find the value of each variable

We have explained the ASA rule of congruency of the triangle

What is an ASA congruency of triangles?

ASA Congruence. Angle-Side-Angle. If two angles in one triangle are congruent to two angles of a second triangle, and also if the included sides are congruent, then the triangles are congruent.

If a triangle PQR is congruent to a triangle ABC, we write it as ∆ PQR ≅ ∆ ABC.

Note that when ∆ PQR ≅ ∆ ABC, then sides of ∆ PQR fall on corresponding equal sides of ∆ ABC and so is the case for the angles.

This means that PQ covers AB, QR covers BC, and RP covers CA;

∠P, ∠Q, and ∠R cover ∠A, ∠B, and ∠C respectively.

Also, between the vertices, there is an existence of one-one correspondence.

That is, P corresponds to A, Q corresponds to B, R corresponds to C and it is written as

P↔A, Q↔B, R↔C

Under this condition, the correspondence ∆ PQR ≅ ∆ ABC is true but is not correct for the correspondence ∆QRP ≅ ∆ ABC.

Hence, we have explained the ASA rule of congruency of the triangle

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Answer: x=3y-29 and y=-8

Step-by-step explanation:

Using the area formula,

Area of the prism = 40mm².

Define area?

The word "area" designates a vacant region. The length and width of a form are used to calculate its area. The units of unidimensional length are feet (ft), yards (yd), inches (in), etc. Yet, the area of a shape is a two-dimensional quantity. Measurements like square inches (in²), square feet (ft²), square yards (yd²), etc. are used to measure anything in a square.

In the figure,

We have 2 equal rectangles and 2 equal triangles.

Now dimensions of the rectangles, l = 4mm and b = 3mm.

Area of 2 rectangles = 2 × 4 × 3

= 24mm².

Height of triangle, h = 4mm and base, b = 4mm.

Area of 2 triangles = 2 × 1/2 × b × h

= 4 × 4

= 16mm².

Therefore, total area of the prism = 24 + 16 = 40mm².

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Answer:

18 students.

Step-by-step explanation:

Total amount is 100

Take 68 and add to 60 to get 128.

Subtract from both numbers until you get to 50.

68 needs 18 subtracted to get to 50.

60 needs 10 to get to 50.

18 plus 10 is 28, which is the excess.

Here, 18 people like only football.

Answer:

i think 40

if 68 =likes foot ball

&60=likes volley ball

here there are available the students that likes both because 68+60=128 but the students are 100 so the students that likes both are 128-100=28

threfore the students that like only football are 40

cause the 68 likes football & the28 likes only football

so to know how many students likek foot ball evaluate like this (68-28=40)

i hope helps you

The theatre sold 178 adult tickets and 261 children tickets for the play.

It is given that the total number of seats is 439 seats.

There are two types of tickets available- children and adults.

The price for adult tickets is $48 and that for children is $28.

Let the number of adult tickets sold be x

Let the number of children's tickets sold be y.

The show was a sold-out

Hence,

x + y = 439                                 [1]

48x + 28y = 15852                    [2]

From equation [1] we get

x = 439 - y

putting this result in equation [2] gives us

48(439 - y) + 28y = 15852

or, 21072 - 48y + 28y = 15852

or, -20y = - 5220

or, y = -5220/ -20

or, y = 261

Therefore,

x + 261 = 439

or, x = 439 - 261

or, x = 178

Hence, 178 adult tickets were sold and 261 children's tickets were sold.

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Answer:

::::::::::::::::::::::::::::::::: don't know so long

ask your teacher to teach u

Answer:

55,278

Step-by-step explanation:

the radius is half of the diameter- 166.5

circumfrence-3.14(d)

3.14x333=55,278

The expression that represents the area of the new field is 400m²-200m+25 (option a)

To begin, let's start by finding the area of the original square field. The formula for the area of a square is the length of one side squared. In this case, the length of one side is 20 meters, so the area is:

Area = (20m)² = 400m²

Now, we need to find the area of the new field, which has one side that is 5 meters longer and one side that is 5 meters shorter than the original square. We can express the new length as (20m + 5m) = 25m, and the new width as (20m - 5m) = 15m.

The area of the new field can be expressed as the product of the new length and the new width:

New area = (25m)(15m)

To simplify this expression, we can use the distributive property of multiplication:

New area = 25m * 15m = (20m + 5m)(20m - 5m)

Expanding the expression using the FOIL method, we get:

New area = (20m)² - (5m)² = 400m² - 25m²

Simplifying this expression further, we get:

New area = 400m² - 25m² = 40m² (10 - m²/16)

Since we don't have any answer options that match this expression exactly, we need to simplify it further. Using the difference of squares, we can write:

New area = 40m² (5 + m/4)(5 - m/4)

Multiplying out the terms inside the parentheses, we get:

New area = 40m² (25 - m²/16)

Distributing the 40m², we get:

New area = 1000m² - 25m⁴/4

Finally, simplifying the expression, we get:

New area = 400m² - 25m + 25

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Bianca is the first to reach the finish line with her speed.

What is speed?

Alberto runs faster in the beginning of the race.

For the first hour of the race, Alberto keeps a 50 km/h pace.

Bianca's running pace is exponential in the meantime.

Bianca is the first to reach the finish line with her speed.

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Answer:  Initially,

Alberto

Albertostart  runs faster.

Alberto maintains a speed of

20km/h during the first hour of the race.

Meanwhile, Bianca's running speed is increasing

The first person to cross the finish line is Bianca

Step-by-step explanation:

The net operating income will be $ 5000.

The profitability of real estate assets that produce income is evaluated using a formula known as net operating income (NOI). NOI is the total revenue from the asset less all running costs that are deemed to be absolutely required.

Here we have  

A product has a selling price of $10 per unit, variable expenses of $6 per unit, and total fixed costs of $35,000.

In total 10,000 units are sold  

The net operating income will be computed by Subtracting all expenditures from all money collected on the product.    

Net operating income = ($10 - $6) × 10000 - $ 35000

= ($10 - $6) × 10000 - $ 35000  

=  $ 40000 - $ 35000

= $ 5000    

Therefore,

The net operating income will be $ 5000.

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The correct option for the midpoint of the line segment , where (-1,-2) and (4,-2), is  (1.5,-2).

To find the midpoint of a line segment, we use the midpoint formula, which states that the coordinates of the midpoint (M) are the average of the coordinates of the endpoints.

The midpoint formula is given by:

M = ((x1 + x2) / 2, (y1 + y2) / 2)

Let's apply this formula to find the midpoint of the line segment AB:

x1 = -1, y1 = -2 (coordinates of point A)

x2 = 4, y2 = -2 (coordinates of point B)

Using the midpoint formula:

M = ((-1 + 4) / 2, (-2 + (-2)) / 2)

 = (3 / 2, -4 / 2)

 = (1.5, -2)

Therefore, the midpoint of the line segment , with endpoints (-1,-2) and (4,-2), is (1.5, -2).

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The given mixed fraction 5 1/4 can be expressed as 21/4 in improper fraction.

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

A mixed fraction is one that has both a correct fraction and a whole number portion, and whose value is consistently greater than 1. An example of a mixed number is 325 3 2 5. When the numerator is always higher than or equal to the denominator, the fraction is said to be inappropriate.

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The ball takes approximately 7.97 seconds to strike the water after being tossed by Zain. When it hits the water, its speed is approximately 8.22 m/s.

To solve this problem, we can use the laws of motion and the principles of projectile motion. Firstly, we need to determine the time it takes for the ball to reach its highest point. The initial vertical velocity of the ball is given as 0.850 m/s. Since the ball stops momentarily at its highest point, its final vertical velocity at that point will be zero. Using the equation of motion for vertical displacement, we can calculate the time taken to reach the maximum height.

The formula for calculating the time taken to reach maximum height is:

time = (final velocity - initial velocity) / acceleration

Since the acceleration due to gravity acts against the initial velocity, the final velocity is zero. Thus, the equation becomes:

0 = 0.850 - 9.8 * time

Solving for time, we find that it takes approximately 0.087 seconds for the ball to reach its highest point.

Next, we need to determine the time it takes for the ball to fall from its highest point to the water's surface. The distance from the highest point to the water's surface is 300 meters, and the acceleration due to gravity is 9.8 m/s^2. Using the formula for calculating time with constant acceleration, we have:

distance = (initial velocity * time) + (0.5 * acceleration * time^2)

Substituting the given values, the equation becomes:

300 = (0 * time) + (0.5 * 9.8 * time^2)

Simplifying the equation, we get:

4.9 * time^2 = 300

Solving for time, we find that it takes approximately 7.97 seconds for the ball to strike the water.

Finally, to determine the speed of the ball when it hits the water, we can use the equation of motion for vertical velocity:

final velocity = initial velocity + (acceleration * time)

Substituting the values, we have:

final velocity = 0.850 + (9.8 * 7.97)

Calculating the final velocity, we find that it is approximately 8.22 m/s. Therefore, the speed of the ball when it hits the water is approximately 8.22 m/s.

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For the given question there are always 425 skiers on the chair lift at any given time.

The chair lift unloads 1700 skiers per hour at the top of the slope. The ride from the bottom to the top takes 15 minutes. We have to determine the number of skiers who are riding on the lift at any given time.

There are a few steps that we can take to solve this problem:

Step 1:Calculate how long the trip is from top to bottom:

The trip from bottom to top takes 15 minutes.

Therefore, the trip from top to bottom would take the same amount of time.

Step 2:Calculate how many trips the lift makes in an hour:

We have to convert 1 hour to minutes.1 hour = 60 minutes

Therefore, 1 hour = 60/15 = 4 trips from top to bottom

Step 3:Calculate how many skiers are riding on the lift at any given time.

The chair lift unloads 1700 skiers per hour at the top of the slope.

So, every 15 minutes, 425 skiers are unloaded at the top.

Since the lift takes 15 minutes to make one trip, there are always 425 skiers on the lift at any given time.

There are always 425 skiers on the chair lift at any given time.

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If the three numbers of a square in the complex plane are \(-19+32i,-5+12i and -22+15i\) , then the fourth complex number \(-2+19i\).

Given \(-19+32i,-5+12i and -22+15i\) are three numbers.

Complex numbers are those numbers which extends the real numbers with an imaginary i. In this \(i^{2}=-1\). Major complex numbers are in the form a+ bi where a and b are real numbers.

let the fourth complex numbers be \(x+yi\). Then according to question;

=\((-22+15i)-(-5+12i)\)

=(cos π/2+i sin π/2) \((x+yi)-(-5+12i)\)

\(-17+3i=-y+12\)\(+(x+5)i\)

Now solving for x and y by equating both sides.

x=-2 and y=29

Put the value of x and y in \(x+yi\)

Z=-2+29i

Hence if the three numbers which forms vertices of a square are \(-19+32i,-5+12i,-22+25i\) then the fourth complex numbers be \(-2+29i\).

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The scale factor of the dilation of the vertices of the cone when dilated is 4.5

The area of a circle is proportional to the square of its radius. Since the base of the cone is a circle

The ratio of the areas of the base of the dilated cone to the original cone is equal to the square of the scale factor.

Let the scale factor be k. Then, we have:

(area of dilated cone's base) / (area of original cone's base) = k²

(729π) / (36π) = k²

k² = 20.25

Taking the positive square root of both sides we get:

k = 4.5

Therefore, the scale factor of the dilation is 4.5.

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To evaluate the integral ∫(9-x^2)/(4x) dx using the substitution x=3sin(θ), we simplify the expression and perform the substitution. The final answer is: ∫(9-x^2)/(4x) dx = (9/4) ln|csc(θ) + cot(θ)| - (9/4)θ + C = (9/4) ln|csc(arcsin(x/3)) + cot(arcsin(x/3))| - (9/4)arcsin(x/3) + C

To evaluate the integral ∫(9-x^2)/(4x) dx using the substitution x=3sin(θ), we follow these steps:

Find the derivative dx/dθ of the substitution x=3sin(θ).

 dx/dθ = 3cos(θ)     [using the derivative of sin(θ) with respect to θ]

Substitute x=3sin(θ) and dx=3cos(θ)dθ into the integral.

 ∫(9-x^2)/(4x) dx = ∫(9-(3sin(θ))^2)/(4(3sin(θ))) * 3cos(θ) dθ

                  = ∫(9-9sin^2(θ))/(12sin(θ)) * 3cos(θ) dθ

                  = ∫(9-9sin^2(θ))/(4sin(θ)) cos(θ) dθ

Simplify the expression inside the integral.

Using the identity sin^2(θ) + cos^2(θ) = 1, we can rewrite the integrand:

(9-9sin^2(θ))/(4sin(θ)) cos(θ) = (9cos^2(θ))/(4sin(θ))

Further simplify the expression.

Using the identity cos^2(θ) = 1 - sin^2(θ), we have:

(9cos^2(θ))/(4sin(θ)) = (9(1-sin^2(θ)))/(4sin(θ))

                       = (9-9sin^2(θ))/(4sin(θ))

                       = (9-9sin^2(θ))/(4sin(θ))

                       = 9/(4sin(θ)) - 9sin(θ)/(4sin(θ))

                       = 9/(4sin(θ)) - 9/4

Evaluate the integral.

∫(9-x^2)/(4x) dx = ∫(9-9sin^2(θ))/(4sin(θ)) cos(θ) dθ

                = ∫(9/(4sin(θ)) - 9/4) dθ

                = (9/4) ln|csc(θ) + cot(θ)| - (9/4)θ + C

Convert back to the original variable x.

Since x=3sin(θ), we need to express θ in terms of x. From x=3sin(θ), we have sin(θ) = x/3, and using the Pythagorean identity sin^2(θ) + cos^2(θ) = 1, we can determine cos(θ) as cos(θ) = √(1 - (x/3)^2).

Therefore, the final answer is:

∫(9-x^2)/(4x) dx = (9/4) ln|csc(θ) + cot(θ)| - (9/4)θ + C

                = (9/4) ln|csc(arcsin(x/3)) + cot(arcsin(x/3))| - (9/4)arcsin(x/3) + C

Simplifying this expression may involve additional trigonometric identities, but the above representation is the simplified form using the given substitution.

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\(X = B(C^{-1})^2 - A\) is a solution to the invertible matrices equation \(C^{-1}(A+X)B^{-1}=I_n\).

We can begin by multiplying both sides of the equation by\((A+X)B^{-1}\):

\(C^{-1}(A+X)B^{-1}(A+X)B^{-1} = I_n(A+X)B^{-1}\)

Simplifying the left-hand side, we get:

\(C^{-1}(A+X)B^{-1}(A+X)B^{-1} = C^{-1}(A+X)(A+X)^{-1}C^{-1} = C^{-1}C^{-1} = (C^{-1})^2\)

Simplifying the right-hand side, we get:

\(I_n(A+X)B^{-1} = (A+X)B^{-1}\)

When we plug these values back into the original equation, we get:

\((C^{-1})^2 = (A+X)B^{-1}\)

Multiplying both sides by B, we get:

\(B(C^{-1})^2 = A+X\)

When we return to the original equation, we get:

\(C^{-1}(B(C^{-1})^2)B^{-1} = I_n\)

Simplifying, we get:

\((C^{-1})^2 = (C^{-1})^2\)

This is a true statement, so the equation has a solution,\(X = B(C^{-1})^2 - A\).

To solve the equation C^{-1}(A+X)B^{-1}=I_n, we first multiplied both sides by \((A+X)B^{-1}\) and simplified the equation to get \((C^{-1})^2 = (A+X)B^{-1}\). We then multiplied both sides by B and substituted the result back into the original equation to get \(C^{-1}(B(C^{-1})^2)B^{-1} = I_n\). Simplifying this equation, we got \((C^{-1})^2 = (C^{-1})^2\), which is a true statement. Therefore, the equation has a solution, X = \(B(C^{-1})^2 - A\).

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can send full pictures to me

1:8

Step-by-step explanation:

for every one cup of milk, there is 8 grams of protein

The difference in the rate of change between Function A and function B is -2.

The difference in the rate of change between function A and function B, we first need to identify the rate of change for each function. The rate of change, also known as the slope, represents how much the dependent variable (y) changes for every unit increase in the independent variable (x).

Let's assume function A is represented by the equation y = 2x + 3, and function B is represented by the equation y = 4x - 1.

For function A: y = 2x + 3, the coefficient of x is 2, indicating that for every unit increase in x, y increases by 2. Therefore, the rate of change for function A is 2.

For function B: y = 4x - 1, the coefficient of x is 4, indicating that for every unit increase in x, y increases by 4. Therefore, the rate of change for function B is 4.

Now, to find the difference in the rate of change between function A and function B, we subtract the rate of change of function B from the rate of change of function A:

Difference in rate of change = Rate of change of function A - Rate of change of function B

                          = 2 - 4

                          = -2

The difference in the rate of change between function A and function B is -2. This means that for every unit increase in x, function B increases at a rate that is 2 units greater than function A. It indicates that function B has a steeper slope and a faster rate of change compared to function A.

In summary, the difference in the rate of change between function A and function B is -2.

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Answer: 9pm

Step-by-step explanation:

Answer:

8:45

Step-by-step explanation:

The point on the shore that minimizes the woman's total travel time to the restaurant is approximately 9.55 km away.

This optimal point is found by calculating the time it takes for the woman to row to the shore and then walk to the restaurant, considering the different speeds of rowing and walking.

To determine the optimal point on the shore, we can use the concept of the time of travel. The time it takes to row to the shore is equal to the distance divided by the rowing speed, which is 3 km divided by 5 km/h, resulting in 0.6 hours. After reaching the shore, the woman needs to walk to the restaurant. The distance she needs to walk is the total distance from the shore to the restaurant minus the distance she rowed to reach the shore. This is equal to 20 km minus 3 km, which is 17 km. The time it takes to walk this distance is 17 km divided by 5 km/h, resulting in 3.4 hours.

To minimize the total travel time, the woman should aim to reduce the time spent walking. As the rowing speed and walking speed are the same, the optimal point on the shore will be the one that requires the least amount of walking. To find this point, we need to determine the distance from the shore to the restaurant where the time spent walking is minimized.

By dividing the total walking time (3.4 hours) by the rowing time (0.6 hours), we can find the ratio between walking and rowing times. In this case, the ratio is approximately 5.67. The distance from the shore to the restaurant can then be calculated by multiplying this ratio by the distance from the shore to the nearest point (3 km). Hence, the distance from the shore to the restaurant, at which the woman should aim to reach, is approximately 5.67 times 3 km, which equals 9.55 km. This is the optimal point on the shore that minimizes the woman's total travel time to the restaurant.

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Responder:

a) 2

b) 5

c) 4

d) 3

Explicación paso a paso:

Debemos encontrar el MCD de los siguientes números

a) 54, 76, 114

encontrar los factores primos de cada

54 = 2 * 3 * 3 * 3

76 = 2 * 2 * 19

114 = 2 * 2 * 2 * 2 * 3 * 3

De los factores anteriores, podemos ver que solo 2 es común a todos los factores, por lo tanto, el MCD de 54, 76 y 114 es 2

b) Para 35, 50 y 120

35 = 5 * 7

50 = 2 * 5 * 5

120 = 2 * 2 * 2 * 3 * 5

De los factores anteriores, podemos ver que solo 5 es común a todos los factores, por lo tanto, el MCD de 35, 50 y 120 es 5

c) Para 12, 16 y 20

12 = 2 * 2 * 3

16 = 2 * 2 * 2 * 2

20 = 2 * 2 * 5

De los factores anteriores, (2 * 2) es común a todos ellos, por lo tanto, el MCD de 12, 16 y 20 es 4

d) Para 56 y 120

56 = 2 * 2 * 2 * 7 = 8 * 7

120 = 2 * 2 * 2 * 3 * 5 = 8 * 3 * 5

De los factores anteriores, podemos ver que solo 8 es común a todos los factores, por lo tanto, el MCD de 56 y 120 es 8.

Por tanto, c = 8

Necesario

24 / c

= 24/8

= 3

Por tanto, el resultado de 24 / c es 3

The compound interval for the given interval is (-∞, ∞).

A compound inequality is a combination of two inequalities that are combined by either using "and" or "or". The process of solving each of the inequalities in the compound inequalities is as same as that of a normal inequality but just while combining the solutions of both inequalities depends upon whether they are clubbed by using "and" or "or".

The given intervals are (-∞, -2] or [-3, ∞).

Now, the compound interval is (-∞, ∞)

Thus, the interval notation is -∞<x<∞

Therefore, the compound interval for the given interval is (-∞, ∞).

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Answer:

B

Step-by-step explanation:

because -25.48 - 393.69 is?

B) jacks current account balance is 368.21

Answer:

Step-by-step explanation:

S=24000x(1.043)^t

Answer:

\(\boxed{\underline{\tt B.\:x=-1}}\)

Step-by-step explanation:

\(\tt 8=2^{(x+4)}\)

(First, convert both sides to the same base):-

\(\tt 2^3=2^{x+4}\)

(Now, cancel the base of 2 on both sides):-

\(\tt 3=x+4\)

(Subtract 4 from both sides):-

\(x+4-4=3-4\)

\(\tt x=-1\)

~