answer quick please!!

Match the following reasons with the statements given.

Prove:

The median from the vertex angle of an isosceles triangle divides the triangle into two congruent triangles.



Given:

RAS is isosceles

AM is median

Prove:

RAM SAM

1. Triangle RAS is isosceles, AM is a median
Reflexive
2. AR = AS
Definition of median
3. AM = AM
Given
4. MR = MS
Definition of isosceles triangle.
5. Triangle RAM congruent to Triangle SAM
SSS

We can infer from the results that Overall, students are less interested in reading magazines than comics.

A random sample is a portion of a larger population that is selected so that each person has an equal probability of being included in the sample. In statistics and scientific research, random sampling is a frequent practise since it helps to guarantee that the sample is representative of the population as a whole and reduces the possibility of bias. There are several ways to choose random samples, such as cluster sampling, stratified random sampling, and basic random sampling. The required sample size is dependent on a number of variables, including the population's size, the level of accuracy wanted, and the population's amount of variability.

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Answer:

Let f be the number of foil balloons Lyla buys, and let t be the number of toy balloons she buys. Then, we can set up a system of linear equations based on the information given:

f + t = 30 (since Lyla buys a total of 30 balloons)

5.49f + 2.29t = 123.10 (since Lyla pays a total of $123.10 for the balloons)

To solve for f and t, we can use the substitution method. From the first equation, we can solve for t in terms of f:

t = 30 - f

Substituting this expression for t into the second equation, we get:

5.49f + 2.29(30 - f) = 123.10

Simplifying and solving for f, we get:

5.49f + 68.70 - 2.29f = 123.10

3.20f = 54.40

f = 17

So Lyla buys 17 foil balloons. We can substitute this value of f back into the first equation to solve for t:

17 + t = 30

t = 13

Therefore, Lyla buys 17 foil balloons and 13 toy balloons.

The estimate volume of the box holding the tissue boxes is 1125 cubic inches.

Let the Volume of each tissue box be 'v'

Number of tissues be 'n'

The estimate volume of the box holding the tissue boxes be V.

As given in Question:

Volume of each tissue box v = 125 cubic inches

Number of tissues n from the attached image (given below);

                                          n = 3×3

                                          n = 9 tissue boxes

The estimate volume of the box holding the tissue boxes V;

                                         V = nv

                                         V = 9 × 125

                                         V = 1125 cubic inches.

The estimate volume of the box holding the tissue boxes is 1125 cubic inches.

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The converse that can be used to prove that the given lines are parallel given each angle pair is:

1. Corresponding angles theorem

2. Same-side interior angles can be used

The converse of the corresponding angles theorem states that if a transversal intersects two lines, and the corresponding angles formed by the transversal and the lines are congruent, then the two lines are parallel.

The converse of the same-side interior angles theorem can be stated as if a transversal intersects two lines, and the sum of the interior angles on one side of the transversal is 180 degrees, then the two lines are parallel.

Therefore we can conclude that:

A. The converse of the corresponding angles theorem

B. The converse of the same-side interior angles can be used

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Answer:    Susie needs to find the length of one side of each square pillow and the circumference of the circular pillow, add them all together, and that is how much fringe she must use.

Equation: √3 + √8 + √16 + 2π

(This might not be what you are looking for but this is how I would answer this question)

Step-by-step explanation:

All decimals to 4 decimal places

Area of a square = side x side

To find the length of each side, square root the area

Pillow 1:

Side = √3

Fringe needed = 1.7321

Pillow 2:

Side = √8

Fringe needed = 2.8284

Pilow 3:

Side = √16

Fringe needed = 4

Circumference of a circle = 2πr

radius = half of the diameter

Pillow 4:

Side = 2π(1)

Side = 2π

Fringe needed = 6.2832

Total: 1.7321 + 2.8284 + 4 + 6.2832 = 14.8437

Answer:

Square pillow A:  √3 ft ≈ 1.73 ft (nearest hundredth)

Square pillow B:  √8 ft ≈ 2.83 ft (nearest hundredth)

Square pillow C:  4 ft

Circular pillow:  6.28 ft

Step-by-step explanation:

The area of a square is the square of the measure of its side length.

Therefore, if the customer wants fringe placed on only one edge of each of 3 different square shaped pillows, we can calculate how much fringe should be used for each pillow by square rooting the given areas.

[tex]\boxed{\textsf{Fringe needed}=\sqrt{\sf Area}}[/tex]

Area = 3 ft²

[tex]\begin{aligned} \implies \textsf{Fringe needed}&=\sqrt{3\; \sf ft^2}\\&=\sqrt{3}\sqrt{\sf ft^2}\\&=\sqrt{3}\; \sf ft\\&\approx1.73 \sf \; ft\;(nearest\;hundredth)\end{aligned}[/tex]

Area = 8 ft²

[tex]\begin{aligned} \implies \textsf{Fringe needed}&=\sqrt{8\; \sf ft^2}\\&=\sqrt{8} \sqrt{\sf ft^2}\\&=\sqrt{8} \; \sf ft\\&\approx 2.83\; \sf ft\;(nearest\;hundredth)\end{aligned}[/tex]

Area = 16 ft²

[tex]\begin{aligned} \implies \textsf{Fringed needed}&=\sqrt{16\; \sf ft^2}\\&=\sqrt{16}\sqrt{\sf ft^2}\\&=4 \; \sf ft\end{aligned}[/tex]

If the same customer also has a circular pillow that is 2 ft in diameter and they want fringe placed all the way around it, we can calculate the amount of fringe to use by calculating the circumference of the circle.

The formula for a circumference of a circle is C = πd, where d is the diameter of the circle.  Given that d = 2 ft and using π ≈ 3.14:

[tex]\begin{aligned}\implies \textsf{Fringe needed for the circular pillow}&=\pi \cdot 2\\&=3.14 \cdot 2\\&=6.28\; \sf ft\end{aligned}[/tex]

The approximate probability that the total aggregate cost of fighting

The approximate probability that less than 1801800 citizens will get vaccinated can be calculated using the de Moivre-Laplace theorem. This theorem states that the probability distribution of the sum of a large number of independent random variables approaches the normal distribution as the number of variables increases. In this case, the random variable is whether or not a citizen gets vaccinated, and the sum is the total number of citizens who get vaccinated.

To calculate the approximate probability, we need to find the mean and standard deviation of the distribution. The mean is equal to the number of citizens times the probability of getting vaccinated, which is 9.10^6 * (1/5) = 1820000. The standard deviation is equal to the square root of the number of citizens times the probability of getting vaccinated times the probability of not getting vaccinated, which is sqrt(9.10^6 * (1/5) * (4/5)) = 1200.

Using the de Moivre-Laplace theorem, we can approximate the probability that less than 1801800 citizens will get vaccinated as the probability that a normal random variable with mean 1820000 and standard deviation 1200 is less than 1801800. This can be calculated using the standard normal distribution:

P(Z < (1801800 - 1820000)/1200) = P(Z < -1.52) = 0.064

Therefore, the approximate probability that less than 1801800 citizens will get vaccinated is 0.064.

The approximate probability that the total aggregate cost of fighting the virus-inflicted illness for all citizens of the country will surpass 7207200000 dollars can be calculated using the Central Limit Theorem (CLT). The CLT states that the sum of a large number of independent random variables approaches the normal distribution as the number of variables increases. In this case, the random variable is the cost of treating a single non-vaccinated individual, and the sum is the total cost of treating all non-vaccinated individuals.

To calculate the approximate probability, we need to find the mean and standard deviation of the distribution. The mean is equal to the number of citizens times the probability of not getting vaccinated times the expected value of the cost of treating a single non-vaccinated individual, which is 9.10^6 * (4/5) * (2000/2) = 7207200000. The standard deviation is equal to the square root of the number of citizens times the probability of not getting vaccinated times the variance of the cost of treating a single non-vaccinated individual, which is sqrt(9.10^6 * (4/5) * (2000^2/12)) = 1633333.33.

Using the CLT, we can approximate the probability that the total aggregate cost of fighting the virus-inflicted illness for all citizens of the country will surpass 7207200000 dollars as the probability that a normal random variable with mean 7207200000 and standard deviation 1633333.33 is greater than 7207200000. This can be calculated using the standard normal distribution:

P(Z > (7207200000 - 7207200000)/1633333.33) = P(Z > 0) = 0.5

Therefore, the approximate probability that the total aggregate cost of fighting the virus-inflicted illness for all citizens of the country will surpass 7207200000 dollars is 0.5.

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There are 15 blue counters in the bag.

Two quantities are compared to form a ratio. An equality of two ratios is a proportion.

We know that the initial ratio of red counters to blue counters was 4:5. Therefore, we can write:

4x : 5x

We also know that 10 more red counters were added to the bag. Therefore, the new number of red counters in the bag is:

4x + 10

The ratio of red counters to blue counters then became 6:5. Therefore, we can write:

(4x + 10) : y = 6 : 5

We can simplify this equation by cross-multiplying:

5(4x + 10) = 6y

20x + 50 = 6y

Dividing both sides by 6, we get:

y = (20x + 50)/6

Simplifying, we get:

y = (10x + 25)/3

Since y has to be a whole number, 10x + 25 has to be divisible by 3. The only value of x that satisfies this condition is x = 2.

Therefore, the initial number of red counters was 4x = 8, and the initial number of blue counters was 5x = 10.

After adding 10 more red counters, the new number of red counters was 18, and the new ratio of red counters to blue counters was 6:5.

To find the new number of blue counters, we can use the equation we derived earlier:

y = (10x + 25)/3

Substituting x = 2, we get:

y = (10(2) + 25)/3 = 15

Therefore, there are 15 blue counters in the bag.

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Answer: A, C, and D all have the sums of -12.45

Step-by-step explanation:
A) -21.89 + 9.44 = -12.45
C) -3.18 - 9.27 = -12.45
D) -5.75 + -6.7 = -12.45

Zero is an even number, but neither a prime number nor a composite number.

Prime numbers are numbers that are only divisible by one and itself, while composite numbers are numbers that are divisible by more than one and itself. Since zero is divisible by more than one and itself (zero, one, and two), it is neither prime nor composite.

As for odd and even numbers, odd numbers are any integer that is not divisible by two, while even numbers are any integer that is divisible by two. Since zero is divisible by two, it is an even number.

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Exploratory Factor Analysis (EFA) is a data analysis technique used to uncover underlying relationships among variables in a dataset. It is a multivariate statistical technique that examines the correlations among multiple observed variables in order to identify underlying latent variables, or "factors". These factors are latent, meaning they are not directly observable or measurable.

EFA helps researchers to understand how the relationships between variables can be organized and explained by underlying latent factors. Specification of EFA includes the following steps:

Exploratory Factor Analysis is a powerful data analysis technique that can uncover the underlying relationships among variables in a dataset. It helps researchers to understand how the relationships between variables can be organized and explained by underlying latent factors. By following the above steps, researchers can appropriately specify and interpret EFA to gain insights from their data.

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Answer:

To find the x-intercepts of the equation y = -(x+7)(x+4), we need to set y = 0 and solve for x. So, we have:

0 = -(x+7)(x+4)

This equation will be true if either (x+7) = 0 or (x+4) = 0. Solving each of these equations, we get:

x+7 = 0 => x = -7

x+4 = 0 => x = -4

Therefore, the x-intercepts of the equation y = -(x+7)(x+4) are x = -7 and x = -4.

Now, we know that the equations y = -(x+7)(x+4) and y = -(x-3) are equivalent. This means that they have the same solutions, or the same x-intercepts. So, we can use the x-intercepts we found for the first equation to determine the x-intercepts of the second equation.

To find the x-intercepts of the equation y = -(x-3), we set y = 0 and solve for x:

0 = -(x-3)

This equation will be true if (x-3) = 0, which gives us:

x-3 = 0 => x = 3

Therefore, the x-intercept of the equation y = -(x-3) is x = 3, which is different from the x-intercepts of the equation y = -(x+7)(x+4). This means that the two equations are not equivalent.

Step-by-step explanation:

Answer:

x-intercepts can be found below

Step-by-step explanation:

The equation:

[tex]y=-(x+7)(x+4)[/tex]

Can also be written as:

[tex]y=-1(x+7)(x+4)[/tex]

In order to find the x-intercepts, we must set each of the factors equal to 0.

[tex]-1=0[/tex]

[tex]x+7=0, x=-7[/tex]

[tex]x+4=0, x=-4[/tex]

The x-intercepts are:

[tex](0,0)[/tex]

[tex](-7,0)[/tex]

[tex](-4,0)[/tex]

The equation:

[tex]y=-(x-3)[/tex]

Can also be written as:

[tex]y=-1(x-3)[/tex]

In order to find the x-intercepts, we must set each of the factors equal to 0.

[tex]-1=0[/tex]

[tex]x-3=0, x=3[/tex]

The x-intercepts are:

[tex](0,0)[/tex]

[tex](3,0)[/tex]

The total number of trips between the zone: a. 1 and 6 is 10863 trips. b. 3 and 10 is 12617 trips. c. 5 and 10 is 11215 trips. d. 4 and 9 is 15560 trips.

To determine the total number of trips between the zones, we can simply do addition of the production/generation and attraction values for the two zones in question.  Based on the values in the table:

a. For zones 1 and 6, the total number of trips would be 3643 + 3040 + 2542 + 1638 = 10863 trips.

b. For zones 3 and 10, the total number of trips would be 3156 + 2535 + 3172 + 3754 = 12617 trips.

c. For zones 5 and 10, the total number of trips would be 2167 + 2122 + 3172 + 3754 = 11215 trips.

d. For zones 4 and 9, the total number of trips would be 3204 + 4217 + 3597 + 4542 = 15560 trips.

Therefore, the total number of trips between the zones are: a. 10863 trips between zones 1 and 6 b. 12617 trips between zones 3 and 10 c. 11215 trips between zones 5 and 10 d. 15560 trips between zones 4 and 9.

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The inequality is given as 12x ≥ 15,000

An inequality in mathematics is a statement that compares two quantities or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

The least number of rides needed for 15000 people is given as 12x ≥ 15,000.

12x ≥ 15,000.

x ≥ 15,000 / 12

x  ≥ 1250

The least number of rides needed for 15000 people is 1250.

If the park is open for 12 hours. 15000 / 12 is the number of persons that can ride in 1 hour

Hence it is not possible for the ride to have 15000 persons in a day

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Answer:

The three sectors of our economy -- private, public and non-profit -- are inextricably intertwined.

The 3 sectors of economy are:

There are three sectors of the economy, each consisting of the following:

Each of these sectors plays a crucial role in the overall economy and contributes to the production and distribution of goods and services.

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Answer:6

Step-by-step explanation:

N=6

⇒6=6  

∴LHS=RHS

The measure of the angle N to the nearest degree for the given triangle is 23 degrees.

Degree and radian both serve as angles' units of measurement in geometry. Two radians (in radians) or 360° can be used to symbolise one whole anticlockwise rotation (in degrees). As a result, degree and radian can be compared as follows:

2π = 360°

The given triangle is an right triangle.

Using the trigonometric functions we can write the relation between the segments as:

Sin (N) = 1.5 / 3.9 = opposite/hypotenuse

N = arcsin (1.5 / 3.9)

N = 22.61 = 23 degrees.

Hence, the measure of the angle N to the nearest degree for the given triangle is 23 degrees.

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The cost of the meal, including the 20% discount, 8% sales tax, and 15% tip, is $43.72.

Suppose a number is 'a'

Suppose another number is 'b'

We want to know how much percent of 'b' is 'a'.

Then, it is calculated as:

[tex]\dfrac{a}{b} \times 100[/tex]

(in percentage)

We are given that;

Items ordered= a 12 piece Grilled Tuscan Chicken Wings, Mozzarella

Fritta and Pan Sauteed Mussels.

Coupon percent off =20%

Sales tax= 8%

Waiter tip= 15%

Now,

Let's start by finding the cost of the appetizers and the pizza before any discounts or taxes are applied:

Grilled Tuscan Chicken Wings: let's assume this is $12

Mozzarella Fritta: let's assume this is $8

Pan Sauteed Mussels: let's assume this is $14

Craft Your Own Pizza: let's assume this is $10 for a small 2-topping pizza

So the total cost of the food before any discounts or taxes is:

$12 + $8 + $14 + $10 = $44

With the 20% coupon, we can apply a discount of:

0.2 x $44 = $8.80

So the new total before taxes is:

$44 - $8.80 = $35.20

Now we can calculate the sales tax on this amount:

0.08 x $35.20 = $2.82

Adding the sales tax to the discounted amount gives:

$35.20 + $2.82 = $38.02

Finally, we can calculate the total cost of the meal after adding the 15% tip:

$38.02 + 0.15 x $38.02 = $43.72

Therefore, by the given percentages the answer will be $43.72.

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25. The inverse of f(x) = 1 + √2 + 3x is f-1(x) = (x - 1 - √2)/3.

26. The inverse of f(x) = e2x - 1 is f-1(x) = (ln(x) + 1)/2.

27. The inverse of y = In(x + 3) is y-1(x) = ex - 3.

28. Log2³² = 5

29. Log8² = 1/3

30.Log5^{1/125}  = -3

31. In(1/e2) = -2

32. Log10⁴⁰ + log10² = 1.6

33. log8 60 - log8 3 - log8 5 = 0

34. In10 + 2In5 = In10 + log10 5

35. 1/3In(x+2)3 + 1/2[Inx - In(x2 + 3x + 2)2] = In[(x+2)3/[(x2 + 3x + 2)2x]]

25. To find the inverse of the function f(x)=1+ √2+ 3x, we need to swap the x and y variables and solve for y.
So, x = 1 + √2 + 3y
Subtract 1 and √2 from both sides:
x - 1 - √2 = 3y
Divide both sides by 3:
y = (x - 1 - √2)/3
Therefore, the inverse of the function is f^-1(x) = (x - 1 - √2)/3

26. To find the inverse of the function f(x) = e^2x-1, we need to swap the x and y variables and solve for y.
So, x = e^2y-1
Add 1 to both sides:
x + 1 = e^2y
Take the natural log of both sides:
ln(x + 1) = 2y
Divide both sides by 2:
y = ln(x + 1)/2
Therefore, the inverse of the function is f^-1(x) = ln(x + 1)/2

27. To find the inverse of the function y=In(x+3), we need to swap the x and y variables and solve for y.
So, x = ln(y + 3)
Take the exponential of both sides:
e^x = y + 3
Subtract 3 from both sides:
y = e^x - 3
Therefore, the inverse of the function is f^-1(x) = e^x - 3

28. log2^32 = 5, because 2^5 = 32

29. log8^2 = 1/3, because 8^(1/3) = 2

30. log5 1/125 = -3, because 5^-3 = 1/125

31. In(1/e^2) = -2, because e^-2 = 1/e^2

32. log10 40 + log10 2.5 = log10 (40 * 2.5) = log10 100 = 2, because 10^2 = 100

33. log8 60 - log8 3 - log8 5 = log8 (60/3/5) = log8 4 = 2/3, because 8^(2/3) = 4

34. In10 + 2in5 = ln(10 * 5^2) = ln(250)

35. 1/3in(x+2)^3 + 1/2 [inx - in(x^2+3x+2)^2] = ln((x+2)^(1/3) * x^(1/2) * (x^2+3x+2)^(-1))

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The line of intersection of the 3x+2y+z=−1  and 2x−y+4z planes is the set of all points (4t-7s-11, t, s), where t and s are parameters. And The line of intersection of the 4x+y+z=0 and 2x−y+3z=2 planes is the set of all points ((-3/6)t+(1/6)s-(1/3), t, s), where t and s are parameters.

The line of intersection of the given planes can be found by solving the system of equations formed by the equations of the planes.

For Exercise 45, we have the system of equations:
3x+2y+z=−1
2x−y+4z=5

To solve this system, we can use the elimination method. We can multiply the second equation by 2 and subtract it from the first equation to eliminate the x variable:

3x+2y+z=−1
-(4x-2y+8z=10)
______________
-x+4y-7z=-11

Now we can express one variable in terms of the other two variables. For example, we can solve for x in terms of y and z:

-x+4y-7z=-11
x=4y-7z-11

The line of intersection of the given planes is the set of all points (x, y, z) that satisfy this equation. We can write the equation of the line in parametric form by letting y=t and z=s:

x=4t-7s-11
y=t
z=s

The line of intersection of the given planes is the set of all points (4t-7s-11, t, s), where t and s are parameters.

For Exercise 46, we have the system of equations:
4x+y+z=0
2x−y+3z=2

We can use the elimination method again to solve this system. We can multiply the first equation by 2 and subtract the second equation from it to eliminate the x variable:

8x+2y+2z=0
-(2x−y+3z=2)
______________
6x+3y-z=-2

Now we can express one variable in terms of the other two variables. For example, we can solve for x in terms of y and z:

6x+3y-z=-2
6x=-3y+z-2
x=(-3/6)y+(1/6)z-(1/3)

The line of intersection of the given planes is the set of all points (x, y, z) that satisfy this equation. We can write the equation of the line in parametric form by letting y=t and z=s:

x=(-3/6)t+(1/6)s-(1/3)
y=t
z=s

The line of intersection of the given planes is the set of all points ((-3/6)t+(1/6)s-(1/3), t, s), where t and s are parameters.

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The rate charged per hour by the first mechanic and the second mechanic.

The total number of hours worked by the two mechanics is 10 hours + 15 hours = <<10+15=25>>25 hours. The total amount charged by the two mechanics is $2400. If we let x be the rate charged per hour by the first mechanic, and y be the rate charged per hour by the second mechanic, we can write the following equations:

x + y = 195 (the sum of the two rates is $195 per hour)
10x + 15y = 2400 (the total amount charged is $2400)

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for y in terms of x:

y = 195 - x

We can then substitute this expression for y into the second equation:

10x + 15(195 - x) = 2400

Simplifying this equation gives us:

10x + 2925 - 15x = 2400

-5x = -525

x = 105

We can then substitute this value of x back into the first equation to find the value of y:

105 + y = 195

y = 90

Therefore, the rate charged per hour by the first mechanic is $105 per hour, and the rate charged per hour by the second mechanic is $90 per hour.

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A performance task is any educational activity or assessment that calls for students to perform in order to demonstrate their comprehension, competency, and knowledge.

Mathematical activity includes the search for patterns as well as experimentation, description, fiddling, invention, picturing, conjecture, and guesswork.

A series of recurrent numbers, symbols, or shapes is referred to in mathematics as a pattern. Every kind of event or thing has a pattern that can be connected to it. A rule that distinguishes between items that are a part of a pattern and those that are not is known as a pattern.

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Complete question:

What is Performance task?

The Degree of the polynomial 6, Leading Coefficient of the polynomial -7 .

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of the variables. It can have constants and/or variables, and can represent equations, functions, or graphs.

The degree of a polynomial is the highest exponent of the variable in the polynomial. The leading coefficient is the coefficient of the term with the highest degree.

In the polynomial -8y⁴+12y-7y⁶-6y²+, the highest exponent is 6, so the degree of the polynomial is 6. The coefficient of the term with the highest degree is -7, so the leading coefficient is -7.

Therefore, the degree of the polynomial is 6 and the leading coefficient is -7.

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Answer:

y=mx+b

It's already in function notation. Unless you need to graph it or show it.

Step-by-step explanation:

Refer to pic...........

The remainder when f(x) is divided by x-1 is 0.

Remainder Theorem states that given a polynomial function and a value for x, the remainder when the polynomial is divided by (x-a) is equal to the value of the polynomial when x=a. This theorem can be used to quickly and accurately find the remainder of a division problem, making it a very useful tool.

The remainder theorem states that if a polynomial f(x) is divided by x-a, then the remainder is f(a). In this case, we want to find the remainder when f(x) is divided by x-1. Therefore, we need to find f(1).

f(1) = 2(1)^(3) + 3(1)^(2) - 12(1) + 7
f(1) = 2 + 3 - 12 + 7
f(1) = 0

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The required four values of θ that satisfy the equation tan θ = -√3 are:

θ = 4π/3 radians (or 240 degrees)
θ = 7π/3 radians (or 420 degrees)
θ = π/3 radians (or 60 degrees)
θ = 2π/3 radians (or 120 degrees)

These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.

Here,
Since the tangent function has a period of π, we can find the angles θ that satisfy the equation tan θ = -√3 by adding or subtracting multiples of π until we find all possible solutions in the desired range.

For θ < 0,

Therefore, one solution for θ in the fourth quadrant is:

θ = π + π/3 = 4π/3 radians (or 240 degrees)

To find another solution, we can add one full period of π to 4π/3 to get:

θ = 4π/3 + π = 7π/3 radians (or 420 degrees)

For θ > 2,

One solution for θ in the first quadrant is,

θ = π/3 radians (or 60 degrees)

One solution for θ in the fifth quadrant is:

θ = 2π - π/3 = 5π/3 radians (or 300 degrees)

To find another solution in the fifth quadrant, we can subtract one full period of π from 5π/3 to get:

θ = 5π/3 - π = 2π/3 radians (or 120 degrees)

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The quadrilateral with the specified value for x has a 45° angle.

A polygon with four sides, four angles, and four vertices is called a quadrilateral.

The Latin words quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral.

A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry.

The Latin words quadri, a variation of four, and latus, meaning "side," are the source of the name.

The exterior angles of the given quadrilateral are x°, 3x°, x°, and 3x°.

We are aware that a quadrilateral's total exterior angles are 360°.

Now, x°+3x°+x°+3x°=360°

8x°=360°

x°=45°

Therefore, the quadrilateral with the specified value for x has a 45° angle.

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The scale factor of dilation for the given shape are:

For A : (0,0)

For B : (2,2)

For C : (2,2)

Magnification is defined as the ratio of the size of the new image to the size of the old image. The center of expansion is a fixed point in the plane. A dilation transform is defined based on the scale factor and dilation center. If the scale factor is greater than 1, the image will be stretched. 

Formula: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

Solution:

Given, A = A' = (0,0)

           B= (2,2) , B' = (4,4)

           C=(3,2) , C' = (6,4)

Scale factor for A = (0,0), it is because that's the center of dilation.

Scale factor for B = (4/2 , 4/2) = (2,2)

Scale factor for C = (6/3 , 4 /2) = (2,2)

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The maximum value of p is 280 and the optimal solution is (x,y,z) = (14, 5, 2).

To maximize p = 10x + 20y + 15z subject to the given constraints, we will use the simplex method. The simplex method is a mathematical technique used to solve linear optimization problems.

Convert the inequalities to equations by adding slack variables. This will give us the following system of equations:
x + 2y + z + s1 = 20
-2y + z - s2 = -5
2x - y + z + s3 = 10

Write the equations in matrix form. The matrix will have the coefficients of the variables on the left-hand side and the constants on the right-hand side.

| 1  2  1  1  0  0 | 20 |
| 0 -2  1  0 -1  0 | -5 |
| 2 -1  1  0  0  1 | 10 |

Convert the matrix to reduced row echelon form using elementary row operations. This will give us the following matrix:

| 1  0  0  1/5  2/5  0 | 14 |
| 0  1  0  1/10 -1/10 0 | 5  |
| 0  0  1 -1/10 3/10 1 | 2  |

From the reduced row echelon form, we can see that the optimal solution is (x,y,z) = (14, 5, 2) and the maximum value of p is 10(14) + 20(5) + 15(2) = 280.

Therefore, the maximum value of p is 280 and the optimal solution is (x,y,z) = (14, 5, 2).

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Answer:

it means if the given sides are approximately equal then the triangles are equal too

Step-by-step explanation:

if the the sides are equal then the triangles are equal too