82°
118°
95°
X°
Image not to scale
Calculate the missing angle x.

The solution to the system of equations is x = 5 and y = -2. Thus, the correct answer is B: x = 5, y = -2.

To find the solution to the system of equations, we can use the graphing function on a calculator. By graphing both equations and examining their intersection point, we can determine the solution.

The system of equations is as follows:

1) y + x = 3

2) y - 2x = -12

First, we rearrange equation 1) to solve for y:

y = 3 - x

Now, we can graph both equations on a graphing calculator or software. By plotting the lines representing the equations, we can see where they intersect, if at all.

Upon graphing, we observe that the two lines intersect at the point (5, -2). This means that the x-coordinate of the intersection is 5, and the y-coordinate is -2.

Therefore, the solution to the system of equations is x = 5 and y = -2. Thus, the correct answer is B: x = 5, y = -2.

It is important to note that in this case, the graphing method yields a single point of intersection, indicating a unique solution. If the two lines were parallel and did not intersect, there would be no solution (option C). Alternatively, if the two lines were coincident, overlapping each other completely, there would be infinitely many solutions (option A). However, in this scenario, the graph confirms that the system has a unique solution at (5, -2).

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Carl works at a veterinarian office. The first dog he sees is a Chihuahua who weighs 3 kilograms. The second dog he sees is a Great Dane who weighs 27 times as much as the Chihuahua. The Great Dane weighs 81 kilograms.

Let's denote the weight of the Chihuahua as "x" kilograms. We know that the Great Dane weighs 27 times as much as the Chihuahua. Therefore, the weight of the Great Dane can be expressed as 27x.

Given that the weight of the Chihuahua is 3 kilograms, we can substitute this value into the equation:

27x = 3

To find the weight of the Great Dane, we need to solve for x:

x = 3 / 27

x = 1 / 9

Therefore, the weight of the Chihuahua is 1/9 kilograms.

Now, we can calculate the weight of the Great Dane by multiplying the weight of the Chihuahua by 27:

Weight of the Great Dane = 27 * (1/9) = 27/9 = 3 kilograms

So, the Great Dane weighs 81 kilograms, which is 27 times the weight of the Chihuahua.

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The true statement is that  (d) the system has no solution

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

The augmented matrix

In the augmented matrix, we have

Rows = 2

Columns = 4

This means that

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

The general rule is that

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

Hence, there is no solution in the system

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The window is 125 meters high and the distance that the ball lands from the base of the building is 50 meters.

The height of the window can be found by using the formula for the distance travelled under constant acceleration, which in this case is due to gravity.

The formula is: d = ut + 0.5at ²

Since the ball was thrown horizontally, the initial vertical velocity (u) is 0. Substituting these values into the equation gives:

d = 05 + 0.510 * (5 ² )

= 0 + 0.51025

= 125 meters

The horizontal distance the ball travels can be found by multiplying the horizontal speed by the time.

So, the horizontal distance is:

d = vt = 10 x 5

= 50 meters

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The full question is:

Una pelota es lanzada horizontalmente desde una ventana con una velocidad inicial que tiene una magnitud de 10 m/s y cae al suelo después de 5 segundos

¿a que altura se encuentra la ventana?

¿a que distancia cae la pelota de la base del edificio?

Which translates to:

A ball is thrown horizontally from a window with an initial velocity that has a magnitude of 10 m/s and falls to the ground after 5 seconds.

How high is the window?

How far does the ball land from the base of the building?

Line M and line N are the same line, since they have the same slope and y-intercept. Therefore, there are infinitely many solutions for the pair of equations, since every point on the line satisfies both equations.

The expression equivalent to the given expression 14x^4y^5/7xr^y^2 is 2x^3y^3/r.

This expression can be simplified as follows: Simplifying the expression 14x^4y^5/7xr^y^2First, we can write the given expression as shown below:14 x 4 * y^5 / (7 * x * r * y^2) = 2 * 7 * x^3 * y^3 / 7 * r * x * y^2 = 2x^2y/rr.

Now, the numerator and the denominator have x, y, and r, and we can cancel them out as shown below:2x^2y/rr = 2xy * x * x / rr * y * y / y * y = 2x^3y^3/r.

Therefore, the expression equivalent to the given expression 14x^4y^5/7xr^y^2 is 2x^3y^3/r.

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Answer: 381 square inches

Step-by-step explanation: The area of a circle with radius r is given by the formula:

A = πr^2

Substituting r = 11 and π = 3.14, we get:

A = 3.14(11)^2

A = 3.14(121)

A = 380.94 (rounded to two decimal places)

Therefore, the area of the circle is approximately 381 square inches.

Answer:

The inverse variation equation that represents this situation is:

xy = k

where x is the number of members, y is the contribution made by each member, and k is a constant of proportionality.

Since each member contributes an equal amount, we can let y be the contribution made by each member. If there are x members, then the total amount contributed is 2000 + xy. Since this total amount is divided equally among the x members, we can set y equal to the total amount divided by x, which gives:

y = (2000 + xy) / x

Multiplying both sides by x, we get:

xy = 2000 + xy

Subtracting xy from both sides, we get:

0 = 2000

This is a contradiction, which means that our assumption that y depends on x is incorrect. Therefore, we cannot write an inverse variation equation that represents this situation.

hope it helps you

The division by zero is not possible and f/g division is undefined, {20, 6, -4, 39} f /g is undefined (because of division by zero)

The scope and image of a given function and its operations.

f = {(2,4), (5,6), (8,-1), (10,3)}

g = {(2,5), (7,1) , ( 8,4), (10,13), (11,5)}

a) f - g (subtraction):

To find the domain of f - g, find the common element in the domain of f must be considered.

In this case the domains of both f and g are {2, 5, 8, 10}.

Therefore, the domain of f - g is {2, 5, 8, 10}.

Now let's compute the image of f - g using the subtraction operation:

f - g = {(2, 4-5), (5, 6-1), (8, -1-4 ), (10 , 3 -13)}

= {(2, -1), (5, 5), (8, -5), (10, -10)}

Images from f to g are {- 1, 5, -5, -10}.

b) f + g (addition):

As in the previous case, the domain of f + g is {2, 5, 8, 10}.

Now let's compute the image of f + g using the addition operation:

f + g = {(2, 4+5), (5, 6+1), (8, -1+4 ), (10 , 3 +13)}

= {(2, 9), (5, 7), (8, 3), (10, 16)}

f + g image is {9, 7, 3, 16 } .

c) f * g (multiplication):

Again, the domain of f * g is {2, 5, 8, 10}.

Now let's use the multiplication operation to compute the f * g image:

f * g = {(2, 45), (5, 61), (8, -14), (10, 313 )}

= { ( 2, 20), (5, 6), (8, -4), (10, 39)}

The f * g image is {20, 6, -4, 39}.

Division operations must ensure that the denominator is not zero. Looking at the function g, we can see that the x value of 7 has no corresponding y value in g.

Therefore, division by zero is not possible and f/g division is undefined.

region of f - g, f + g, f * g = {2, 5, 8, 10}

region of f / g is undefined (because of division by zero) of f Images - g = {-1, 5, -5, -10} f + g

images in {9, 7, 3, 16} f * g

images in {20, 6, -4, 39} f /g is undefined (because of division by zero).

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When proving that the opposite angles of a parallelogram are congruent, the proofs are;

B. Opposite sides are congruent.

D. Corresponding parts of congruent triangles are congruent.

The properties of a parallelogram are;

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The general solution of the matrix equation is determined as x₁ = 3x₄.

x₂ = -x₃ - 4x₄, x₃ = x₃, x₄ = x₄.

The general solution of the matrix is calculated by applying the following method as shown below;

The given matrix equation;

[1   4   4   13]

[2  5   5  14]

The solution of the matrix equation is determined as;

R₂ - 2R₁ = [1   4   4   13]

               [ 0 -3  -3, -12]

From the row operation, the values of x₁, x₂, x₃ and x₄ is determined as;

-3x₂ = 3x₃ + 12x₄

x₂ = -x₃ - 4x₄

x₁ = -4x₂ - 4x₃ - 13x₄

x₁ = -4(-x₃ - 4x₄) -  4x₃ - 13x₄

x₁ = 3x₄.

The general solution;

x₁ = 3x₄.

x₂ = -x₃ - 4x₄

x₃ = x₃

x₄ = x₄

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The flow rate for the ordered 1 L hyperalimentation solution for 1 hour, with a drop factor of 15 gtt/mL, is approximately 250 gtt/min.

To calculate the flow rate in gtt/min, we need to use the information provided about the ordered volume, drop factor, and time. Here are the steps to determine the flow rate:

Step 1: Convert the ordered volume to mL if necessary. In this case, 1 liter (L) is equivalent to 1000 mL.

Step 2: Determine the total number of drops needed for the ordered volume by multiplying the volume in mL by the drop factor.

Total drops = Volume (mL) x Drop factor (gtt/mL)

Total drops = 1000 mL x 15 gtt/mL

Total drops = 15000 gtt

Step 3: Divide the total number of drops by the time in minutes to calculate the flow rate in gtt/min.

Flow rate (gtt/min) = Total drops / Time (min)

Flow rate (gtt/min) = 15000 gtt / 60 min

Flow rate (gtt/min) ≈ 250 gtt/min

Therefore, the flow rate for the ordered 1 L hyperalimentation solution for 1 hour, with a drop factor of 15 gtt/mL, is approximately 250 gtt/min.

It's important to note that this calculation assumes a constant flow rate and does not take into account any adjustments or interruptions that may occur during the infusion. The flow rate may vary based on factors such as the specific administration set used, the viscosity of the solution, and any specific instructions or guidelines provided by medical professionals.

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Answer:  cos∅ = (3√11)/11

Step-by-step explanation:

See image

Answer:

cos∅ = 3/√11

Step-by-step explanation:

If tan ∅ = √(2)/3

We know the relationship:

As given, putting the value to this equation we get:

We know that sec∅ = 1/cos∅

Hence cos ∅ = 1/ sec∅

Putting the value of sec∅, we get:

This is an interesting method by using square relationship!

The scatter plot shows (b) [positive linear] association.

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

The image of the scatter plot

On the scatter plot, we can see that

The points appear to be on a straight line

Also, we can see that

As the x values increases the y values increases

This represents a [positive linear] association.

Hence, the association is a [positive linear] association.

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The equation of the line given the table values, we need to identify the slope and y-intercept. However, with only two y-values provided (13 and 18),

For example, if the two points on the line were (x1, 13) and (x2, 18), we could calculate the slope using the formula m = (y2 - y1) / (x2 - x1). With the slope and one point, we could determine the equation of the line in slope-intercept form.

But without the x-values or any additional information, we cannot determine the equation of the line accurately. We would need more data points or some other form of information to find the equation of the line.

To determine the equation of the line given the table values, we need to identify the slope and y-intercept. However, with only two y-values provided (13 and 18), it is not possible to accurately determine the equation of the line. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept. In this case, we cannot determine the slope or the y-intercept with the given information.

To find the equation of a line, we typically require at least two points or additional information such as the slope. With only two y-values provided, it is insufficient to determine the equation of the line accurately.

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The location would need to produce $16.50 per hour to achieve a revenue of $78,000 per year, be open 100 hours each week, and maintain a 10% profit margin.

To calculate the production needed per hour, we'll follow these steps:

Determine the weekly revenue:

The annual revenue is given as $78,000. To calculate the weekly revenue, we divide it by the number of weeks in a year:

$78,000 / 52 weeks = $1,500 per week.

Calculate the revenue per hour:

To find the revenue per hour, we divide the weekly revenue by the number of hours the location is open per week:

$1,500 / 100 hours = $15 per hour.

Calculate the production needed per hour:

Now that we know the revenue per hour, we can calculate the production needed per hour. Since the profit margin is not mentioned, we'll assume it is 10% (as given in the question):

Revenue per hour + 10% profit margin = Production needed per hour

$15 + (10% of $15) = $15 + $1.50 = $16.50

Therefore, the location would need to produce $16.50 per hour to achieve a revenue of $78,000 per year, be open 100 hours each week, and maintain a 10% profit margin.

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The length of the longer wire is 82 feet.

Let's denote the length of the longer wire as L. According to the given information, the shorter wire is attached to the ground 16 feet from the base of the pole, and the longer wire is attached to the ground 32 feet from the base of the pole.

We can form two similar right triangles using the wires. The height of each triangle is the height of the pole, and the base of each triangle is the distance from the base of the pole to where the wire is attached to the ground.

In the first triangle, the shorter wire creates an angle with the ground. Let's denote this angle as θ. Since we are given the cosine of this angle, we can use the cosine function to find the height of the pole in terms of θ and the base of the triangle:

cos(θ) = adjacent/hypotenuse = 16/L

Given that cos(θ) = 8/41, we can substitute this value into the equation:

8/41 = 16/L

To solve for L, we can cross-multiply and solve for L:

8L = 41 * 16

L = (41 * 16)/8

L = 82

Therefore, the length of the longer wire is 82 feet.

In summary, the length of the longer wire is 82 feet, as determined by using the cosine of the angle formed by the shorter wire and the ground, and considering the similarity of the triangles formed by the wires and the pole.

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We can isolate the x term by subtracting  8 from both sides of the equation, giving us 4x=12. dividing by 4 on each side gives us x=3.

So, our answer is x=3.

Step-by-step explanation:

[tex]4x + 8 = 20 \\ 4x = 20 - 8 \\ 4x = 12 \\ x = \frac{12}{4 \\ } \\ x = 3ans [/tex]

hope that it helps

The areas under the curve of the z-scores are 0.5098, 0.4357 and 0.1254

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

(a) z = -0.69 to 0.69

This is represented as

Area = P(-069 < z < 069)

Using a graphing calculator, we have

Area = 0.5098

(b) z = -1.52 to 0

This is represented as

Area = P(-1.52 < z < 0)

Using a graphing calculator, we have

Area = 0.4357

(c) z = -0.75 to -0.38

This is represented as

Area = P(-1.52 < z < -0.38)

Using a graphing calculator, we have

Area = 0.1254

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Answer:

-2<=y<=-7

Step-by-step explanation:

The inverse of the equation is determined as [tex]y = \log_{6}(-3x)[/tex].

option D is the correct answer.

The inverse of the equation is calculated by applying the following method;

The given equation;

y = - 6ˣ/3

The inverse of the equation is calculated as;

multiply through by 3

[tex]-3x = 6^y[/tex]

Take the logarithm of both sides of the equation with base -6:

[tex]\log_{6}(-3x) = y[/tex]

Finally, replace y with x to obtain the inverse equation as follows;

[tex]y = \log_{6}(-3x)[/tex]

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The radius of the spherical ball, correct to one decimal place, is approximately 8.5 cm.

To find the radius of a spherical ball when the volume is given, we can use the formula for the volume of a sphere:

[tex]Volume = (4/3) * π * r^3[/tex]

Given that the volume of the ball is 5000 cm^3, we can set up the equation as follows:

[tex]5000 = (4/3) * π * r^3[/tex]

To find the radius, we need to isolate it in the equation. Let's solve for r step by step:

1. Divide both sides of the equation by (4/3) * π to isolate r^3:

 [tex]r^3 = 5000 / [(4/3) * π][/tex]

2. Simplify the right side of the equation:

  r^3 = 3750 / π

3. Take the cube root of both sides to solve for r:

  r = (3750 / π)^(1/3)

Using a calculator, we can approximate the value of r:

  r ≈ 8.532

Therefore, the radius of the spherical ball, correct to one decimal place, is approximately 8.5 cm.

It's important to note that the value of π used in the calculation should be accurate to the required level of precision. In this case, we have used the standard value of π (approximately 3.14159).

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Janet's savings in January is $800

A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.

Represent Mary's savings by x and Janet's savings by y

7/4 = x/y

40/100 × x = 40x/100 = 2x/5

New savings for Mary =

x -2x/5 = 5x - 2x)/5 = 3x/5

50/100 × y = y/2

New savings for Janet =

y + y/2 = 3y/2

3y/2 + 3x/5 = 2040

15y + 6x = 20400

7y = 4x

y = 4/7x

Substitute (4/7)x for y

15( 4/7) x + 6x = 20400

(60/7 )x + 6x = 20400

60x + 42x = 142800

102x = 142800

x = 142800/102

x = $ 1400

y = 4/7 × 1400

y = $800

Therefore, the savings for Janet in January is $800.

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The correct answer is C. It is the graph of f(x) translated 11 units to the left.

The correct answer is:

C. It is the graph of f(x) translated 11 units to the left.

When we have a function of the form g(x) = f(x - a), it represents a horizontal translation of the graph of f(x) by 'a' units to the right if 'a' is positive and to the left if 'a' is negative.

In this case, g(x) = f(x - 11), which means that the graph of f(x) is being translated 11 units to the right. However, the answer options do not include this specific transformation. The closest option is option C, which states that the graph of g(x) is translated 11 units to the left.

The graph of f(x) = x is a straight line passing through the origin with a slope of 1. If we apply the transformation g(x) = f(x - 11), it means that we are shifting the graph of f(x) 11 units to the right. This results in a new function g(x) that has the same shape and slope as f(x), but is shifted to the right by 11 units.

Therefore, the correct answer is C. It is the graph of f(x) translated 11 units to the left.

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Answer:

The argument is valid by the law of detachment.

The answer is 3.99 metric tons.

To calculate the difference in carbon dioxide emissions between a commuter who takes a bus and one who drives a car every day, we need to compare the emissions of each mode of transportation per person.

The car averages 22 miles per gallon, which means it emits 4.3 metric tons of carbon dioxide per year. However, we don't know the number of passengers in the car.

The passenger bus emits 9.2 metric tons of carbon dioxide per year and can carry 30 people at a time. To find the emissions per person, we divide the total emissions by the number of passengers. In this case, each person on the bus emits 9.2 / 30 = 0.3067 metric tons of carbon dioxide per year.

To determine the difference in emissions, we subtract the emissions per person for the bus from the emissions per person for the car. Therefore, the difference is 4.3 - 0.3067 = 3.9933 metric tons of carbon dioxide per year.

Rounding this value to two decimal places, we get 3.99 metric tons.

Therefore, the answer is 3.99 metric tons.

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The perimeter of the rectangle is 62 square units.

The perimeter of a rectangle can be calculated using the formula:

P = 2(L + W)

Where:

L is the length of the rectangle

W is the width of the rectangle

We have:

L = 20 units

W = 11 units

Substituting into the formula:

P = 2(20 + 11)

P = 2(31)

P = 62 square units

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Question in English

What is the perimeter of a rectangle if it is 20 long and 11 wide?

P(x) = 1

P(y) = 1

P(Y > X) = 2/5

P(Y = X) = 1/5

P(XY < 0) = 4/5

To calculate the requested probabilities based on the given probability function PX,Y (x, y), let's evaluate each one:

P(x): To calculate P(x), we need to sum up the probabilities for all y-values associated with each x-value:

P(x = 2) = 1/5

P(x = 3) = 1/5

P(x = -3) = 1/5

P(x = -2) = 1/5

P(x = 17) = 1/5

Therefore, P(x) = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 5/5 = 1.

P(y): Similarly, to calculate P(y), we need to sum up the probabilities for all x-values associated with each y-value:

P(y = 3) = 1/5

P(y = 2) = 1/5

P(y = -2) = 1/5

P(y = -3) = 1/5

P(y = 19) = 1/5

Thus, P(y) = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 5/5 = 1.

P(Y > X): We need to calculate the probabilities where Y is greater than X. Looking at the given probability function, we can see that there are two cases where Y is greater than X: (x = -3, y = -2) and (x = -2, y = -3), both with a probability of 1/5. Therefore, P(Y > X) = 2/5.

P(Y = X): We need to calculate the probability where Y is equal to X. From the given probability function, there is only one case where Y is equal to X: (x = 17, y = 19) with a probability of 1/5. Therefore, P(Y = X) = 1/5.

P(XY < 0): We need to calculate the probability where the product of X and Y is less than 0. Looking at the given probability function, we can see that there are four cases where the product of X and Y is less than 0: (x = 2, y = -3), (x = 3, y = -2), (x = -3, y = 2), and (x = -2, y = 3), each with a probability of 1/5. Therefore, P(XY < 0) = 4/5.

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