a line with slope 3 is 2 units away from the origin. find the area of the triangle formed by this line and the coordinate axes.

The coordinates of the point P after the rotation is P' ( 5 , -2 )

The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.

90° clockwise rotation: (x,y) becomes (y,-x)

90° counterclockwise rotation: (x,y) becomes (-y,x)

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

Given data ,

Let the point be represented as P

The coordinates of P = P ( 5 , 2 )

Now , when the point P is rotated by an angle of 270° about the origin ,

On 270° clockwise rotation: (x,y) becomes (-y,x)

And , on 270° counterclockwise rotation: (x,y) becomes (y,-x)

So , assume the rotation is counterclockwise ,

The coordinates of P after rotation is P' ( 5 , -2 )

And , assume the rotation is clockwise ,

The coordinates of P after rotation is P' ( -5 , 2 )

Hence , the coordinates of P after rotation is P' ( 5 , -2 )

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Answer: 1.18 possibilities 2. 36 possibilities

Step-by-step explanation:

1. 1o, 1g, 1h, 2o, 2g, 2h, 3o, 3g, 3h, 4o, 4g, 4h, 5o, 5g, 5h, 6o, 6g, 6h

2. hw1 hw2 hw3 hw4 hw5 hw6, hg1 hg2 hg3 hg4 hg5 hg6, tw1 tw2 tw3 tw4 tw5 tw6, tg1 tg2 tg3 tg4 tg5 tg6, cw1 cw2 cw3 cw4 cw5 cw6, cg1 cg2 cg3 cg4 cg5 cg6

Answer:

1/

Step-by-step explanation:

1/3+1/2=5/6

1-5/6=1/6

1/

To ride the Ferris wheel, you need 2 tickets.

And to ride the roller coaster, you need 5 tickets.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Trevor loves riding Ferris wheels and roller coasters.

Let x represents the ticket of Ferris wheel.

And y represents the ticket of roller coaster.

While visiting the Putnam County Fair, he first went on the Ferris wheel 1 time and the roller coaster 5 times, using a total of 27 tickets.

x + 5y = 27   {equation 1}

Then, after taking a break and having a snack, Trevor went on the Ferris wheel 1 time and the roller coaster 1 time, using a total of 7 tickets.

x + y = 7    {equation 2}

Subtracting equation 2 to equation 1,

we get,

4y = 20

y = 5

x = 2.

Therefore, it takes 2 and 5 tickets to ride each attraction.

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Let's call the number of days of labor x, and the number of square feet y.

From the information provided, we can set up the following equation:

What does a math equation mean?

A mathematical statement that shows the equality of two mathematical expressions is the definition of an equation in algebra. As an illustration, the two equations 3x + 5 and 14 are joined by the equal sign to get the equation 3x + 5 = 14.

3.89y + 122.42x = 2882.48

We also know that y = x + 189

We can substitute the second equation into the first equation:

3.89(x + 189) + 122.42x = 2882.48

Expanding and simplifying:

3.89x + 730.91 + 122.42x = 2882.48

x = (2882.48 - 730.91) / (3.89 + 122.42) = 22.98 days

So the renovation took 22.98 days.

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7.9 x 10⁻¹¹ is the probability of people who need correction for there eyesight.Yes, it is a significantly number of adults requiring eyesight.

The probability of no more than 21 out of 21 randomly selected adults needing correction for their eyesight would be calculated using the binomial probability formula:

(n choose k) ×  [tex]p^{k}* (1-p)^{n-k}[/tex]

where n is the total number of trail. k is the number of successful trials (the number of adults not needing correction), p is the probability of a successful trial (the probability of an adult not needing correction)which is:

1-0.74 =0.26)

(n choose k) is the binomial coefficient, which is calculated by:

n! / (k! × (n-k)!).

So, the probability of no more than 21 out of 21 randomly selected adults needing correction for their eyesight would be:
(21 choose 21) ×0.26²¹ ×0.74⁰= 0.26²¹ = 7.9 x 10⁻¹¹

This is a very low probability, indicating that it is highly unlikely that no more than 21 out of 21 randomly selected adults would not need correction for their eyesight.

Yes, it is a significantly number of adults requiring eyesight correction. 74% is a high percentage.

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Professor Rodgers can select the group of 4 students in 11880 ways.

Here the professor has to select 4 students from a group of 12. hence we see that

to select the first student, the professor can do so in 12 ways.

To select the second student, the professor now has 11 students left. Hence he can do in 11 ways.

To select the third student, he is left with 10 students, hence the thirst student can be selected in 10 ways

The fourth student can be selected in 9 ways.

Hence, Professor can select the group in 12 X 11 X 10 X 9 ways

= 11880 ways.

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Answer: √196 = 14

Step-by-step explanation: mere guess

The distance from Jim's house to the mall is given as follows:

11.25 miles.

Suppose that we have two points with coordinates given as follows:

[tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]

Then the equation for the distance between these two points is given as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The coordinates are given as follows:

Hence the distance is given as follows:

[tex]D = \sqrt{(17 - 8)^2+(13 - 1)^2}[/tex]

D = 15 units.

Each unit represents 0.75 miles, hence the distance in miles is given as follows:

15 x 0.75 = 11.25 miles.

The problem is given by the image presented at the end of the answer.

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The angle of elevation to the balloon of the runner the greatest distance from the balloon is 83.13 degrees.

The concept used in this problem is Trigonometry. Specifically, the problem uses the tangent function, which is one of the three main trigonometric ratios (sine, cosine, and tangent) used to relate the angles and sides of a right triangle.

To solve this problem, we can use the tangent function of trigonometry, which relates the opposite side (the distance from the runner to the balloon) to the adjacent side (the distance from the runner to the point on the highway) and the hypotenuse (the distance from the point on the highway to the balloon).

Let's call the angle of elevation of the runner closest to the balloon as angle A and the angle of elevation of the runner farthest from the balloon as angle B.

tan(A) = opposite / adjacent = (1500 - 421.2) / 421.2 = 878.8 / 421.2

tan(B) = opposite / adjacent = (1500 + 421.2) / 421.2 = 1921.2 / 421.2

We can use the inverse tangent function (arctan) to find the angle of elevation of the runner the greatest distance from the balloon.

B = arctan(1921.2 / 421.2)

The result is in radians, to convert the angle from radians to degrees, we can use the conversion factor of 180/pi.

B = arctan(1921.2 / 421.2) = arctan(4.5536) = 83.13 degrees (approx)

so, the angle of elevation to the balloon of the runner the greatest distance from the balloon is 83.13 degrees.

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The value x = -3 is a solution for the inequality at option C.

-x - 6 > -3.5

To check this, we just need to evaluate the given inequalities in x = -3, then we can see if the inequality is true or false.

For example, the first one:

-4 - 6 < -3.5

Does not depend on x, so we can ignore that.

The next one is:

-r - 6 > 3.5

Evaluating it on -3 we get:

3 - 6 > 3.5

-3 > 3.5

this is false.

The next one is:

-x - 6 > -3.5

Evaluating we wll get:

3 -6 > -3.5

-3 > -3.5

This is true, so this one is the correct option.

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Answer:104 miles in 2 hours.

Step-by-step explanation:

so first since we need to know how much he drove in 2 hours we just divide 156 by 3 to get 52 and then multiply 52 by 2 since we need to know how many miles he traveled in 2 hours then you get your final answer of

104

The fifth term of the expression is 1215x²y⁴.

Binomial theorem is the method of expanding an expression consisting of two terms raised to any power.

By binomial theorem,

(x - 3y)⁶ = 6C₀ x⁶ + 6C₁ x⁵ (3y) + 6C₂ x⁴ (3y)² + 6C₃ x³ (3y)³ + 6C₄ x² (3y)⁴ + 6C₅ x (3y)⁵ + 6C₆ (3y)⁶

Simplifying the combination part,

            = x⁶ + 6x⁵(3y) + 15x⁴(3y)² + 20x³(3y)³ + 15x²(3y)⁴ + 6x(3y)⁵ + (3y)⁶

            = x⁶ + 18x⁵y + 135x⁴y² + 540x³y³ + 1215x²y⁴ + 1458xy⁵ + 729y⁶

Hence the fifth term of the expression is 1215x²y⁴.

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Answer:

D. 1/48

Step-by-step explanation:

Each event (spinning a 3, spinning orange, rolling an even number) is an independent event, so the overall probability is the product of the three individual probabilities.

For each event,

p(event) = (number of desired outcomes)/(total number of possible outcomes)

p(spinning a 3) = 1/6

p(spinning orange) = 1/4

p(even number) = 3/6 = 1/2

p(spinning a 3 then spinning orange then rolling an even number) =

= 1/6 × 1/4 × 1/2

= 1/48

Answer: D. 1/48

Answer:

1/48

Step-by-step explanation:

First look at the spinner- there is only one three out of six, so the spinner is 1/6

Now looking at the second spinner- there are four spaces and one orange- giving us 1/4

And finally for the die there are six sides and three are even- which is 3/6

And in order to get our final answer we will multiply 1/6 * 1/4 * 3/6 which equals 1/48

The expression that represents Sandy’s earnings is 5x - 24

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

Cost price = $24

Selling price = 5 per jar

This means that the total sales is

Total = 5 * x

Evaluate

Total = 5x

The earnings is the difference between the total sales and the cost price

Sp, we have

Earnings = 5x - 24

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The inequality to represent the constraints will be:

x + y ≥ 325

x + 2y = 600

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Let x = number of vegetarian meals

Let y = number of meats.

The inequality to represent the constraints will be:

x + y ≥ 325

x + 2y = 600

In this case, the daily budget is 600.

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The area of the polygon U is 272 cm².

The area is the volume contained within the boundary of a 2D shape. It is written as a square and is measured in square metres or centimetres, etc.

The idea of area can be thought of as the area inside a particular shape or space. It refers to the volume of space occupied. As a shape gets bigger, its area and perimeter get bigger as well. Area is distinct from volume and only refers to the area occupied by a flat or 2D object.

As they work with different 2D shapes and calculate each one's area, kids will learn that different shapes require the use of different formulas and methods to find the area.

Step1:

3/12 = s/u =k

s t/s u=f² =(s/u)² =s/16

17/s u=s/16

step2:

s u = 17.16 = 272 cm²

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The mass of the marble lifter by a sculpture is 0.0306 kg.

A cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.

We know the volume of a cuboid is (length×width×height).

Therefore, The volume of this cuboid is (1×0.6×0.3) = 0.18 m³.

The marble has a density of 2.7g/cm which is equivalent to 0.17kg/meter.

We know Mass = volume×density.

Therefore, The mass of the marble is 0.17×10.18 kg.

= 0.0306 kg.

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221 degree is the direction of B to the nearest degree.

We have to find the vector B. We will substructure Equations

-9i - 8j - 5i - 4j = -14i -12j

                       = 2(-7i-6j)

From here you get the value of vector B. That is minus seven i and minus of six j. Now we can see that this is both. The signs are negative so it should lie in 3rd chord event.

And for third quarter went in their direction or we can say Angelo factor B is want A D. Plus theater. So when I. D. Plus and universal marvelous of -6 divided by -7 that provides us one or d. plus 41 degree. That is 221 degree.

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Answer:  In this question, we are trying to find the difference in price between one apple and one banana. We can set up a system of two equations with two variables to represent the information given in the problem. Let x be the price of one apple in cents and y be the price of one banana in cents.

The first equation represents the information that Dan paid $5.70 for 5 apples and 3 bananas:

5x + 3y = 570

The second equation represents the information that Chris paid $4.70 for 3 apples and 5 bananas:

3x + 5y = 470

We can use these equations to solve for the value of x (the price of one apple) in terms of y (the price of one banana).

We can use the first equation and solve for x:

5x = 570 - 3y

x = (570 - 3y)/5

We can then substitute this expression of x into the second equation:

3((570 - 3y)/5) + 5y = 470

By multiplying both sides of the equation by 5 and 3 respectively, we can get the equation in a form that we can solve for y and then substitute back for x.

We can solve for y by subtracting 3((570 - 3y)/5) from both sides:

5y = 470 - 3((570 - 3y)/5)

Expanding and simplifying the right side of the equation:

5y = 470 - 3(114 - y)

5y = 470 - 342 + 3y

y = (470 - 342)/8

We can substitute this value of y back into the first equation and solve for x

x = (570 - 3y)/5

x = (570 - 3(470 - 342)/8)/5

x = (570 - 441)/5

Therefore, the price of one apple is (570 - 441)/5 = 129 cents more than the price of one banana.

Step-by-step explanation:

Answer:

Construct an angel bisector

The system of linear equations: 2x-y=18 & 4x-3y = 16 has no solution.

The system of linear equations has no solution if the equations are inconsistent, meaning that there is no set of values for the variables that satisfies all of the equations simultaneously. One way to check for inconsistency is to try to find the solution by solving for one of the variables in one equation and then substituting it into another equation to see if both equations are satisfied. If the equations yield different values for the same variable, then the system has no solution.

In this case, the system of linear equations:

2x-y=18

4x-3y = 16

Has no solution. We can solve for x in the first equation and then substitute it into the second equation. If the equation yields a different value for y, then the system has no solution.

2x-y=18

2x=y+18

x=y/2 + 9

Now, substituting x into the second equation:

4x-3y=16

4(y/2 + 9) - 3y = 16

2y + 36 - 3y = 16

-y = -20

This result implies that y is not a real number, so the system of equations has no solution.

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Answer:

Your answer is Identitive property

Answer:

y=1/2x-5

Step-by-step explanation:

Parallel lines always have the same slope. Thus, since you know y=1/2+1 is parallel you know the slope is 1/2 as in y=mx+b, m is the slope. In addition, you know the y-intercept as -5. So the equation is y=1/2x-5

Answer:

y=1/2x-5

Step-by-step explanation:

to be parallel it needs to have the same slope so the slope is the same

0,-5 is the y intercept so -5 is the y intercept

The angle, ∠B has 2 possible angles, one is 41.81° and the other will be 138.19°

In ΔABC we have been given that

AB = 6 cm

BC = 9 cm

A formula for the area of a triangle is

1/2 X one side X oth sde X sin(common angle)

Hence if we consider AB and BC with common angle, ∠B we get

1/2 X 6 X 9 X sinB = 18

or, sinB = 18/27

or, sinB = 2/3

Now since sin is positive in 2 quadrants, we will have 2 possible values for ∠B

one will be 41.81° and the other will be (180 - 41.81)° = 138.19°

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The angle relationship between ∠1 and ∠2 are as follows:

When parallel lines are cross by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, same interior angles, vertically opposite angles etc.

Therefore. let's find the relationship of the angle 1 and 2 in the parallel lines cut by the transversal.

Hence, the relationship are:

1. Same side interior angles

2. alternate interior angles

3. corresponding angles.

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By solving a system of equations we will see that the larger number is 21 and the smaller one is 6.

Let's define the variables:

x = smaller number

y = larger number.

We know that the larger of two numbers is 9 more than twice the smaller, so we can write:

y -2x = 9

The sum of the numbers is 3 less than five times the smaller.

x + y = 5x - 3

Then we have a system of equations:

y -2x = 9

x + y = 5x - 3

Now we can isolate y on the first equation to get:

y = 9 + 2x

We can substitute that on the other equation to get:

x + 9 + 2x = 5x - 3

3x + 9 = 5x - 3

9 + 3 = 5x - 3x

12 = 2x

12/2 = x

6 = x

And the value of y is:

y = 9 + 2x

y = 9 + 2*6 = 21

These are the two numbers.

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 The binomial distribution is a discrete probability distribution used in probability theory and statistics to explain the number of successes in a set number of trials, where each trial can only result in success or failure. The probability mass function (PMF) shown below defines the binomial distribution as follows:

P(a) = ⁿСₐ * p^a* (1-p)^(n-a)

Where:

a: the number of successes in n trials

n: the total number of trials

p: the probability of success in one trial

ⁿСₐ : n! / (a! * (n-a)!)

      the binomial coefficient, which shows how many different ways there are to select k successes from n trials.

    A variety of phenomena, including coin tossing, die rolling, and other tests with a set number of trials and only two possible outcomes, can be usefully modelled using the binomial distribution.

In a blind tasting test, if participants are unable to distinguish between bottled and tap water, we can assume that their guesses are random. The probability of accurately predicting the type of water in this situation is 50%.

The likelihood that 8 out of 9 people will properly predict their water type is

(1/2)^8 * (1/2)^1 = (1/2)^9 = 1/512

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The missing value in the space provided is given as follows:

75.

A proportional relationship is modeled as follows:

y = kx.

In which k is the constant of proportionality.

The constant for the relationship in this problem is given as follows:

k = 125/5 = 100/4 = 25/1 = 25.

Hence the relationship is given as follows:

y = 25x.

The missing value is the output when x = 3, hence:

y = 25(3)

y = 75.

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