Triangle BCD has vertices B(-8,3), C(-4, 6), and D(2, 0). If the triangle is reflected across the x-axis and dilated by a scale factor of 0. 5 with respect to the origin, what are the coordinates of the vertices of triangle B"C"D"?

let's firstly convert the mixed fraction to an improper fraction.

[tex]\stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{trail mix}}{\cfrac{4}{3}}\div \stackrel{bags}{4}\implies \cfrac{4}{3}\div \cfrac{4}{1}\implies \cfrac{4}{3}\cdot \cfrac{1}{4}\implies \cfrac{4}{4}\cdot \cfrac{1}{3}\implies \stackrel{per~bag}{\cfrac{1}{3}}[/tex]

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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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 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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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 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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Over a period of 5 years, the amount that you would have to pay monthly is given as  $3,201.37

To calculate the monthly mortgage payment for a house that costs $621,900 with an interest rate of 5.4% over 5 years, you can use the following formula:

P = (r(1 + r)^n) / (((1 + r)^n) - 1) * L

Where:

P = monthly payment

r = monthly interest rate (5.4%/12 = 0.0045)

n = total number of payments (5 years x 12 = 60)

L = the loan amount ($621,900)

Plugging in the values, we get:

P = (0.0045(1 + 0.0045)^60) / (((1 + 0.0045)^60) - 1) * 621,900

P = $3,201.37

So you have to pay  $3,201.37 monthly over 5 years.

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The correct equation for Jeff after every cost will be   y = 750 -100x

Cost of the television = $750

Loan amount paid per month = $100

Amount put in savings = $200

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Since the amount of $200 is being saved, this means that it is not going away or is being spent. Now, as per the question, the initial remaining balance with Jeff is 750. The balance decreases by the loan amount of 100 per month.

This means that the amount is reduced by = 100x.

Therefore, the equation describing the scenario is -

y = 750 -100x

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Answer: √196 = 14

Step-by-step explanation: mere guess

The number of times more intense that the earthquake in Alaska was than the one in Japan was 1, 000 times more intense.

The Richter magnitude is determined by measuring the height of the greatest wave that has ever been seen at a given distance from the seismic source.

Each order of magnitude is 10 times more intense than the previous one since the Richter scale is a base-10 logarithmic scale. To put it another way, a two is ten times as intense as a one, and a three is one hundred times stronger.

This means that the number of times more intense that the earthquake in Alaska was than the one in Japan was:

= 10 x 10 x 10

= 1, 000 times

Note : Alaska and Japan earthquake difference:

= 9  - 6

= 3

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The three inequalities that define the shaded region are given as follows:

The inequality that defines the values below the vertical line y = 2 is given as follows:

y < 2.

(open interval as the line is dashed).

The increasing line has an intercept of 0 and slope of 2, with values to the right being shaded and the line being dashed, hence the inequality is given as follows:

y > 2x.

The decreasing line has an intercept of -2 and a slope of -1, with values to the left being shaded, with a closed interval, as the line is shaded, hence the inequality is given as follows:

y ≤ -x - 2.

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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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 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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Step-by-step explanation:

please attached for details

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

Because a 30-year mortgage has a longer term, your monthly payments will be lower and your interest rate on the loan will be higher.

A 30-year fixed-rate mortgage is commonly used to refer to conventional loans. Conventional loans are not backed by the government; however, a 30-year fixed FHA, USDA, or VA loan that is insured by the government is available. Rocket Mortgage® does not currently provide USDA loans.

A 30-year fixed-rate mortgage is a house loan with a 30-year repayment period and an interest rate that remains constant during the loan’s duration. When you take for a 30-year fixed-rate home loan, the amount you make each month remains the same until the loan is paid off.

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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:

Step-by-step explanation:

won 140

lost 140-50=90

Ratio wins to losses: 14:9

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

Answer: 50

Step-by-step explanation:

i don't know how i got this but yeah its 50

The ratio of female birds is 3/7.

One way to express something as a percentage of another is to use a ratio, which is a mathematical concept.

By typically dividing two figures, ratios contrast them. If you were comparing one data point (A) to another data point, your formula would be A/B. (B). You are multiplying information A by information B, as indicated by this. For instance, if A is 5 and B is 10, your ratio will be 5/10.

The pet store has 12 male birds for every 9 female birds.

total birds = 12 + 9 = 21 birds.

So, the ratio of female birds =  female birds / total birds

                                              = 9/21

                                              = 3/7

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Answer:

1/

Step-by-step explanation:

1/3+1/2=5/6

1-5/6=1/6

1/

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:

In an equilateral pentagon, all angles have equal degree measures, so to find the degree measure of one angle, we need to find the sum of the degree measures of the interior angles and then divide by the number of angles.

Step 1: Find the sum of the degree measures of the interior angles of the pentagon:

180 * (5 - 2) = 540 degrees

Step 2: Divide the sum by the number of angles:

540 degrees / 5 angles = 108 degrees

The degree measure of angle E is 108 degrees.

The degree measure of angle E is 108°.

We can use interior angels theorm.

The sum of the interior angles of a pentagon can be calculated using the formula:

Interior angle sum = (n - 2) × 180

where n is the number of sides of the polygon.

In this case, n = 5, so the sum of the interior angles of the pentagon is (5 - 2) × 180 = 540°.

Since angle A and angle B are both equal to 108°, we can say that:

angle A + angle B = 2 × 108 = 216°.

So, the sum of the remaining three interior angles (angles C, D, and E) is:

540 - 216 = 324°

Since each of these three angles is equal, the measure of each angle must be 324° divided by 3, or:

324 ÷ 3 = 108°

So, the degree measure of angle E is also 108°.

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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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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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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:

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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