last month, you worked 140 hours. This month, you reduced your hours by 15 percent. How many hours did you work? brainly

The price that should be charged to maximize profits:  $80.5 (option a).

To determine the price that should be charged to maximize profits, we need to find the quantity that maximizes the firm's profit function. The profit function can be calculated by subtracting the total costs from the total revenue.

First, let's find the total revenue function. The demand equation given is P = 78 − 15Q, where Q = Q1 + Q2. We can rearrange this equation to express Q in terms of P: Q = (78 - P) / 15.

The total revenue function is calculated by multiplying the price (P) by the quantity (Q): TR = P * Q. Substituting Q, we get TR = P * [(78 - P) / 15].

Next, we need to find the total cost function. The marginal costs associated with producing in the two plants are MC1 = 3Q1 and MC2 = 2Q2. The total cost is the sum of the costs in both plants: TC = MC1 + MC2. Substituting the respective marginal cost equations, we get TC = 3Q1 + 2Q2.

Finally, we can calculate the profit function by subtracting the total cost from the total revenue: Profit = TR - TC.

Now, to find the price that maximizes profits, we need to differentiate the profit function with respect to price (P) and set it equal to zero. By solving this equation, we can find the value of P that maximizes profits.

Taking the derivative of the profit function with respect to P and setting it equal to zero, we get d(Profit)/dP = 0. Solving this equation will give us the value of P that maximizes profits.

After solving the equation, we find that P = $80.5 maximizes profits. Therefore, the price that should be charged to maximize profits is A) $80.5.

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Answer:

x = - 4

Step-by-step explanation:

∠ FEI and ∠ IED form ∠ FED , that is

∠ FEI + ∠ IED = ∠ FED ( substitute values )

x + 66 + x + 61 = 119

2x + 127 = 119 ( subtract 127 from both sides )

2x = - 8 ( divide both sides by 2 )

x = - 4

The width of the frame is 1 inch.

To determine the width of the frame, we must subtract the area of the picture from the total area.

Therefore: total area - picture area = frame area

261.44 - 168 = 93.44 square inches

The frame area can also be calculated by multiplying the frame width by 2 (since there are two sides of the frame) and adding it to the picture dimensions.

Thus:2w + 12 = length2w + 14 = width where w is the width of the frame.

Using the above equations, we can solve for w: 2w + 12 = 14, 2w = 2, and w = 1

Therefore, the width of the frame is 1 inch.

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Answer:

  (d)  x² -2x +3

Step-by-step explanation:

You want the quotient (x³ - 3x² + 5x - 3) ÷ (x - 1).

The constant in a product will be the product of the constants in the factors. That is if (x² +bx +c) is a factor of the cubic, we must have ...

  -1·c = -3 . . . . . . . where the other factor is (x -1), having constant -1

  c = 3

Only one answer choice matches: x²-2x+3.

Using synthetic division to find the entire quotient can be almost as fast.

The tableau is shown in the attachment. It tells you the quotient is ...

  x² -2x +3

__

Additional comment

"The entry in the left part of the table" is the zero of the binomial divisor. The divisor (x-1) is zero when x=1, so that entry is 1.

<95141404393>

Answer: I think it is 5

Therefore, The Volume of ORNAMENT ( B )  is  5^3  =  125  TIMES LARGER than the VOLUME of  ORNAMENT ( A ).

Hence, The VOLUME of ORNAMENT (B)  is  125 TIMES LARGER than the VOLUME of ORNAMENT (A).

MAKE A PLAN:

We know that the Height of ORNAMENT ( B )  is FIVE (5) Times Larger than the Height of ORNAMENT ( A ).  We need to Find the Ratio of their Volumes.

1) - Let the height of Ornament ( A )  be  hA   and the height of Ornament

   ( B )  be, hB

2) - We know the  hB  =  5  *   hA

3) - Since the Ornaments are Mathematically Similar, Their Volumes are Proportional to the Cube of their heights.

4) - Calculate The Ratio of their Volumes:

     (hB )^3 / (hA )^3  (5  *  hA )^3  /  (hA )^3

Therefore, The Volume of ORNAMENT ( B )  is  5^3  =  125  TIMES LARGER than the VOLUME of  ORNAMENT ( A ).

Hence, The VOLUME of ORNAMENT (B)  is  125 TIMES LARGER than the VOLUME of ORNAMENT (A).

I hope this helps you!

Answer:

a) 13

b) B

Step-by-step explanation:

y = x² - 3, where x= 4

• y= 4²-3

•y = 16-3

•y = 13.

(Hope I answered your question)

The height of the rectangular recycling bin is 7 ft.

To find the height of the rectangular recycling bin, we can use the formula for the surface area of a rectangular box:

Surface Area = 2lw + 2lh + 2wh

Given:

Length (l) = 16 ft

Width (w) = 9 ft

Surface Area = 638 ft²

Substituting these values into the surface area formula, we have:

638 = 2(16)(9) + 2(16)h + 2(9)h

638 = 288 + 32h + 18h

638 = 288 + 50h

350 = 50h

h = 350 / 50

h = 7

Therefore, the height of the rectangular recycling bin is 7 ft.

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The correct expression for the maximum number of cars that can be parked in the parking lot is 4c + 15. Option C

Given that there are 4 main rows with an equal number of parking spots in each row, and each row can accommodate c cars, the total number of parking spots in the main rows is 4c.

Additionally, there are 15 parking spots specifically allocated for store employees.

To find the maximum number of cars that can be parked in the parking lot, we need to add the number of parking spots in the main rows and the number of parking spots for employees.

Expression:

Total number of cars = Number of cars in main rows + Number of cars in employee spots

Number of cars in main rows = 4c

Number of cars in employee spots = 15

Therefore, the maximum number of cars that can be parked in the parking lot is:

Total number of cars = 4c + 15

This expression represents the sum of cars parked in the main rows and the cars parked in the employee spots, giving us the maximum capacity of the parking lot. Option C.

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The interval between neighboring x value is 1

the ratio between neighboring y-values 1

To find interval between neighboring x value, we subtract as follows

interval = 2 - 1 = 3 - 2 = 4 - 3 = 5 - 4 = 1

To find the ratio between neighboring y-values, we divide

ratio = 4 / 1 = 16/4 = 256 / 16 = 1024 / 256 = 4

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complete question

The table below represents an exponential function.

x

1

2

3

4

5

y

1

4

16

256

1,024

What is the interval between neighboring

X-values shown in the table?

What is the ratio between neighboring y-values?

There exists two solutions to the absolute value function |0.5x + 1| = 5.

The absolute value function in this problem is defined as follows:

|0.5x + 1| = 5.

The first solution is obtained as follows:

0.5x + 1 = -5

0.5x = -6

x = -6/0.5

x = -12.

The second solution is obtained as follows:

0.5x + 1 = 5

0.5x = 4

x = 4/0.5

x = 8.

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Answer:

Vertical Stretch

Step-by-step explanation:

The parent function [tex]f(x)=|x|[/tex] when multiplied by 2.5 is a vertical stretch of the absolute value equation. I've attached a graph so you can see the difference between the two functions.

[tex]{\huge{\blue{\bold{\mathfrak{Step\:by\:step\: solution}}}}}[/tex]

To divide 80,000,000 by 200, we can follow these steps:

1. Write out the division problem: 80,000,000 ÷ 200

2. Divide the first digit of the dividend (8) by the divisor (2), which gives us 4.

3. Write 4 above the second digit of the dividend (0), which gives us 40.

4. Subtract 40 from 80, which gives us 40.

5. Bring down the next digit of the dividend (0), which gives us 400.

6. Divide 400 by 200, which gives us 2.

7. Write 2 above the 0 in the dividend, which gives us 4000.

8. Subtract 4000 from 4000, which gives us 0.

So the answer is 400,000. To write it in standard form, we move the decimal point 5 places to the left, which gives us:

[tex]\purple{4 \times {10}^{5}} [/tex]

The answer is:

400,000

Work/explanation:

Divide:

80 000 000 ÷ 200

[tex]\sf{400,000}[/tex]

The answer is already in standard form.

Based on the analysis, the only statement that must be true is: -[tex]f^{(-1)(-8)} = -7[/tex]

Given that f is a one-to-one function, it implies that it has an inverse function denoted as [tex]f^{(-1)}.[/tex] The inverse function undoes the operation of the original function, such that [tex]f(f^{(-1)(x))} = x[/tex] for any x in the domain.

Now let's analyze the given options:

1. [tex]f^{(-1)(-8)} = 5[/tex]: We cannot determine the truth of this statement based on the given information. It depends on the behavior of the function f and its inverse.

2.[tex]f^{(-1)(-7)} = 8:[/tex] This option contradicts the given information. The value of f(-7) is -8, so the inverse function evaluated at -8 should yield -7, not 8.

3. [tex]f^{(-1)(5)} = -2[/tex]: We cannot determine the truth of this statement based on the given information. It depends on the behavior of the function f and its inverse.

4.[tex]f^{(-1)(-2)} = -5:[/tex]We cannot determine the truth of this statement based on the given information. It depends on the behavior of the function f and its inverse.

5.[tex]f^{(-1)(-8)} = -7:[/tex] This option aligns with the given information. The value of f(-7) is -8, so the inverse function evaluated at -8 should yield -7.

6. [tex]f^{(-1)(5)} = -7:[/tex] We cannot determine the truth of this statement based on the given information. It depends on the behavior of the function f and its inverse.

Based on the analysis, the only statement that must be true is:

[tex]f^{(-1)(-8)} = -7[/tex]

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Angle J is equal to 90°.Hence, the measure of Angle J is 90°.

Kayla can see that the measure of Angle I and Angle J form a straight line. Since Kayla knows that a straight line has an angle measure of 180°, what is the measure (in degrees) of Angle J

Given,The angle formed by angle I and J is a straight line which measures 180°.We need to find the measure of angle J.To find the measure of angle J, we need to find out the angle measure of angle I.

From the above information, we know that the angle formed by angle I and J is a straight line that measures 180°.So,Angle I + Angle J = 180°Substitute Angle I in terms of Angle J. We know that the angles are supplementary and they add up to 180 degrees.

If we know the measure of one of the angles, we can find the measure of the other angle as well.So ,Angle I = 180° - Angle JNow, substitute the value of Angle I in the above equation.Angle I + Angle J = 180°(180° - Angle J) + Angle J = 180°180° - Angle J + Angle J = 180°

Thus, Angle J is equal to 90°.Hence, the measure of Angle J is 90°.

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Using the function rule y = 5 + 5x, we can fill in the table as follows:

x | y

0 | 5

1 | 10

2 | 15

3 | 20

4 | 25

To fill in the table using the function rule y = 5 + 5x, we can substitute different values of x into the equation and calculate the corresponding values of y.

Let's create a table:

x | y

0 | 5 + 5(0) = 5 + 0 = 5

1 | 5 + 5(1) = 5 + 5 = 10

2 | 5 + 5(2) = 5 + 10 = 15

3 | 5 + 5(3) = 5 + 15 = 20

4 | 5 + 5(4) = 5 + 20 = 25

Using the function rule y = 5 + 5x, we can substitute each value of x into the equation to find the corresponding value of y. For example, when x = 0, y = 5. When x = 1, y = 10, and so on.

Therefore, the completed table is:

x | y

0 | 5

1 | 10

2 | 15

3 | 20

4 | 25

These values satisfy the given function rule y = 5 + 5x.

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Mill A and Mill B should be operated for 6 days each in order to meet the contract order most economically

Let's define the variables:

- Let 'x' represent the number of days mill A is operated per week.

- Let 'y' represent the number of days mill B is operated per week.

We need to minimize the cost function, which is the sum of the operating costs for both mills:

Cost = 1000x + 800y

Now, let's consider the production constraints:

For the HIGH grade flour:

Mill A produces 6 quintals per day, so the total weekly production is 6x.

Mill B produces 2 quintals per day, so the total weekly production is 2y.

To meet the contract requirement of 12 quintals per week, we have the constraint:

6x + 2y ≥ 12

For the MEDIUM grade flour:

Mill A produces 2 quintals per day, so the total weekly production is 2x.

Mill B produces 2 quintals per day, so the total weekly production is 2y.

To meet the contract requirement of 8 quintals per week, we have the constraint:

2x + 2y ≥ 8

For the LOW grade flour:

Mill A produces 4 quintals per day, so the total weekly production is 4x.

Mill B produces 12 quintals per day, so the total weekly production is 12y.

To meet the contract requirement of 24 quintals per week, we have the constraint:

4x + 12y ≥ 24

The graph will have the axes 'x' and 'y' representing the number of days mill A and mill B are operated, respectively.

Let's solve the problem graphically:

To plot each constraint, we can convert them into linear equations:

1) 6x + 2y ≥ 12

  Rewrite as: 3x + y ≥ 6

  Plot the line: 3x + y = 6

  From the graph, Mill A should be operated for 2 days per week while Mill B should be operated for 6 days per week.

2) 2x + 2y ≥ 8

  Rewrite as: x + y ≥ 4

  Plot the line: x + y = 4

  From the graph, Mill A should be operated for 4 days per week while Mill B should be operated for 4 days per week.

3) 4x + 12y ≥ 24

  Rewrite as: x + 3y ≥ 6

  Plot the line: x + 3y = 6

  From the graph, Mill A should be operated for 6 days per week while Mill B should be operated for 2 days per week.

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Answer: Assuming that you're asking what the y-intercept is, 11.2.

Step-by-step explanation:

y = mx + c,

where m is the slope and c is the y-intercept.

To calculate the slope, we use the formula:

m = (y2 - y1) / (x2 - x1),

where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively.

Using the coordinates of points A and B, we have:

m = (7 - 0) / (3 - 8)

m = 7 / (-5)

m = -7/5

Now we can substitute the values of the slope (m) and the coordinates of one point (A) into the slope-intercept form to solve for the y-intercept (c):

0 = (-7/5)(8) + c

0 = -56/5 + c

To isolate c, we can add 56/5 to both sides:

56/5 = c

Therefore, the y-intercept of the line passing through points A (8, 0) and B (3, 7) is (0, 56/5) or 11.2 when expressed as a decimal.

Answer:

The unit rate is 25$

Step-by-step explanation:

The unit rate gives the amount by which the money in the his account increases per month. It measures the rate of increase in the account.Which in this case the unit rate is 25$

Answer:

9 and -i

Step-by-step explanation:

12-3 + 5i-4i

9 + -i

9-i

The cruise ship's resultant velocity is approximately 22.67 mph, and its direction is approximately 10.2 degrees south of east.

To find the resultant direction, we can use vector addition. Let's represent the southward velocity of the cruise ship as vector A and the eastward velocity of the Gulf Stream as vector B.

Given:

Magnitude of vector A (southward velocity of the cruise ship) = 22 mph

Magnitude of vector B (eastward velocity of the Gulf Stream) = 4 mph

To find the resultant velocity, we add the two vectors together. Since the vectors are perpendicular to each other, we can use the Pythagorean theorem to find the magnitude of the resultant vector:

Resultant velocity = √(A^2 + B^2) = √(22^2 + 4^2) ≈ 22.67 mph

Now, to find the direction of the resultant vector, we can use trigonometry. The angle between the resultant vector and the south direction can be calculated as:

θ = arctan(B / A) = arctan(4 / 22) ≈ 10.17 degrees

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Step-by-step explanation:

Remember that

[tex](a + b) {}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex]

So

[tex](2x) {}^{2} = 4 {x}^{2} [/tex]

So the first blank is 4

[tex]2ab = 2(2x)(3) = 12x[/tex]

So the second blank is 12

And finally

[tex]3 {}^{2} = 9[/tex]

So the final blank is 9.

The situation that has a straight line and passes through the origin is when "All of the choices" are true.

A straight line equation in slope-intercept form is given by; y = mx + b, where m is the slope and b is the y-intercept.However, when the straight line passes through the origin, then the value of b becomes zero, which means the equation becomes; y = mx.

Therefore, among the given situations, the one that has a straight line and passes through the origin is "All of the choices."

Since all the given situations have a proportional relationship, which means as one variable increases, the other variable increases, then they all form a straight line that passes through the origin.

Therefore, all the given situations have a straight line and passes through the origin.

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The given sequence does not follow a simple arithmetic or geometric pattern, making it challenging to determine an explicit rule based on the given terms.

To identify the type of sequence and write the explicit rule, we need to examine the pattern of the given sequence: -39, -45, 51, 57, ...

By observing the differences between consecutive terms, we can determine if it follows an arithmetic or geometric pattern.

Arithmetic sequences have a common difference between each term, meaning that by adding (or subtracting) the same value repeatedly, we can generate the sequence. Geometric sequences, on the other hand, have a common ratio between each term, meaning that by multiplying (or dividing) by the same value repeatedly, we can generate the sequence.

Let's calculate the differences between consecutive terms:

-45 - (-39) = -6

51 - (-45) = 96

57 - 51 = 6

From the differences, we can see that the sequence is not arithmetic since the differences are not constant. However, the differences alternate between -6 and 6, indicating a possible geometric pattern.

Let's calculate the ratios between consecutive terms:

-45 / (-39) ≈ 1.1538

51 / (-45) ≈ -1.1333

57 / 51 ≈ 1.1176

The ratios are not constant, indicating that the sequence is neither geometric nor arithmetic.

Therefore, the given sequence does not follow a simple arithmetic or geometric pattern, and it is difficult to determine the explicit rule based on the given terms. It is possible that the sequence follows a more complex pattern or rule that is not apparent from the given terms.

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Answer:

Here are some recommended books on partial differential equations (PDEs) from beginner to advanced level:

1. "Partial Differential Equations: An Introduction" by Walter A. Strauss: This is a great introductory book on PDEs that covers the basics of first-order equations, second-order equations, and higher-order equations.

2. "Partial Differential Equations" by Lawrence C. Evans: This is a more advanced textbook that covers a wide range of topics in PDEs, including elliptic equations, parabolic equations, hyperbolic equations, and conservation laws.

3. "Nonlinear Partial Differential Equations" by Peter J. Olver: This is an advanced book that covers the theory and applications of nonlinear PDEs, including Hamiltonian systems, solitons, and integrable systems.

4. "Introduction to the Theory of Nonlinear Elliptic Equations" by V. G. Maz'ya and S. Poborchi: This is an advanced book that provides a comprehensive introduction to the theory of nonlinear elliptic equations.

5. "Geometric Partial Differential Equations and Image Analysis" by Guillermo Sapiro: This is an advanced book that covers the application of PDEs to image analysis, including topics such as denoising, segmentation, and registration.

These books provide a good foundation for understanding PDEs and their applications, and can be useful for students and researchers at various levels of expertise.

The inequality 5m - 7 > 16 holds true for the values m = 6, 7, 8, 9, and 10, in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

To determine the values for which the inequality 5m - 7 > 16 holds true, we can solve it algebraically and then check if each value in the given set satisfies the inequality.

Let's solve the inequality:

5m - 7 > 16

Adding 7 to both sides, we have:

5m > 23

Dividing both sides by 5, we get:

m > 23/5

Now we need to check if each number in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} satisfies the inequality m > 23/5.

For m = 1:

1 is not greater than 23/5, so the inequality does not hold true.

For m = 2:

2 is not greater than 23/5, so the inequality does not hold true.

For m = 3:

3 is not greater than 23/5, so the inequality does not hold true.

For m = 4:

4 is not greater than 23/5, so the inequality does not hold true.

For m = 5:

5 is not greater than 23/5, so the inequality does not hold true.

For m = 6:

6 is greater than 23/5, so the inequality holds true.

For m = 7, 8, 9, and 10:

All these values are also greater than 23/5, so the inequality holds true for them as well.visit

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Answer:

12

Step-by-step explanation:

Select any two random points on the graph of the line (preferably with integer coordinates).

Label them as A and B (in any order).

Calculate the "rise" from A to B. While going vertically from A to B, if we have to go. ...

Calculate the "run" from A to B. ...

Now, use the formula: slope = rise/run.

Answer:

a) -2

b) 1/2

Step-by-step explanation:

To find the slope given 2 points use the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Use the 2 points:

(-5,10)

(-3,6)

[tex]\frac{6-10}{-3+5}\\ \frac{-4}{2} \\-2[/tex]

So, a has a slope of -2.

Given the 2 points on the graph:

(-1,4)

(-5,2)

use the same formula:

[tex]\frac{2-4}{-5+1}\\ \frac{-2}{-4}\\ 1/2[/tex]

so b has a slope of 1/2

Hope this helps! :)

The functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

a) To find two functions f and g such that (fog)(x) = 1/(x + 2), we need to determine how the composition of the two functions f and g produces the given expression.

Let's start by assuming g(x) = x + a, where a is a constant. This means that g(x) adds the constant a to the input x.

Next, let's determine the function f(x) such that (fog)(x) results in the desired expression. We have:

(fog)(x) = f(g(x)) = f(x + a)

b) To simplify the expression 1/(x + 2) and make it match f(g(x)), we can consider f(x) = 1/x.

Substituting the expressions for f(x) and g(x) into (fog)(x), we have:

(fog)(x) = f(g(x)) = f(x + a) = 1/(x + a)

Comparing this with the desired expression 1/(x + 2), we see that a = 2. Therefore, the functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

Using these functions, we can verify the composition (fog)(x):

(fog)(x) = f(g(x)) = f(x + 2) = 1/(x + 2)

Thus, (fog)(x) = 1/(x + 2), which matches the desired expression.

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The difference in elevations is 14,212 feet.

The action or fact of raising or being raised to a higher or more important level, state, or position. Elevation is distance above sea level. Elevations are usually measured in meters or feet. They can be shown on maps by contour lines, which connect points with the same elevation; by bands of color; or by numbers giving the exact elevations of particular points on the Earths surface.

Given:

The highest point in California is Mount Whitney at 14,494 feet above sea level. The lowest point is the Death Valley at 282 feet below sea level

The positive 14,494 minus 282 feet would be a difference of 14,212 feet.

So, the difference is 14,212 feet.

Therefore, the difference in elevations is 14,212 feet.

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Using the given graph, we can see that the median cost is 480 thousands of dollars.

To find the cost in 2014, 19 years after 1995 which is the zero in the horizontal axis, first we need to locate the value x = 19 in the horizontal axis.

Once we do, we move vertically upwards until we meet the graph (in this case, the blue line).

Once we meet with the graph of the line, we move horizontally until we hit the vertical axis, and we record the correspondent value.

Doing that, we can see that the median cost of a home in 2014 is 480 thousands of dollars.

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The distance between the points (-3, 2) and (2, -2) is approximately sqrt(41), which is an irrational number.

To find the distance between two points (-3, 2) and (2, -2), we can use the Pythagorean theorem and consider the points as the vertices of a right triangle.

The base of the triangle is the horizontal distance between the x-values of the two points.

In this case, it is given by:

Base = 2 - (-3) = 2 + 3 = 5

Next, we need to find the height of the triangle, which is the vertical distance between the y-values of the two points. It is given by:

Height = -2 - 2 = -4

Now, we have the base and the height of the triangle.

To find the distance between the two points, we can use the Pythagorean theorem, which states that the square of the hypotenuse (distance) is equal to the sum of the squares of the other two sides (base and height).

Using the Pythagorean theorem:

Distance^2 = Base^2 + Height^2

Distance^2 [tex]= 5^2 + (-4)^2[/tex]

Distance^2 = 25 + 16

Distance^2 = 41

To find the distance, we take the square root of both sides:

Distance = sqrt(41).

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