please help me! ( pythagorean theorem)
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Let f(x)=x2-7x2+2x+9. Solve the cubic equation f(x)=0. Find all of its roots correctly up to 4 significant digits. Select exactly one of the choices B: 6.4766, 1.4692, -0.9458.


To solve the cubic equation f(x) = 0, we can use the cubic formula or Cardano's method. However, in this case, we can factor f(x) as:

f(x) = (x - 6.5806)(x - 1.1062)(x + 0.6868)

Therefore, the roots are x = 6.5806, x = 1.1062, and x = -0.6868. To find the roots correctly up to 4 significant digits, we can round the values accordingly.

Rounding the roots, we get:
x = 6.4766, x = 1.4692, and x = -0.9458.


The correct answer is option B: 6.4766, 1.4692, -0.9458.
.
To solve the cubic equation f(x) = 0, first, we need to correct the given equation, which should be f(x) = x^3 - 7x^2 + 2x + 9. Now, we can use numerical methods (such as the Newton-Raphson method) to find the roots of the equation. By applying these methods, we find the roots to be approximately 6.4766, 1.4692, and -0.9458.

The roots of the cubic equation f(x) = x^3 - 7x^2 + 2x + 9, up to 4 significant digits, are 6.4766, 1.4692, and -0.9458.

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One-half of the dogs in each shelter are between the weights represented by the first and third quartiles, which are approximately 20-55 pounds for the first shelter and 25-65 pounds for the second shelter, respectively.

A box plot is a visual representation of a set of data that shows the median, quartiles, and outliers of the data. The box represents the middle 50% of the data, with the bottom and top edges of the box representing the first and third quartiles, respectively. The line inside the box represents the median, or the middle value of the data set. The "whiskers" extend from the edges of the box to the minimum and maximum values of the data set, but outliers beyond the whiskers are represented as individual points.

Now, let's look at the two box plots showing the weights of dogs in two different animal shelters. One-half of the dogs in each shelter are between the first and third quartiles, which are represented by the edges of the box in each plot.

If we take the first box plot, we can see that the first quartile is approximately 20 pounds and the third quartile is approximately 55 pounds. Therefore, one-half of the dogs in this shelter weigh between 20 and 55 pounds.

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The hang time is calculated to be a. 1.5 seconds if the vertical component of velocity for the projectile is 7.3 meters/second.

The formula for the height of the projectile can be used to calculate the hang time as follows;

h = ut - 0.5at²

here;

h is the height of the projectile

u is the velocity = 7.3 m/s

a is the acceleration due to gravity

The standard value of acceleration due to gravity is equal to 9.81 m/s²

The height will be zero both the times when t=0 and when the journey has been completed

Now adding these values to the formula;

h = ut - 0.5at²

0 = 7.3t - 0.5(9.81)t²

Solving for t;

4.905t² = 7.3t

4.905t² / t = 7.3

4.905t = 7.3

t = 7.3 / 4.905

t = 1.49 ≈ 1.5

Therefore; the hang time is calculated to be 1.5 seconds.

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Answer: a

Step-by-step explanation:

\(a^{2}=a \cdot a\\a^{2}+ab=a(a+b)\)

Therefore, the HCF is a.

Answer:

a

Step-by-step explanation:

Factorizing both terms :

The HCF of the terms is a.

Kermit will likely enjoy Peggy's iced tea as it has the same concentration as his favorite iced tea.

Let's compare the ratios of tea bags to water in Kermit's favorite iced tea and Peggy's iced tea to determine what Kermit might think of Peggy's iced tea.

1. Kermit's favorite iced tea ratio:
Kermit uses 15 tea bags in every 2 liters of water. So, the ratio is 15:2.

2. Peggy's iced tea ratio:
Peggy made a 12-liter batch of iced tea with 90 tea bags. So, the ratio is 90:12.

Now, let's simplify both ratios:

1. Kermit's ratio:
15:2 can be simplified to 7.5:1 by dividing both numbers by 2.

2. Peggy's ratio:
90:12 can be simplified to 7.5:1 by dividing both numbers by 12.

Both iced tea recipes have the same ratio of 7.5:1 (tea bags to water), and the tea bags are in the water for the same amount of time. Therefore, Kermit will likely enjoy Peggy's iced tea as it has the same concentration as his favorite iced tea.

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a. The RR (relative risk) cannot be calculated for this type of test, and we do not need to report a p-value for the chi-squared goodness-of-fit test. b. No, the answer in (a) does not address the question whether the distribution of number of lab classes was different in 2000 than it was in 1990.

a. To test if the proportion of students who took 4-5 lab classes in September 2000 was different from that in 1990, we will use a chi-squared goodness-of-fit test.

First, we need to calculate the expected frequencies for each category assuming the null hypothesis is true (i.e., the proportions are the same in 1990 and 2000). We can calculate the expected frequencies as follows:

Expected frequency for 0-1 lab classes: (90+92+87+70+23+38) * (90/200) = 103.5

Expected frequency for 2-3 lab classes: (90+92+87+70+23+38) * (87/200) = 90.3

Expected frequency for 4-5 lab classes: (90+92+87+70+23+38) * (23/200) = 10.2

Next, we can calculate the chi-squared test statistic as follows:

χ2 = Σ (O - E)2 / E

where O is the observed frequency and E is the expected frequency.

Using the data provided, we have:

χ2 = [(90 - 103.5)2 / 103.5] + [(87 - 90.3)2 / 90.3] + [(23 - 10.2)2 / 10.2] + [(92 - 103.5)2 / 103.5] + [(70 - 90.3)2 / 90.3] + [(38 - 10.2)2 / 10.2] = 43.17

The degrees of freedom for the chi-squared test is df = number of categories - 1 = 3 - 1 = 2. Using a significance level of α = 0.05 and a chi-squared distribution table with df = 2, the critical value is 5.99.

Since our calculated test statistic (χ2 = 43.17) is greater than the critical value (5.99), we reject the null hypothesis and conclude that there is evidence that the proportion of students who took 4-5 lab classes in September 2000 was different from that in 1990.

The RR (relative risk) cannot be calculated for this type of test, and we do not need to report a p-value for the chi-squared goodness-of-fit test.

b. No, the answer in (a) does not address the question whether the distribution of number of lab classes was different in 2000 than it was in 1990. The chi-squared goodness-of-fit test only tests whether the proportions in the three categories are the same between 1990 and 2000, but it does not tell us whether the overall distribution has changed. To address this question, we could use a chi-squared test for independence, which would allow us to test whether there is a relationship between the year (1990 vs. 2000) and the number of lab classes taken.

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Answer:

150

Step-by-step explanation:

By answering the given question, we may state that  Rounding to the expressions closest 1000: The audience of 472 individuals equals 0.

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

a) To the nearest 100: The audience of 472 individuals is rounded up to 500.

b) Rounding to the closest 1000: The audience of 472 individuals equals 0. (since 472 is closer to 0 than to 1000 when rounding to the nearest thousand).

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The correct interval for which the function h is decreasing is x < 1, which matches with option B: (-∞, 0, 1).

Function h is decreasing over the interval x < 1.

To determine the interval over which the function is decreasing, we need to analyze the behavior of the function's derivative. However, since the derivative of h is not provided, we can make use of the given options to determine the correct interval.

Option A: (-∞, 0, 0)

This option does not match any of the provided answer choices.

Option B: (-∞, 0, 1)

This option suggests that the function is decreasing for x less than 1. It matches one of the answer choices, so it could be a potential solution.

Option C: (1, ∞, 0)

This option indicates that the function is increasing for x greater than 1. It contradicts the given answer choices, as it states that the function is increasing only.

Option D: Reset

This option is not relevant to determining the interval over which the function is decreasing.

The correct interval for which the function h is decreasing is x < 1, which matches with option B: (-∞, 0, 1).

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Answer:

x=8

Step-by-step explanation:

the addition of all the angles must equal 360(the 4 angles on the intersection) degrees

125+125=250

360-250=110

110/2=55

7*8-1=55

A function equation in slope-intercept form to model the situation are as follows;

Slope: 3.

Y-intercept: 48.

Equation: y = 3x + 48.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Since the liquid started at a temperature of 48 degrees and drops 3 degrees per minute, an equation that model the situation is given by:

y = mx + c

y = 3x + 48

Next, we would fill in the table as follows. At x = 0, the temperature of liquid (y) is given by:

y = 3(0) + 48

y = 48.

At x = 1, the temperature of liquid (y) is given by:

y = 3(1) + 48

y = 51.

At x = 2, the temperature of liquid (y) is given by:

y = 3(2) + 48

y = 54.

At x = 3, the temperature of liquid (y) is given by:

y = 3(3) + 48

y = 57.

At x = 4, the temperature of liquid (y) is given by:

y = 3(4) + 48

y = 60.

At x = 5, the temperature of liquid (y) is given by:

y = 3(5) + 48

y = 63.

At x = 6, the temperature of liquid (y) is given by:

y = 3(6) + 48

y = 66.

At x = 7, the temperature of liquid (y) is given by:

y = 3(7) + 48

y = 69.

At x = 8, the temperature of liquid (y) is given by:

y = 3(8) + 48

y = 72.

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t3(x)  = f(a) + f'(a)(x-a) + (1/2)f''(a)(x-a)^2 + (1/6)f'''(a)(x-a)^3.

To find t3(x) we need to find the coefficient of polynomials by using the formula for nth degree taylor polynomial.

what is taylor polynomials?

This are approximations of a function, which become generally better as n increases. It is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point.

using the nth degree taylor polynomial formula:

tn(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...... + f^(n)(a)(x-a)^n/n!

where f^(n)(a) is the nth derivative of f evaluated at x=a.

By calculating we get t3(x) as

t3(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3!

       = f(a) + f'(a)(x-a) + (1/2)f''(a)(x-a)^2 + (1/6)f'''(a)(x-a)^3.

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Answer:

no

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: x has no solutions

Step-by-step explanation:

|x-1| + 5 = 2

|x-1| + 5 - 5 = 2-5

|x-1| + 5 - 5 = -3

|x-1| = -3 ==> Absolute value functions can't be negative. Hence, there is no solution.

x has no solutions

The calculated cost of the dryer is $475.

Let's assume that the cost of the dryer is x dollars.

According to the problem, the cost of the washer is $54 more than the dryer.

Therefore, the cost of the washer is (x + $54).

We are given that the combined cost of the washer and the dryer is $1004. So we can set up the equation:

x + (x + $54) = $1004

Simplifying the equation:

2x + $54 = $1004

2x = $950

x = $475

Therefore, the cost of the dryer is $475.

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Each one of the smaller angles  x = 120 degrees and the larger angle = 2x = 2 × 120 = 240 degrees

The angle of an octagon can be found as follows;

An octagon is a polygon that has 8 sides.

The sum of angles in an octagon is 1080 degrees.

Therefore,

x + x + x + x + x + x + x + 2x = 1080

Hence,

9x = 1080

divide both sides by 9

x = 1080 / 9

x = 120

Therefore, each one of the smaller angles  x = 120 degrees and the larger angle = 2x = 2 × 120 = 240 degrees

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The correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E. Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:

Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:

She will be receiving a 2% raise per year. Her salary will increase $14,000 every year. The percent increase of her salary is 120% every year. Her salary is always 0.2 times the previous year's salary. The percent increase of her salary is 20% every year.

To calculate the salary of the vice president after n years of becoming a vice president, we use the given formula:

S(n) = 70000(1.2)

S(n) = 84000

The salary of the vice president after one year of becoming a vice president: S(1) = 70000(1.2)

S(1) = 84000

The percent increase of her salary is: S(n) = 70000(1.2)n

S(n) - S(n-1) / S(n-1) × 100%

S(n) - S(n-1) / S(n-1) × 100% = (70000(1.2)n) - (70000(1.2)n-1) / (70000(1.2)n-1) × 100%

S(n) - S(n-1) / S(n-1) × 100% = 20%

Therefore, the correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E.

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Answer:

b

Step-by-step explanation:

100/5= 20

he was charhed 20

Answer:

NO.2- SSA is not the method to show the congruency of two triangles.

Answer:

__________________

I think the answer is A.

the first one

__________________

Answer:

A

Step-by-step explanation:

The option that gives the greater distance is 6 diagonal runs.

A rectangle is a 2-dimensional quadrilateral with four right angles and two diagonals of equal length that bisect each other.

The diagonal of a rectangle divides a rectangle into two right triangles. In order to determine the length of the diagonal, the Pythagoras theorem would be used.

The Pythagoras theorem: a² + b² = c²

Where:

a = length

b = base

c = hypotenuse

125² + 85²

=

15,625 + 7,225 = 22,850

c =√ 22,850 = 151.16

Total distance run if you run 6 diagonal runs = 151.16 x 6 = 906.97m

Total distance run if you run 7 field runs = 85 x 7 = 595

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The standard deviation of the boys' marks is 0.33.

Standard deviation is a measure of the amount of variation or dispersion of a set of values from the mean. It is calculated as the square root of the variance. It is the most commonly used measure of spread. It is used to measure the degree of variation from the mean of the data set. It is a measure of the variability of the data. It is usually expressed as a positive number.

The standard deviation of the boys' marks can be calculated by subtracting the mean of the girls' marks from the mean of all 12 marks, and then dividing by the number of boys.

To calculate the mean of the girls' marks, add the three marks together (92 + 80 +71) and divide by 3 (243/3 = 81).

To calculate the mean of all 12 marks, add all 12 marks together (92 + 80 + 71 + …) and divide by 12 (1044/12 = 84).

Therefore the mean of the boys' marks is 84 - 81 = 3.

Now we can calculate the standard deviation of the boys' marks by dividing this value by the number of boys (3/9 = 0.33).

Therefore, the standard deviation of the boys' marks is 0.33.

Standard deviation is a measure of the spread of data around the mean. In this case, the boys' marks had a lower standard deviation than the overall marks, indicating that the boys' marks were more consistent than the girls' marks. This could be due to the fact that there were fewer boys taking the exam, so the boys had a smaller spread of scores than the girls.

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The use of intersecting lines in a drawing to indicate areas of shadow and depth is called "cross-hatching."

Cross-hatching is a technique used in drawing and other visual arts to create the illusion of shadows, volume, and depth. It involves drawing a series of intersecting parallel lines or strokes in close proximity to one another. By varying the density, spacing, and direction of these lines, an artist can create areas of darker shading or indicate the contours and three-dimensional form of an object.

The intersecting lines create a pattern that visually simulates the effect of shadows and adds dimensionality to the artwork. Cross-hatching is a versatile and effective method to enhance the realism and visual impact of a drawing, and it is commonly employed in various art forms such as sketching, illustration, and pen-and-ink techniques.

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Answer:

f(g(x))=1x^2 +-2x+1

Step-by-step explanation:

your inputs should be

1

-2

1

If f(x) = \(x^{2}\), g(x) = \(x -1\) then f(g(x)) = \(1x^{2} -2x+1\).

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given

f(x) = \(x^{2}\)

g(x) = \(x -1\)

f(g(x)) = \((x-1)^{2}\)

It is in the form of \((a-b)^{2}=a^{2} -2(a)(b) +b^{2}\)

= \(x^{2} -2(x)(1) +1^{2}\)

= \(x^{2} -2x+1\)

f(g(x)) = \(1x^{2} -2x+1\)

Hence, If f(x) = \(x^{2}\), g(x) = \(x -1\) then f(g(x)) = \(1x^{2} -2x+1\).

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Answer: Slope: 0.1     Y-Int: 18

Step-by-step explanation:

the equation would be y = 0.1x + 18

so its pretty obvious

Answer: One way to find the least common multiple of two numbers is to first list the prime factors of each number. Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

You can multiply 1/3 by 4 to equal 12 giving you your answer

Answer:

Step-by-step explanation:

4  pencils were broken

1/3 * 12 is 4

An Agile methodology aims for customer satisfaction through early and continuous delivery of useful software components developed by an iterative process using the bare minimum requirements.

Agile methodology is a software development approach that emphasizes flexibility, collaboration, and iterative development. It focuses on delivering value to customers by prioritizing their satisfaction and adapting to changing requirements throughout the development process. Agile methodologies, such as Scrum or Kanban, promote regular and incremental delivery of working software components.

This allows customers to provide feedback early on, ensuring that the final product meets their needs. By using an iterative approach, Agile methodologies enable teams to continuously refine and improve the software based on customer feedback and changing priorities. The emphasis on delivering useful software components and involving customers throughout the development process sets Agile apart from traditional waterfall methodologies.

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Answer:

find the volume of cone and then form the following equation

volume of cone=1/3 x base area x height

volume of cuboid= base area x height

The volume of water will be equal in both therefore u can easily form an equation.

1/3Xπ3²X10= 5X3Xh

then solve for h