (CDF) of the variable's data with the expected CDF of a normal distribution. The test produces a test statistic and a p-value. Similarly, if the p-value is above the chosen significance level, it suggests the variable follows a normal distribution.

5. Skewness and kurtosis: Skewness measures the symmetry of a distribution, while kurtosis quantifies the shape of the distribution's tails. A normal distribution has skewness and kurtosis values close to zero. Assessing these measures can provide insights into the departure from normality.

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The slope of the line tangent to the graph is, 4

Since, The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

A line's slope is the change in y coordinate in relation to the change in x coordinate.

The net change in y-coordinate is denoted by y, whereas the net change in x-coordinate is denoted by x.

As a result, the change in y-coordinate in relation to the change in x-coordinate is given by,

m = difference in y/difference in x

    = dy/dx

We have to given that;

Equation is,

y = x² + 1

Now, Differentiate y = x² + 1 with respect to x we get;

y' = 2x + 0

y' = 2x

Since we have to find the slope

At point (2, 5),

So put x =2 we get,

y' = 2 x 2

y' = 4

Hence,

The slope of the line tangent to the graph y = x² + 1 is, 4

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Answer:

10 years old

Step-by-step explanation:

lets break it down:

6 more means +6

four times means *4

so if her son is x years old, she is 4x+6

since we know she's 46, we know that 4x+6=46

now we just solve the equation

4x+6=46

-6 on both sides

4x=40

/4 on both sides

x=10

The monthly subscription fee on a cellphone contract option pays for​:

By paying the monthly subscription fee, the expenses involved in establishing a link between your mobile device and the mobile network are taken care of. This feature enables you to initiate phone calls, transmit written messages, and access internet connectivity.

Your carrier's monthly subscription fee will encompass a payment for the device if you are leasing or financing it through them.

Your monthly payment contributes to the expenditure of catering for customer assistance. If you encounter any issues with the service, you may contact this team for assistance.

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The ordered pairs on the graph with the given equation will be of the form (x, 2).

Given a linear equation,

-4y = -8

We have to find the ordered pairs on the given graph.

Dividing both sides of the equation by -4,

y = 2

So for any point on the line, the y coordinate will be 2.

So any general point on the graph will be of the form, (x, 2).

Graph is a line parallel to the X axis.

Hence the orderd pairs are of the form (x, 2).

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================================================

Explanation:

The standard form for linear equations is Ax+By = C. Anything perpendicular to this would be of the form Bx-Ay = D.

The equation 2x+3y = 9 gives

The perpendicular template goes from Bx-Ay = D to 3x-2y = D.

Plug in the coordinates of (1,-2) to compute D.

3x-2y = D

D = 3x-2y

D = 3*1 - 2*(-2)

D = 7

Therefore, the perpendicular equation is 3x-2y = 7

-----------------------

We need to solve this system

[tex]\begin{cases}2x+3y = 9\\3x - 2y = 7\end{cases}[/tex]

to locate point M.

There are a few methods. I'll use substitution.

Solve the 1st equation for x.

2x+3y = 9

2x = -3y+9

x = (-3y+9)/2

x = -1.5y + 4.5

Then substitute this into the other equation to solve for y.

3x - 2y = 7

3( x ) - 2y = 7

3( -1.5y+4.5 ) - 2y = 7

-4.5y + 13.5 - 2y = 7

-6.5y + 13.5 = 7

-6.5y = 7-13.5

-6.5y = -6.5

y = -6.5/(-6.5)

y = 1

Use that to determine x.

x = -1.5y + 4.5

x = -1.5*1 + 4.5

x = 3

Point M is located at (x,y) = (3, 1)

------------------------

Use the distance formula to find the distance from A(1,-2) to M(3,1)

[tex]A = (x_1,y_1) = (1,-2) \text{ and } M = (x_2, y_2) = (3,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-3)^2 + (-2-1)^2}\\\\d = \sqrt{(-2)^2 + (-3)^2}\\\\d = \sqrt{4 + 9}\\\\d = \sqrt{13}\\\\d \approx 3.605551\\\\[/tex]

Segment AM is exactly [tex]\sqrt{13}[/tex] units long.

That is approximately 3.605551 units.

You can use a tool like GeoGebra to confirm the answers are correct.