if P is the incenter of jkl find each measure

The table which shows the equivalent ratios is Table 3.

Column 1   Column 2   Ratio

2                  24             1:12

5                  60             1:12

6                  72              1:12

7                  84               1:12

What is ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other.

The first table is -

Column 1   Column 2

2                  36

4                  48

5                  60

6                  72

Reduce the column 1 and column 2 values to its simplest form to get the ratio.

The ratio values are for row 1 - 1:18, row 2 - 1:12, row 3 - 1:12 and row 4 - 1:12.

So, row 1 has different ratio than other three rows.

The second table is -

Column 1   Column 2

2                  22

3                  39

4                  48

6                  72

Reduce the column 1 and column 2 values to its simplest form to get the ratio.

The ratio values are for row 1 - 1:18, row 2 - 1:13, row 3 - 1:12 and row 4 - 1:12.

So, row 1 has different ratio and row 2 has different ratio than other two rows.

The third table is -

Column 1   Column 2

2                  24

5                  60

6                  72

7                  84

Reduce the column 1 and column 2 values to its simplest form to get the ratio.

The ratio values are for row 1 - 1:12, row 2 - 1:12, row 3 - 1:12 and row 4 - 1:12.

So, all rows have same ratios.

The fourth table is -

Column 1   Column 2

2                  28

3                  36

4                  48

6                  72

Reduce the column 1 and column 2 values to its simplest form to get the ratio.

The ratio values are for row 1 - 1:14, row 2 - 1:12, row 3 - 1:12 and row 4 - 1:12.

So, row 1 has different ratio than other three rows.

Therefore, table 3 has equivalent ratios.

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The solution to the given fractional equation is x = -4

32/x - 8 = 24/x - 10

collect like terms

32/x - 24/x = -10 + 8

(32-24) / x = -2

8/x = -2

cross product

8 = -2 × x

8 = -2x

divide both sides by -2

x = 8/-2

x = -4

Check:

32/x - 8 = 24/x - 10

32/-4 - 8 = 24/-4 - 10

-8 - 8 = -6 - 10

-16 = -16

Therefore, the equation has the solution x = -4

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Answer:

Abigail wants the hairdresser to cut off 1/4 of the total length of her hair, which is 32 inches long.

To find out how many inches the hairdresser cuts, we can multiply the total length of her hair by 1/4:

32 inches * 1/4 = 8 inches

So the hairdresser cuts off 8 inches of Abigail's hair.

[tex]\stackrel{\textit{not distributed yet}}{\cfrac{x+1}{(x-2)(x+1)}\stackrel{\downarrow }{\text{\LARGE -}}\cfrac{x-2}{(x-2)(x+1)}}\implies \stackrel{\textit{already distributed}}{\cfrac{x+1}{(x-2)(x+1)}\stackrel{\downarrow }{\text{\LARGE +}}\cfrac{-x+2}{(x-2)(x+1)}} \\\\\\ \cfrac{x+1-x+2}{(x-2)(x+1)}\implies \cfrac{3}{(x-2)(x+1)}[/tex]

Answer:

The error is in the 3rd step.  The denominator should be 3, not -1.

Step-by-step explanation:

The third step has an error.  The second fraction is subtracted from the first.  The calculation should have been (x+1) - (x-2).  x+1-x+2 = 3.

See the attached worksheet.

The number of different ways the medals can be awarded is (finalists) * (finalists -1) / 2.

We have two medals (gold and silver) and "n" finalists. The question asks for the number of ways the medals can be awarded.

This is a combination problem, where we have to select 2 items (medals) out of n items (finalists) without regard to the order.

The number of ways to select k items out of n items without regard to the order is given by the binomial coefficient (n choose k), which is calculated as:

nCk = n! / (k!(n-k)!)

where n is the total number of items, k is the number of items selected and ! denotes factorial.

So, in this problem, we have to calculate the number of ways to select 2 medals out of n finalists, the binomial coefficient is:

nC2 = n! / (2!(n-2)!) = n*(n-1)/2

so the number of different ways the medals can be awarded is n*(n-1)/2

Therefore, the number of different ways the medals can be awarded is (finalists) * (finalists -1) / 2.

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Factoring, utilizing square roots, completing the square, and the quadratic formula are the four ways for solving a quadratic equation.

To factor a quadratic equation, do the following:

1. In standard form, transform the equation such that one side is zero.

2. Take into account the non-zero side.

3. Make each component equal to zero (Remember: a product of factors is zero if and only if one or more of the factors is zero).

4. Solve each of the resultant equations.

Factoring cannot solve all quadratic problems. For example, x²- 3x = 3 cannot be solved using this approach. Completing the square is one approach for solving quadratic equations; graphing the result is another.

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Answer:

  18

Step-by-step explanation:

You want the number of vertices such that the number of pairs of vertices is 153.

The number of n objects taken 2 at a time is ...

  N = (n)(n -1)/2

You want to find n for N=153.

We notice that multiplying by 2 gives a near square:

  2N = n(n -1)

The square root of this will have a value approximately equal to n-1/2:

  n -1/2 ≈ √(2·153) = √306 ≈ 17.5   ⇒   n = 18

We can check this:

  (18)(17)/2 = 9·17 = 153

The mystic rose with 153 lines has 18 vertices.

__

Additional comment

We could solve the quadratic equation 306 = n(n-1) by any of several means. The method used here is about the fastest.

If you want to get formal about solving the equation this way, you can define z = n-1/2, then the equation becomes ...

  306 = (z +1/2)(z -1/2) = z² -1/4

  306.25 = z²   ⇒   z = 17.5   ⇒   n = 18

By leaving off the 0.25 addition to 306, the root we get is slightly low, but still close enough to 17.5 to show us what the answer is.

Answer:

B. (50)

Step-by-step explanation:

So, looking at PEMDAS,

Parenthesis,

Exponents,

Multiplication,

Division,

Addition,

Subtraction.

We have no parenthesis and no exponents.

But, we have multiplication.

62x1=62

According to the identity property of 1, any number multiplied by 1 retains its identity. In other words, any number multiplied by one remains unchanged. The number remains constant because multiplying by one produces one copy of the number.

So, next, we have an addition problem.

62+2=64.

And now, subtraction.

64-14=50.

So, the final answer is 50 or known as B.

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Answer:

x=4

Step-by-step explanation:

3x+4=x+12

     -4    -4

3x=x+8

-x   -x

2x=8

/2   /2

x=4

The down payment is 400, the monthly payment is 65 and the length of the plan is 7 months. An arithmetic sequence is a sequence of numbers such that the difference between any two consecutive numbers is constant.

Arithmetic refers to the branch of mathematics that deals with numbers and the basic operations of addition, subtraction, multiplication, and division. An arithmetic sequence is a specific type of mathematical pattern where each term is obtained by adding a constant value to the previous term.

Here is the way to determine the monthly payment:

(1,060 - 400) / 7 = (660) / 7 = 65

As you can see the down payment is 400 and the last value in the sequence is 1060, so the total amount of the plan is 1060.

Also, the difference between any two consecutive terms is 110, as we can see that from the sequence:

510 - 400 = 110

620 - 510 = 110

730 - 620 = 110

840 - 730 = 110

950 - 840 = 110

1060 - 950 = 110

So the length of the plan is 7 months as the sequence contains 7 terms.

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The exact magnitude of BD is q - 3p

Consider the following diagram.

Here, in trapezium ABCD, side DC is parallel to side AB

and DC=3AB

Given that M is the midpoint of DC

From definition of midpoint, DM = MC

The magnitude of DM or MC would be

= 1/2 ​DC

= (1/2) × 3 × AB

= (3/2) × AB

= (3/2) p

From given figure we can observe that BD = BC + CD

so, BD = BC - CD

BD = q - 3p​

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The complete question is:

ABCD is a trapezium with AB parallel to DC and DC=3AB. M is the midpoint of DC. AB=p​, BC=q​.

Find the exact magnitude of BD.

Answer:

The equation of a straight line passing through the origin can be written in the form y = mx, where m is the slope of the line. To find the equation of a line that is perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line.

A line that is perpendicular to a line with the equation ax²-2hxy-by², we can find the slope of the given line by taking the derivative with respect to x.

The slope of the line is -2hy/ax.

The negative reciprocal of this slope is ax/2hy.

So the equation of the line perpendicular to ax²-2hxy-by² and passing through the origin is y = ax/2hy * x.

Note that if a = 0, the line is parallel to Y-axis and if b = 0, the line is parallel to X-axis.

The side-length of the given square is 4 units and the equation used to represents the length of the diagonal AC is given by y = -x + 6 .

As given in the question,

In the given square ABCD,

Coordinates of the vertices of the square is given by :

A(2,4), B(-2,4), C(-2,8), and D(2,8)

All the side - length of the square are of equal measure.

Side-length of AB = √ ( 4 - 4 )² + ( -2 -2 )²

                              = √ 16

                              = 4 units

Equation of the diagonal AC is given by :

( y - 4 ) / ( x - 2 ) = ( 8 - 4 ) / ( - 2 -2 )

⇒( y - 4 ) / ( x - 2 ) = 4 / -4

⇒ y - 4 = -1 ( x - 2 )

⇒ y = -x + 2 + 4

⇒ y = -x + 6

Therefore, the side-length of the given square is 4 units and equation of the diagonal AC is y = -x + 6.

The given question is incomplete, I answer the question in general according to my knowledge:

Square ABCD with vertices A(2,4), B(-2,4), C(-2,8), and D(2,8) over the x-axis. Find the length of each side and equation to represent the length of diagonal AC of the given square ?

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Note that in the above distance-time graph, Sue was traveling for 210 minutes, while she was stationary for 150 minutes.

Note that if the x-axis of the graph is calibrated to 30 minutes per unit/calibration. When examined you'd note that the total number of hours of the trip is from 2 pm to 8 pm which is 6 hours or 360 minutes.

The part of the graph that depicts when Sue was traveling is all the part of the pink curve that is at an incline while the part that represents when she was stationary is when the curve was horizontal.

Adding up the minutes when the graph was at an incline gives a total of 210 minutes.

Thus, the number of times Sue spent being stationery is:
360 - 210

= 150 minutes. This also corresponds with the number of times the graph is horizontal.

Thus, Sue was moving for 210 minutes and stationery for 150 minutes.

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Note that in the above distance-time graph, Sue was traveling for 210 minutes, while she was stationary for 150 minutes.

What is the justification for the above result?

Note that if the x-axis of the graph is calibrated to 30 minutes per unit/calibration. When examined you'd note that the total number of hours of the trip is from 2 pm to 8 pm which is 6 hours or 360 minutes.

The part of the graph that depicts when Sue was traveling is all the part of the pink curve that is at an incline while the part that represents when she was stationary is when the curve was horizontal.

Adding up the minutes when the graph was at an incline gives a total of 210 minutes.

Thus, the number of times Sue spent being stationery is:

360 - 210

= 150 minutes. This also corresponds with the number of times the graph is horizontal.

Thus, Sue was moving for 210 minutes and stationery for 150 minutes.

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Answer: (3, -3)

Step-by-step explanation:

2x = 4y + 18 => 2x - 4y = 18   (1)

-5x - 6y = 3   (2)

Multiply both (1) by 5, and (2) by -2

10x - 20y = 90   (3)

10x + 12y = -6    (4)

(3)-(4):

-32y = 96

y = -3

x = 3

Answer:

Step-by-step explanation:

2,4

A mixture contains 200 oz of juice that contains 60% tomato juice and 100 oz vegetable juice that contains 20% tomato juice. The concentration tomato juice in the resulting mixture is 40%.

Percentage is used to represent a fraction of a hundred.

Let:

w1 = weight of tomato juice in juice 1

w2 = weight of tomato juice in vegetable juice

Hence,

w1 = 60% x 200 oz = 120 oz

w2 = 20% x 100 z = 20 oz

Total weight of tomato juice = 100 + 20 = 120 oz

Total weight of the mixture = 200 oz + 100 oz = 300 oz.

Hence, the concentration of the tomato juice in the final mixture is:

concentration = total weight of tomato juice/ total weight of mixture

                       = 120/300

                       = 2/5 = 40%

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By using speed calculation and the Pythagorean theorem, it can be concluded that the contestant is moving down at a rate of 11.8 feet/second.

In speed calculation, speed is defined as the distance traveled in a certain unit of time. Speed can be calculated by dividing the distance by time:

Speed = distance / time

We will need the Pythagorean theorem to solve the problem as well. It says that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the two shorter sides:

c² = a² + b²

Now we take a look at the problem.

The height of the pole = 50 feet

Distance between pole and anchor = 50 feet

Time = 7 seconds

We want to know the speed of a contestant, that is the distance traveled in 6 seconds.

Let c be the distance traveled, a be the height of the pole and b be the distance between the pole and the anchor.

We will use the Phtagorast Theory to find c:

c² = a² + b²

   = 50² + 50²

   = 2500 + 2500

   = 5000

c = √5000

  = 70.7 feet

Rate or speed the contestant moving down the line:

Rate = distance / time

        = 70.7 / 6

        = 11.8 feet/second

Thus, the contestant is moving down at a rate of 11.8 feet/second.

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The values are calculated as Part A : $3611.6245, Part B : 21.81% and Part C : $1107.75.

Mark Down percentage is the percentage of reduction in the original price of an item.

Mark down percentage = [(original price - selling price) / original price] × 100

Part A :

Original price = $4248.97

Markdown = 15%

0.15 = (4248.97 - x) / (4248.97)

4248.97 - x = 637.3455

x = 4248.97 - 637.3455

x = $3611.6245

Reduced price of the refrigerator is $3611.6245.

Part B :

Selling price = $1270.55

Original price = $1625

Mark up percentage = [(1625 - 1270.55) / (1625)] × 100

                                  = [354.45 / 1625] × 100

                                  = 21.81%

Part B :

Selling price = $886.20

Mark down percentage = 20%

0.2 = (x - 886.2) / x

0.2x = x - 886.2

x - 0.2x = 886.2

0.8x = 886.2

x = $1107.75

Hence the selling price, mark down percentage and original price has been calculated as $3611.6245, 21.81 % and $1107.75 respectively.

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The histogram displays the frequency distribution of a variable in intervals, showing shape, central tendency and variability.

The histogram of the wr.hnd variable in the overview information in R utilizing the hist capability would show a graphical portrayal of the recurrence dissemination of the information. It would show the quantity of perceptions (i.e., the recurrence) in various spans (i.e., canisters) of the wr.hnd variable. This can give knowledge into the appropriation of the information, like the shape, focal propensity, and changeability.

A precise depiction for the histogram of wr.hnd could include:

The histogram shows the recurrence appropriation of the wr.hnd variable.

The wr.hnd variable is partitioned into stretches or canisters, and the level of each bar addresses the quantity of perceptions in that span.

The histogram gives a visual portrayal of the shape, focal propensity, and changeability of the wr.hnd information.

The histogram shows the recurrence circulation of a variable in spans, showing shape, focal propensity and changeability.

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The symbol used in the ratio is given by :

1. If we are using ' : ' symbol it is called colon.

2. If we are using ' \ ' symbol it is called by.

3. Third way we use word 'to' to represent the ratio.

As given in the question,

Different symbols used to represent the ratio of two numbers.

Let us consider two number be 'x' and 'y'.

1. Ratio can be represented in the form x : y.

Used symbol ' : ' is known as colon.

2. Ratio can be represented by fraction form.

x / y

Here 'x' is called numerator and y is called denominator.

3. Third way to write ratio is word 'to'

x to y.

Therefore, symbols used to represents the ratio of any given numbers is called 'colon' , 'by' , and 'to'.

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The volume of the box in shape of a rectangular prism is solved to be

716 inches³

Three-dimensional object with six faces is called a rectangular prism (two at the top and bottom and four are lateral faces).

The prism has rectangular-shaped faces on each side. As a result, there are three sets of matching faces in this picture. Rectangular prisms are sometimes known as cuboids due to their shape.

In the given problem the formula used for volume of prism is

= length * width * height

= 358 * 1/2 * 4

= 716 inches³

The prism has a volume of 716 inches³

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The volume of the rectangular prism with a length of 358 inches, width of 1/2 inches and a height of 4 inches is 716 in³.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is width, h is height and l is length.

Given that;

Plug the given values into the above formula and simplify.

V = w × h × l

V = 1/2 in × 4 in  × 358 in

V = 716 in³

Therefore, the volume of the box is 716 in³.

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The acute angles are 54,36  and the larger angle is 54 .

What is triangle ?

Triangle can be defined in which it consists of three sides , three angles and sum of the three angles is always 180 degrees.

sin(x+9) = cos(2x)

2x+ x+9 = 90

3x =90-9 = 81

x = 81/3 = 27

x+9 = 27 + 9 = 36

2x = 27*2 = 54

sin36= 0.58

cos54 = 0.58

the two acute angles are 54 and 36 degrees

The larger angle = 2x = 2* 27 = 54

Hence, The acute angles are 54,36  and the larger angle is 54 .

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Using proportions and similar triangle theorem, the value of x is 54.6m

A comparable triangle is a triangle that is similar to another triangle in shape but may not be identical in size. If and only if two triangles have equal matching angles and side ratios, two triangles are said to be similar.

In this problem, we can use the concept of proportion and similar triangle theorem to find the value of x.

This is represented mathematically as;

45.5 / 80.5 = x / 96.6

Cross multiply both sides and solve for x

45.5 * 96.6 = 80.5 * x

4395.3 = 80.5x

x = 4395.3 / 80.5

x = 54.6

The value of x is 54.6m

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On solving the provided question we can say that quadratic equation  x^2 - 2x - 8=0 => (x-4)(x-2) = 0 = > x = 4, 2

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

we have a quadratic equation -

x^2 - 2x - 8=0

(x-4)(x-2) = 0

x = 4, 2

by help of prime factorization

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Answer:

9

Step-by-step explanation:

810/90 = d

d=90

Answer:

d = 9

Step-by-step explanation:

to solve, divide each term by 90 and then simplify

90d = 180

[tex]\frac{90d}{90}[/tex] = [tex]\frac{810}{90}[/tex]

[tex]\frac{810}{90}[/tex] = 9

[tex]d[/tex] = 9

The amount of the 60 milligram dose that is still active in the dog’s bloodstream after 3 hours, after 4.25 hours, and after n hours respectively are as follows;

f(3) = 60(0.80)^3.

f(4.25) = 60(0.80)^4.25.

f(n) = 60(0.80)^n.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = ab^x

Where:

Since 20% of the medicine becomes ineffective every hour, this ultimately implies that the relationship is geometric and the rate of change (decay rate) is given by:

Rate of change (decay rate) = 100 - 20 = 80% = 0.8

After 3 hours, the active dose is given by:

f(3) = 60(0.80)^3

After 4.25 hours, the active dose is given by:

f(4.25) = 60(0.80)^4.25

After n hours, the active dose is given by:

f(n) = 60(0.80)^n

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Complete Question:

Medicine taken by a patient breaks down in the patient’s blood stream and dissipates out of the patient’s system. Suppose a dose of 60 milligrams of anti-parasite medicine is given to a dog and the medicine breaks down such that 20% of the medicine becomes ineffective every hour.

How much of the 60 milligram dose is still active in the dog’s bloodstream after 3 hours, after 4.25 hours, and after n hours?

A scale factor of 1/3 for the transformation is discovered using proportions.

In accordance with the rule of three, a percentage is a component of a total amount.

If both the new and original dimensions are known, the scaling factor may be determined. A figure's scale factor can be calculated using the following simple formula: Dimension of the original shape minus the dimension of the new shape is the scale factor.

When applying the proportion to this situation, the scale factor of the transformation is 1/3 because each coordinate was multiplied by 3 throughout the transformation process.

A scale factor of 1/3 for the transformation is discovered using proportions.

The complete question is,

DO,K = (9, 6) (3, 2) (3, 2) Scale factor is

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The range of the function is (0, 30), which represents the possible values of the boat's value in thousands of dollars.

An equation is a mathematical statement that uses symbols, numbers, and/or variables to represent a relationship between two or more quantities. It usually contains an equal sign, indicating that the expressions on both sides of the equal sign have the same value. Equations are used to solve problems and find unknown values by manipulating the symbols and solving for the variable.

Here,

The given graph does not represent an exponential function as the values of y do not increase or decrease at a constant rate. However, we can approximate the values and find an exponential function that fits the data points closely.

Using the two given points (0, 30) and (1, 24), we can find the base of the exponential function as follows:

y = abˣ

30 = ab⁰ (at x=0, y=30)

24 = ab¹ (at x=1, y=24)

Dividing the second equation by the first, we get:

24/30 = (ab¹)/(ab⁰)

0.8 = b

Now we can substitute the value of b in one of the equations to find a:

30 = a(0.8)⁰

a = 30

So the exponential function that fits the data points closely is:

y = 30(0.8)ˣ

The y-intercept of this function is 30, which means that the initial value of the boat is $30,000.

The domain of the function is all real numbers (x can be any value representing time in years).

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