A conjecture and the flowchart proof used to prove the conjecture are shown. Given: Measure of angle B C D equals 45 degrees. Prove: Triangle A C B is an obtuse triangle. Art: Triangle A B C. A ray passes through point D that extends horizontally right forming an exterior angle B C D. Drag an expression or phrase to each box to complete the proof.

The solutions to the original polynomial equation X(x^3-10x^2+28x-24) = 0 are x = 0, x = 2, and x = 6.

To find the solutions to the polynomial equation X(x^3-10x^2+28x-24) = 0, we can use synthetic division. Synthetic division is a method used to divide polynomials by a linear binomial of the form (x - c), where c is a constant.

Let's start by factoring the cubic polynomial x^3 - 10x^2 + 28x - 24. By inspecting the coefficients, we can determine that x = 2 is a root of the polynomial. Using synthetic division, we can divide the polynomial by (x - 2) to obtain a quadratic polynomial.

2 | 1 -10 28 -24

| 2 -16 24

|_________________________

1 -8 12 0

The result of the synthetic division is the quadratic polynomial x^2 - 8x + 12. Now we need to find the roots of this quadratic polynomial. We can either factor it or use the quadratic formula.

Factoring the quadratic equation x^2 - 8x + 12 = 0, we have:

(x - 2)(x - 6) = 0

So the solutions to the quadratic equation are x = 2 and x = 6.

Therefore, the solutions to the original polynomial equation X(x^3-10x^2+28x-24) = 0 are x = 0, x = 2, and x = 6.

Note: Synthetic division is a method used to simplify polynomial division, but it is not applicable to finding all the roots of a polynomial. In this case, we were able to identify one root (x = 2) by inspection and then proceed with synthetic division to simplify the problem.

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Answer:

x^2−7x+12      so -7x

Step-by-step explanation:

Alicia have to pay $10,000 and her insurance will pay $10,500.

What is limit of coverage in insurance?

This limit is the most the insurer will pay for sums as damages because of bodily injury or property damage included within the products-completes operations hazard during the policy period.

Given that Alicia has a collision deduction of $500 and a bodily injury coverage limit of $50,000.

And there is a verdict to compensate the injured person for $40,000

Therefore Alicia have to pay

$50,000-$40,000 = $10,000

And her insurance will pay

$10,000 + $500 = $10,500

Hence Alicia have to pay $10,000 and her insurance will pay $10,500.

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Let X denote any process. The negation for the statement: "For all processes X, if X runs without an error, then X is correct." is "There exists a process X such that X runs without an error and X is not correct."

In logic, negation, also called the logical complement, is an operation that takes a proposition P to another proposition "not P", written \(\neg\) P, \({\displaystyle {\mathord {\sim }}P}\) or \(\overline{P}\).

It is interpreted intuitively as being true when P is false, and false when P is true.

To write the negation for the statement "For all processes X, if X runs without an error, then X is correct," you would say:
There exists a process X such that X runs without an error and X is not correct.

In this negation, we're stating that there is at least one process (X) that can run without an error, but it is still not correct.

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Answer:

8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Factors of 24 and 40

24:  1, 2, 3, 4, 6, 8, 12, 24

40:  1, 2, 4, 5, 8, 10, 20, 40

8 comes as the GCF of both

Approximately 84% of scores fall between the mean and z = -1 for normally distributed scores.

In a normal distribution, approximately 68% of the scores fall within one standard deviation of the mean, both above and below. Z-scores are used to describe the location of a score relative to the mean, in terms of standard deviations.

A z-score of -1 indicates that a score is 1 standard deviation below the mean. So, if we consider all the scores that are 1 standard deviation below the mean or closer to the mean, then we would have a total of 68% of the scores, which includes the mean.

And, if we consider only the scores that are between the mean and 1 standard deviation below the mean, then we would have 84% of the scores. Hence, approximately 84% of scores would fall between the mean and z = -1 for normally distributed scores.

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The argument is not valid. The argument presented does not follow a valid logical structure.

Valid arguments are those where the conclusion necessarily follows from the given premises. In this case, the conclusion that "Lynn is busy" cannot be definitively derived from the given premises.

The premises state that Lynn works either part time or full time and that if she does not play on the team, she does not work part time.

It is also stated that if Lynn plays on the team, she is busy. Finally, it is mentioned that Lynn does not work full time.

Based on these premises, we cannot conclusively determine whether Lynn is busy or not. It is possible for Lynn to work part time, not play on the team, and therefore not be busy.

Alternatively, she may play on the team and be busy, but the argument does not establish whether she works part time or full time in this scenario.

To make a valid argument, additional information would be needed to establish a clear link between Lynn's work schedule and her busyness. Without that additional information, we cannot logically conclude that Lynn is busy solely based on the premises provided.

Valid arguments and logical reasoning to understand how premises and conclusions are connected in a valid argument.

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Answer:

6 unit to the right, 14 unit up

Step-by-step explanation:

I think I'm not sure if I'm correct sorry if you get it wrong

The total value in cents of all coins in the any row would be 16 cents.

In the pattern you described, the coins are arranged in rows such that each subsequent row has one more coin than the previous row. Let's analyze the values of the coins to determine the total value in cents of all the coins in the th row.

Assuming the values of the coins are as follows:

Penny: 1 cent

Nickel: 5 cents

Dime: 10 cents

We can observe that the pattern repeats after every three coins. The first three coins in the pattern are penny, nickel, dime. These coins have a total value of 1 + 5 + 10 = 16 cents.

For the subsequent rows, the pattern repeats with an offset of 3. For example, in the fourth row, the coins are penny, nickel, dime, which have the same total value as the first row, i.e., 16 cents.

So, regardless of the value of "th" (the row number), the total value in cents of all the coins in that row will always be 16 cents.

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Answer:

4+7x-2

Step-by-step explanation:

i dont know how nit is the anwser put i got it right

Answer:

D

Step-by-step explanation:

Answer:

D. 6y/x²

Step-by-step explanation:

6×y= 6y

x squared =x²

Answer:

the secend equation

\(y = - x + 9\)

Step-by-step explanation:

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The number of square centimeters of the wheel that the label cover is: B. 36,784 over 7 square centimeters.

Mathematically, the area of a circle can be calculated by using this mathematical expression:

Area = πr²

Where:

r represents the radius of a circle.

Area = 22/7 × 22²

Area = 10,648/7 square centimeters.

The area of the side of the wheel can be calculated as follows:

Area = 2πrh

Area = 2 × (22/7) × 22 × 16 = 15,488/7 square centimeters.

Therefore, the total surface area of the wheel is given by:

Total surface area = 2(10,648/7) + 15,488/7

Total surface area = 21,296/7 + 15,488/7

Total surface area = 36,784/7 square centimeters.

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Answer:

15,488/7

Step-by-step explanation:

The lateral surface area of the cylinder can be calculated as:

Lateral Surface Area = 2πrh,

where r is the radius of the base and h is the height of the cylinder.

Given that the radius of the wheel is 22 centimeters and the height is 16 centimeters, we can substitute these values into the formula:

Lateral Surface Area = 2 * (22/7) * 22 * 16

Lateral Surface Area = 2 * (22/7) * 352

Lateral Surface Area = (2 * 22 * 352) / 7

Lateral Surface Area = 15,488 / 7 square centimeters

Therefore, the label covers an area of 15,488/7 square centimeters of the wheel.

Apologies I know I'm a bit late, Happy Juneteenth!

Answer:

KL = 3

Step-by-step explanation:

Point K is on line segment \overline{JL} JL .

Given:

JL=4x

JK=2x+3

KL=x

Determine the numerical length of KL .

Note that:

J-------K-------L

JK + KL = JL

Step 1

We solve for x

JL = JK + KL

4x = 2x + 3 + x

4x = 3x + 3

Collect like terms

4x - 3x = 3

x = 3

Step 2

We solve for KL

KL = x

x = 3

Hence,

KL = 3

Answer:

3

Step-by-step explanation:

It's correct

Yes, it would be a scalene triangle. This can happen.

The Triangle sides have to be greater than c.

a+b > c

With the given inches, substitute it into the equations:

a = 3 in

b = 5 in

c = 9 in

3 + 5 > 9

Solve.

9 > 9

This is False since because a + b is not > c. a + b is equal to c.

Answer:

8.

Step-by-step explanation:

4^3 / 2^3

= 64 / 8

= 8.

Factoring the sum or difference of cubes involves using specific formulas to simplify expressions.

The sum of cubes formula, a^3 + b^3 = (a + b)(a^2 - ab + b^2), and the difference of cubes formula, a^3 - b^3 = (a - b)(a^2 + ab + b^2), allow us to break down these expressions into more manageable factors.

To factor the sum or difference of cubes, you can use the following formulas:

Sum of Cubes: a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Cube difference: (a - b)(a - b)(a - b)(a - b)(a - b)

Sum of Cubes:

The sum of cubes formula states that the sum of two cubes, a^3 + b^3, can be factored into (a + b) multiplied by the quadratic expression a^2 - ab + b^2.

For example, let's factorize 8x^3 + 27:

We can identify a = 2x and b = 3, so using the sum of cubes formula:

8x^3 + 27 = (2x + 3)(4x^2 - 6x + 9)

Difference of Cubes:

The difference of cubes formula states that the difference between two cubes, a^3 - b^3, can be factored into (a - b) multiplied by the quadratic expression a^2 + ab + b^2.

For example, let's factorize 64y^3 - 125:

We can identify a = 4y and b = 5, so using the difference of cubes formula:

64y^3 - 125 = (4y - 5)(16y^2 + 20y + 25)

Factoring the sum or difference of cubes involves using specific formulas to simplify expressions. The sum of cubes formula, a^3 + b^3 = (a + b)(a^2 - ab + b^2), and the difference of cubes formula, a^3 - b^3 = (a - b)(a^2 + ab + b^2), allow us to break down these expressions into more manageable factors. Factoring such expressions can be useful in various algebraic calculations and simplifications.

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Answer:

2700

Step-by-step explanation:

25 percent of 10800 is 2700. hope this helped, this was a bit rushed!xx

Answer:

sry I need points

Step-by-step explanation: If you hadn't done it to me I wouldn't do it to you

The slope of the line represents the ratio of the change in y to the change in x, indicating that for every increase of 5 units in x, the y-coordinate increases by 2 units. The y-intercept (-4) is the value of y when x is zero.

The equation of a line in standard form is given by Ax + By = C, where A, B, and C are constants. In this case, the slope of the line is 2/5, which means that for every increase of 5 units in x, the y-coordinate increases by 2 units. This can be represented as the fraction 2/5 or the decimal 0.4. The y-intercept is given as (0, -4), which means that when x is zero, the y-coordinate is -4.

To find the equation, we substitute the slope and y-intercept into the standard form equation. Plugging in the slope, we have 2x - 5y = C. We can use the y-intercept to determine the value of C. Substituting x = 0 and y = -4 into the equation, we get 2(0) - 5(-4) = C, which simplifies to 20 = C. Therefore, the equation of the line is 2x - 5y = 20. However, to express the equation in standard form, we need to make sure the coefficients are integers and the constant term is on the opposite side of the equation. By multiplying the entire equation by -1, we get -2x + 5y = -20, which is the final equation in standard form.

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Answer:

y=8.

Step-by-step explanation:

1) if according to the condition slope=0, then the slope-interception form of the required equation is: y=i, where i - interception;

2) if according to the condition the point (4;8) belongs to the required equation, then the required equation is: y=8

Answer:

the y intercept is (0,-4) or just -4

Step-by-step explanation:

Answer:

(x-13)^2+(y+16)^2=12.56

Step-by-step explanation:

Answer:

500 ml

Step-by-step explanation:

1 liter = 1 000 ml

1 / 2 liters = 1000 ml /2 = 500 ml

1000ml - 500 ml = 500 ml

Answer:

(a) See attachment

(b) Mara's rectangle

Step-by-step explanation:

Given

Mara

\(Area =15cm^2\)

Ashton

\(Area =9cm^2\)

Solving (a): Draw the rectangles

First, we need to calculate the possible dimension of both rectangles.

Area is calculated as:

\(Area = Length * Width\)

For Mara

\(15 = Length * Width\)

Possible values of length and width are:

\(Length = 5cm\)

\(Width = 3cm\)

This is so because:

\(5cm * 3cm = 15cm^2\)

For Ashton

\(9 = Length * Width\)

Possible values of length and width are:

\(Length = 4.5cm\)

\(Width = 2cm\)

This is so because:

\(4.5cm * 2cm = 9cm^2\)

See attachment for diagram

Solving (b): Rectangle with bigger area

Mara's rectangle has a bigger area because \(15cm^2 > 9cm^2\)

The kind of sample being used in this scenario is a simple random sample.

A simple random sample is a subset of a population where each member of the population has an equal chance of being selected. In this case, all 126 students' names are written on identical slips of paper and placed into a large glass jar. By randomly selecting 14 slips from the jar, the professor ensures that each student has an equal probability of being chosen.

Simple random sampling is a commonly used sampling method because it provides an unbiased representation of the population and allows for generalization of the findings to the larger group. It helps to minimize selection bias and increase the chances of obtaining a representative sample.

By using a simple random sample, the professor ensures that the 14 students selected for further analysis or study are chosen in a fair and unbiased manner, allowing for accurate conclusions and generalizations to be made about the entire class of 126 students.

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Answer: A  (-1/6)   B.(1/2)

Step-by-step explanation:

a. 1/3z=-2

1=(-2)(3z)

1=-6z

(-1/6)=z

B. 6y=3

y=3/6

y=1/2

\(\it tan60^o=\dfrac{AB}{BC} \Rightarrow \sqrt3=\dfrac{AB}{50} \Rightarrow AB=50\sqrt3\approx50\cdot1,732\approx87\ m\)

The number of ways you can select n elements from N elements by using factorial (!) when n=2 and N=10 is 45.

Factorial is a crucial mathematical operation that is used to determine the number of possible arrangements or the ordered set of numbers. Daniel Bernoulli is credited with discovering the factorial function's well-known interpolating feature. Numerous mathematical ideas, including probability, permutations and combinations, sequences and series, etc., use the factorial concept. A factorial function, in essence, multiplies a number by each number below it until it equals 1. For instance, the factorial of 3 is equal to 6 and reflects the multiplication of the integers 3, 2, and 1.

Now,

The number of ways you can select n elements from N elements when n=2 and N=10 is \(\frac{N!}{n!(N-n)!}\)

=\(\frac{10!}{2!(8)!}\)

=\(\frac{10 \times 9 \times \times 8!}{8! \times 2 !}\)

=45

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Answer:

The common denominator is 15.

2 3/5 = 13/5 = 39/15

1 1/3 = 4/3 = 20/15

Answer:

39/15 and 20/15

Step-by-step explanation:

Given function:

Rewrite 2 3/5 and 1 1/3 by a number that is equivalent to 5 and 3:

Multiply each numerator by how much times it turned into 15:

Simplfly the fraction terms:

Therefore, 39/15 and 20/15 is equivalent to 2 3/5 and 1 1/3.