The table displays the scores of students on a recent exam. Find the mean of the
scores to the nearest 10th.
Score Number of Students
70
6
75
80
85
90
95
3
9
5
7
8
2

Answer:

2(M - 14) = 64

M - 14 = 32

M = 46

Answer:

Relative maximum at x=0; Relative minimum at x=8/3

Step-by-step explanation:

To find the relative maximums and the relative minimums, you must first find the first derivative of the function. The first derivative of this function is 6x^2-16x. Simply it and you get 2x(3x-8). X would be equal to 0 and 8/3. Next, make a number line where you put 0 and 8/3 have a value of zero.

        +                           -                                 +      

-------------------0----------------------------8/3-----------------------

Plug in a value of x<0 to get the region left of 0. Say we use -1, we get -2(-3-8), which is positive, meaning that it is increasing there. From 0 to 8/3, if we use 1, we get 2(3-8), which is decreasing. If we use 3, we get 6(9-8), which is increasing. From this, we can see that when x=0, the graph has a relative maximum. When x=8/3, the graph has a relative minimum.

Answer:

(-13, -9) and (-5, -9)

Step-by-step explanation:

The given equation of the hyperbola is:

[tex]\dfrac{(y+9)^2}{25}-\dfrac{(x+9)^2}{16}=1[/tex]

As the y²-term of the given equation is positive, the transverse axis is vertical, and so the hyperbola is vertical (opens up and down).

The standard equation for a vertical hyperbola is:

[tex]\boxed{\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1}[/tex]

where:

Compare the given equation with the standard equation to find the values of h, k, a and b:

The formula for the co-vertices of a vertical hyperbola is (h±b, k).

Substitute the values of b, h and k into the formula:

[tex]\begin{aligned}\textsf{Co-vertices}&=(h\pm b,k)\\&=(-9\pm 4, -9)\\&=(-13,-9)\;\;\textsf{and}\;\;(-5, -9)\end{aligned}[/tex]

Therefore, the co-vertices of the given hyperbola are:

The co-vertices of the hyperbola are (-4, -9) and (-14, -9).

To find the co-vertices of the hyperbola defined by the equation:

[(y + 9)² / 25] - [(x + 9)² / 16] = 1

We can compare the equation to the standard form of a hyperbola:

[(y - h)² / a²] - [(x - k)² / b²] = 1

In this case, we have h = -9 and k = -9.

The co-vertices of a hyperbola lie on the transverse axis, which is the line passing through the center of the hyperbola. The center of the hyperbola is given by (h, k), which in this case is (-9, -9).

For a hyperbola with the equation in this form, the co-vertices are located a units to the right and left of the center. In this case, since the equation is [(y + 9)² / 25] - [(x + 9)² / 16] = 1, we have a = 5.

Therefore, the co-vertices are located at (-9 ± a, -9), which gives us:

(-9 + 5, -9) = (-4, -9)

(-9 - 5, -9) = (-14, -9)

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El movimiento en línea recta se refiere al desplazamiento de un objeto en una trayectoria rectilínea, es decir, sin cambios de dirección.

En este tipo de movimiento, la velocidad y la aceleración del objeto pueden variar, pero su dirección se mantiene constante a lo largo del recorrido.

El movimiento en línea recta puede ser uniforme o no uniforme. En el caso del movimiento uniforme, la velocidad del objeto es constante, lo que implica que el desplazamiento realizado en intervalos iguales de tiempo es también constante.

Por otro lado, en el movimiento no uniforme, la velocidad cambia a lo largo del tiempo, resultando en diferentes desplazamientos en intervalos de tiempo iguales.

La descripción matemática del movimiento en línea recta se basa en conceptos como la posición, la velocidad y la aceleración. La posición se refiere a la ubicación del objeto en relación a un punto de referencia, la velocidad representa la tasa de cambio de la posición y la aceleración indica la tasa de cambio de la velocidad.

El estudio del movimiento en línea recta es fundamental en la física y tiene aplicaciones en diversas áreas, como la mecánica, la cinemática, la dinámica y la física de partículas.

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Answer: The statement that correctly describes the data is:

The typical value is 17. Most values are close to 17, except 4, which is an extreme value.

This is because the value 17 appears most frequently in the data set, making it the mode or the typical value. The value 4 is an extreme value as it is the minimum value in the data set. The maximum value of 18 is not the typical value because it is not as representative of the overall distribution of ages in the data set as the mode, which is 17.

Step-by-step explanation:

The cubic function with the desired properties is:

f(x) = (-3/4)x³ - (9/4)x² - (113/4)x + 63/4

To find the values of a, b, c, and d, we can use the given information about the relative maximum, relative minimum, and point of inflection.

Relative Maximum:

The point (-7, 163) is a relative maximum. At this point, the derivative of the cubic function is equal to zero. Taking the derivative of the cubic function, we have:

f'(x) = 3ax² + 2bx + c

Setting x = -7 and f'(-7) = 0, we get:

49a - 14b + c = 0

Relative Minimum:

The point (5, -125) is a relative minimum. At this point, the derivative of the cubic function is equal to zero. Taking the derivative of the cubic function, we have:

f'(x) = 3ax² + 2bx + c

Setting x = 5 and f'(5) = 0, we get:

75a + 10b + c = 0

Point of Inflection:

The point (-1, 19) is a point of inflection. At this point, the second derivative of the cubic function changes sign. Taking the second derivative of the cubic function, we have:

f''(x) = 6ax + 2b

Setting x = -1, we get:

-6a + 2b = 0

Solving the system of equations formed by the above three equations, we can find the values of a, b, c, and d.

49a - 14b + c = 0

75a + 10b + c = 0

-6a + 2b = 0

Solving these equations, we find:

a = -3/4

b = -9/4

c = -113/4

d = 63/4

Therefore, the cubic function with the desired properties is:

f(x) = (-3/4)x³ - (9/4)x² - (113/4)x + 63/4

The equation is y = 7.75x, where x is the number of hours Steven babysits and y is the amount he charges.

To represent the relationship between the number of hours Steven babysits (x) and the amount he charges (y), we can use a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept.

From the given information, we can identify two data points:

(4, 31.00) and (8, 62.00)

Using these points, we can calculate the slope (m) using the formula:

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

m = (62.00 - 31.00) / (8 - 4)

m = 31.00 / 4

m = 7.75

Now, we can substitute one of the points and the slope into the equation to find the y-intercept (b).

Using the point (4, 31.00):

31.00 = 7.75(4) + b

31.00 = 31.00 + b

b = 0

Therefore, the equation that represents the relationship between the number of hours Steven babysits (x) and the amount he charges (y) is:

y = 7.75x

The equation is y = 7.75x, where x is the number of hours Steven babysits and y is the amount he charges.

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Answer:

H= [4 -1

      4 0]

Step-by-step explanation:

The point A divides the line segment AB into the ratio 3:1, while the point B divides it into the ratio 1:3.

1. To find the ratio in which each point divides AB, we need to calculate the distances from each endpoint to the dividing point.

2. Let's calculate the distance from point A to the dividing point. The x-coordinate of point A is -7, and the y-coordinate is -14. Similarly, the x-coordinate of point B is 5, and the y-coordinate is 10.

3. We'll use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:

  distance = sqrt((x2 - [tex]x1)^2 + (y2 - y1)^2)[/tex]

4. Applying the distance formula, we find the distance from point A to the dividing point:

[tex]distance_A[/tex] = sqrt((5 -[tex](-7))^2 + (10 - (-14))^2)[/tex]

             = sqrt((5 + [tex]7)^2 + (10 + 14)^2)[/tex]

             = sqrt([tex]12^2[/tex] + [tex]24^2[/tex])

             = sqrt(144 + 576)

             = sqrt(720)

             = 12√5

5. Similarly, let's calculate the distance from point B to the dividing point:

[tex]distance_B[/tex] = sqrt((-7 - [tex]5)^2 + (-14 - 10)^2)[/tex]

             = sqrt((-[tex]12)^2 + (-24)^2)[/tex]

             = sqrt(144 + 576)

             = sqrt(720)

             = 12√5

6. The dividing ratio can be determined by comparing the distances from each endpoint to the dividing point. Since distance_A:distance_B = 3:1, we conclude that point A divides the line segment AB into the ratio 3:1, and point B divides it into the ratio 1:3.

Thus, the endpoints A and B divide the line segment AB into the ratios 3:1 and 1:3, respectively.

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Answer:

the ratio for point C is 1 : 2.

the ratio for point D is 3 : 1.

the ratio for point E is 2 : 1.

Step-by-step explanation:

I just got it right on the test

Ki Tae used 54 meters of fencing to construct a 6-sided outdoor dog pen. Two of the sides are each 15 meters long, while the remaining four sides are each 6 meters long.

Let's solve the problem step by step. We know that Ki Tae used a total of 54 meters of fencing to construct a 6-sided outdoor dog pen. Two of the sides have a length of 15 meters each.

Let's denote the length of the remaining four sides as "x."

Since the dog pen has six sides, we can set up an equation based on the total length of the fencing:

15 + 15 + x + x + x + x = 54

Simplifying the equation, we have:

30 + 4x = 54

Subtracting 30 from both sides, we get:

4x = 24

Dividing both sides by 4, we find:

x = 6

Therefore, each of the remaining four sides has a length of 6 meters.

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Answer:

(- 4, - 4 )

Step-by-step explanation:

x - 5y = 16 → (1)

4x - 2y = - 8 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate x

- 4x + 20y = - 64 → (3)

add (2) and (3) term by term to eliminate x

(4x - 4x) + (- 2y + 20y) = - 8 - 64

0 + 18y = - 72

18y = - 72 ( divide both sides by 18 )

y = - 4

substitute y = - 4 into either of the 2 equations and solve for x

substituting into (1)

x - 5(- 4) = 16

x + 20 = 16 ( subtract 20 from both sides )

x = - 4

solution is (- 4, - 4 )

Answer:

Step-by-step explanation:

a) To solve the equation tan θ = 1/√3, we can find the angle whose tangent is 1/√3 by taking the inverse tangent (arctan) of 1/√3.

θ = arctan(1/√3)

θ ≈ 30.0°

Therefore, the angle in standard position that satisfies tan θ = 1/√3 is approximately 30.0°.

b) To solve the equation 2cos θ = √3, we can isolate the cosine term by dividing both sides of the equation by 2.

cos θ = √3 / 2

Now, we can find the angle whose cosine is √3/2 by taking the inverse cosine (arccos) of √3/2.

θ = arccos(√3/2)

θ ≈ 30.0°

Therefore, the angle in standard position that satisfies 2cos θ = √3 is approximately 30.0°.

The nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

To determine the number of Lasix 20 mg tablets that should be administered to the patient, we need to calculate how many tablets are equivalent to the prescribed dose of 80 mg.

Given that each Lasix tablet contains 20 mg of the medication, we can divide the prescribed dose (80 mg) by the dosage strength of each tablet (20 mg) to find the number of tablets needed.

Number of tablets = Prescribed dose / Dosage strength per tablet

Number of tablets = 80 mg / 20 mg

Number of tablets = 4 tablets

Therefore, the nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

It is important to note that this calculation assumes that the Lasix tablets can be divided or split if necessary. However, it is crucial to follow the specific instructions provided by the prescribing physician or consult with a pharmacist if there are any concerns about the appropriate administration of the medication.

Additionally, it is important to consider any additional instructions, such as the frequency and timing of administration, as specified by the physician's order.

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Answer:

x = - 5 , x = 2

Step-by-step explanation:

f(x) = x² + 3x - 10

to find the zeros let f(x) = 0 , that is

x² + 3x - 10 = 0

consider the factors of the constant term (- 10) which sum to give the coefficient of the x- term (+ 3)

the factors are + 5 and - 2 , since

5 × - 2 = - 10 and 5 - 2 = + 3 , then

(x + 5)(x - 2) = 0 ← in factored form

equate each factor to zero and solve for x

x + 5 = 0 ( subtract 5 from both sides )

x = - 5

x - 2 = 0 ( add 2 to both sides )

x = 2

the zeros are x = - 5 , x = 2

The true statement about the transformation is that the second trapezoid is a dilation of the first trapezoid with a scale factor of 2.

The given transformation involves two trapezoids with identical angle measures but different side lengths. Let's analyze the two trapezoids and determine the statement that is true about the transformation.

First Trapezoid:

Side lengths: 4, 2, 6, 2

Second Trapezoid:

Side lengths: 8, 4, 12, 4

To determine the relationship between the side lengths of the two trapezoids, we can compare the corresponding sides.

Comparing the corresponding sides:

4 / 8 = 2 / 4 = 6 / 12 = 2 / 4

We can observe that the corresponding sides of the two trapezoids have the same ratio. This indicates that the side lengths of the second trapezoid are twice the lengths of the corresponding sides of the first trapezoid. Therefore, the statement that is true about the transformation is:

The second trapezoid is a dilation of the first trapezoid with a scale factor of 2.

A dilation is a type of transformation that produces an image that is the same shape as the original figure but a different size. In this case, the second trapezoid is obtained by scaling up the first trapezoid by a factor of 2 in all directions.

This transformation preserves the shape and angle measures of the trapezoid but changes its size. The corresponding sides of the second trapezoid are twice as long as the corresponding sides of the first trapezoid.

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Answer:

$6240

Step-by-step explanation:

given likelihoods:

sunny day = 14% = 0.14

cloudy day = 26% = 0.26

rainy day = 60% = 0.60

profits:

profit on a sunny day = $40,000

profit on a cloudy day = $14,000

Loss on a rainy day = -$5,000

expected profit = (probability of sunny day * profit on sunny day) + (probability of cloudy day * profit on cloudy day) + (probability of rainy day * loss on rainy)

expected profit = (0.14 * $40,000) + (0.26 * $14,000) + (0.60 * -$5,000)

=6240

The amount of tax owed is $13,420

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

Single with a taxable income of ​$61,000

Using the table of marginal tax, we have

Tax = 22%

So, we have

Tax = 22% * 61000

Evaluate

Tax = 13420

Hence, the amount of tax owed is $13,420

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Answer:

This is an equation of a parabola.

[tex](y+6)^2=4(x+1)[/tex]

Step-by-step explanation:

A conic section is a curve obtained by the intersection of a plane and a cone. The three major conic sections are parabola, hyperbola and ellipse (the circle is a special type of ellipse).

The standard equations for hyperbolas and ellipses all include x² and y² terms. The standard equation for a parabola includes the square of only one of the two variables.

Therefore, the equation y² - 4x + 12y + 32 = 0 represents a parabola, as there is no x² term.

As the y-variable is squared, the parabola is horizontal (sideways), and has an axis of symmetry parallel to the x-axis.

The conic form of a sideways parabola is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

To write the given equation in conic form, we need to complete the square for the y-variable.

Rearrange the equation so that the y-terms are on the left side:

[tex]y^2 + 12y = 4x - 32[/tex]

Add the square of half the coefficient of the y-term to both sides of the equation:

[tex]y^2 + 12y+\left(\dfrac{-12}{2}\right)^2 = 4x - 32+\left(\dfrac{-12}{2}\right)^2[/tex]

    [tex]y^2 + 12y+\left(-6\right)^2 = 4x - 32+\left(-6\right)^2[/tex]

         [tex]y^2 + 12y+36 = 4x - 32+36[/tex]

         [tex]y^2 + 12y+36 = 4x +4[/tex]

Factor the perfect square trinomial on the left side of the equation:

[tex](y+6)^2=4x+4[/tex]

Factor out the coefficient of the x-term from the right side of the equation:

[tex](y+6)^2=4(x+1)[/tex]

Therefore, the equation of the given conic section in conic form is:

[tex]\boxed{(y+6)^2=4(x+1)}[/tex]

where:

The conic section of the equation y² - 9x + 12y + 32 = 0 is a parabola

The given equation is

y² - 9x + 12y + 32 = 0

The above equation is an illustration of a parabola equation

The standard form of a parabola is

(x - h)² = 4a(y - k)²

Where

(h, k) is the center

While the general form of the equation is

Ax² + Dx + Ey + F = 0

In this case, the equation y² - 9x + 12y + 32 = 0 takes the general form

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The estimated population of the state in the year 2022 is 19,280,700 people.

The given equation represents the population of a certain state as a function of time, where p is the population in thousands of people and t is the number of years since 2010.

The equation is given as p = 80.7t + 18,312.3.

To estimate the population of the state, we substitute the value of t into the equation. For example, if we want to estimate the population in the year 2022 (12 years since 2010), we substitute t = 12 into the equation:

p = 80.7(12) + 18,312.3

= 968.4 + 18,312.3

= 19,280.7.

The estimated population of the state in the year 2022 is 19,280,700 people.

We can estimate the population for any given year by substituting the corresponding value of t into the equation.

It's important to note that the population is given in thousands of people, so we multiply the final result by 1,000 to obtain the population in actual numbers.

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Answer:

-9(x+1) < 12x+9

if you need me to solve it here it is:

-9x - 9 < 12x + 9

     + 9           +9

-9x      < 12x + 18

-12x       -12x

-18x     <          18

(divide by -18 on both sides)

x < - 1

Therefore, any number is that is greater than -1 will work for this inequality.

Hope this helps!

The x-intercepts of the function y = (x-5)(x+3) are 5 and -3.

To find the x-intercepts of the function y = (x-5)(x+3), we need to set y equal to zero and solve for x.

The x-intercepts are the values of x where the graph of the function intersects or crosses the x-axis.

Set y = 0:

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

Apply the zero-product property:

The product of two factors is equal to zero if and only if at least one of the factors is equal to zero.

Therefore, we can set each factor equal to zero and solve for x.

Setting x-5 = 0:

x - 5 = 0

x = 5

Setting x+3 = 0:

x + 3 = 0

x = -3.

The x-intercepts of the function y = (x-5)(x+3) are x = 5 and x = -3.

These are the values of x where the graph of the function crosses the x-axis.

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Answer:

x=50

Step-by-step explanation:

Make this equal to 180.

x+3x-35+x-35 = 180

5x = 180 + 70

5x=250

x=50

The calculated value of m in the triangular prism is 13

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

The triangular prism

Where, we have

Volume = 1170

The volume of the triangular prism is calculated as

Volume = Base area * Height

So, we have

1/2 * m * 18 * 10 = 1170

Evaluate the products

This gives

90m = 1170

So, we have

m = 13

Hence, the value of m is 13

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Answer:

So we have $11.64 in American dollars and £5 in British pound coin

Step-by-step explanation:

To solve this problem, we can use a system of equations. Let x be the number of American dollars and y be the number of British pound coins. Then we have:

x + y/1.65 = 20.25 (since each British pound coin is worth 1.65 American dollars)

x = 17 - y (since there are 17 items altogether)

Substituting the second equation into the first, we get:

(17 - y) + y/1.65 = 20.25

Multiplying both sides by 1.65, we get:

28.05 - y + y = 33.4125

y = 33.4125 - 28.05

y = 5.3625

Therefore, we have 5 British pound coins and:

x = 17 - y = 17 - 5.3625 = 11.6375

Answer:

8/15

Step-by-step explanation:

1/15(4 + 1/20(4)

4/15 + 4/20  I can reduce 4/20 to 1/5

4/15 + 1/5

4/15 + 3/15 = 7/15

Together they can get 7/15 of the job done.  15/15 - 7/15 is 8/15.

That means that they have 8/15 left to do.

Helping in the name of Jesus.

a)In a typical week, Maybelle will earn a total of: $600 + $250 = $850

b) Her total earnings for the week would be: $600 + $300 = $900

c)  Her paycheck will be reduced by $100.

d) Her wage earnings should remain the same assuming she still works at least 40 hours per week.

To calculate Maybelle's earnings in a typical week, we first need to determine the minimum number of hours she works. Since she earns $15 per hour for at least 40 hours per week, her minimum wage earnings are:

$15 x 40 = $600

In addition to her wage earnings, Maybelle earns a commission of 10% for each pair of shoes she sells. Since she is expected to sell $2,500 worth of shoes every week, her commission earnings are:

$2,500 x 0.10 = $250

b) If Maybelle sells $3,000 worth of shoes in one week, her commission earnings would be:

$3,000 x 0.10 = $300

On top of her wage earnings of $600 (based on working at least 40 hours at $15 per hour)

c) If customers return $1,000 worth of shoes the next week, Maybelle's commission earnings will not be affected. However, her wage earnings will be reduced by the amount of the returned shoes, which is $1,000 x 0.10 = $100.

d) With an economic downturn and sales slump, Maybelle's earnings from commission will likely decrease since she will sell fewer shoes. However, her total earnings will likely decrease due to the decrease in commission earnings.

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The limit of the trigonometric expression is equal to 0.

In this problem we find the case of a trigonometric expression, whose limit must be found. This can be done by means of algebra properties, trigonometric formula and known limits. First, write the entire expression below:

[tex]\lim_{\Delta x \to 0} \frac{\cos (\pi + \Delta x) + 1}{\Delta x}[/tex]

Second, use the trigonometric formula cos (π + Δx) = - cos Δx to simplify the resulting formula:

[tex]\lim_{\Delta x \to 0} \frac{1 - \cos \Delta x}{\Delta x}[/tex]

Third, use known limits to determine the result:

0

The limit of the trigonometric function [cos (π + Δx) + 1] / Δx evaluated at Δx → 0 is equal to 0.

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The percentage of profit on a $1200 investment resulting in a $350 profit is 29.17%.

The percentage of profit on a $1200 investment that results in a $350 profit can be calculated using the formula:

Percentage of profit = (Profit / Investment) x 100

In this case, the profit is $350 and the investment is $1200. Plugging these values into the formula:

PercThe percentage of profit on a $1200 investment that results in a $350 profit can be calculated using the formula:

Percentage of profit = (Profit / Investment) x 100

In this case, the profit is $350 and the investment is $1200. Plugging these values into the formula:

Percentage of profit = (350 / 1200) x 100

Calculating this expression gives us:

Percentage of profit = 0.2917 x 100 = 29.17%

Therefore, the percentage of profit on a $1200 investment resulting in a $350 profit is 29.17%.

To calculate the percentage of profit, we divide the profit by the investment and then multiply by 100 to express it as a percentage. In this case, the profit is $350 and the investment is $1200. Dividing $350 by $1200 gives us 0.2917. Multiplying this by 100 gives us 29.17%. This means that the profit of $350 represents 29.17% of the initial investment of $1200.entage of profit = (350 / 1200) x 100

Calculating this expression gives us:

Percentage of profit = 0.2917 x 100 = 29.17%

Therefore, the percentage of profit on a $1200 investment resulting in a $350 profit is 29.17%.

To calculate the percentage of profit, we divide the profit by the investment and then multiply by 100 to express it as a percentage. In this case, the profit is $350 and the investment is $1200. Dividing $350 by $1200 gives us 0.2917.

Multiplying this by 100 gives us 29.17%. This means that the profit of $350 represents 29.17% of the initial investment of $1200.

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The conditions that prove that the triangles ΔABC and ΔXYZ are similar, ΔABC ~ ΔXYZ, based on the order of the lettering are;

BA/YX = BC/YZ = AC/XZ

AC/XZ = BA/YX, ∠A ≅ ∠C

Similar triangles are triangles that have the same shape (the same two or all three interior angles in each triangle) but in which may have different sizes.

Triangles are similar if they equivalent ratio for their sides and and if the angles in each triangle are congruent to the angles in the other triangle

Therefore, the conditions that indicates that two triangles are that one triangle is a scaled image of the other triangle, therefore, the ratio of the corresponding sides of the triangles are equivalent, which indicates;

ΔABC is similar to ΔXYZ if we get;

A condition that indicates that two triangle are similar is the Side Angle Side, SAS, similarity postulate, which states that two triangles are congruent if the ratio of two corresponding sides are equivalent and the angle between the two sides in the two triangles are congruent, therefore;

ΔABC is similar to ΔXYZ if we get;

Learn more on similar triangles here: https://brainly.com/question/29782809

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