a boat is tied with a rope to a dock that is 12 feet tall. along the water, the boat is 16 feet from the dock. how long is the rope connecting the boa

Based on the Hypotenuse-Length Theorem of Congruence (HL), the values of x and y that will make both right triangles congruent are:

x = 8 and y = 4

Two triangles are said to be congruent if the three sides and three angles are equal in all directions.

Two right triangles are congruent to each other by the Hypotenuse-Length Congruence Theorem (HL) if the hypotenuse length and one leg of a right triangle are congruent to the hypotenuse length and leg of the other right triangle.

Thus, for both right triangles to be congruent, it means that their hypotenuse and one of their corresponding legs must be equal to each other.

Use this to create two equations and solve them to get the value of x and y.

Equal Hypotenuse:

    x + y = 3y

⇒ x +4 -4 = 3y -4

⇒ x = 3y -4              ------------------------ (1)

Equal legs:

x = y +4                    _______________ (2)

Find the value of y, by substituting x = (y + 4) into eqn. 1.

   y + 4 = 3y - 4

⇒ -2y = -8

⇒ y = 4

Find the value of x, by substituting y = 4 into eqn. 2.

   x = y + 4

⇒ x = 4 +4

⇒ x = 8

Therefore, based on the Hypotenuse-Length Theorem of Congruence (HL), the values of x and y that will make both right triangles congruent are: x = 8 and y = 4.

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Answer:

12a^3 +2a^2+23a+18

Step-by-step explanation:

The total number of hours Erica works in a week when she babysits for 8 hours can be expressed using the following equation: Total Hours Worked = 8 x Number of Babysitting Days per Week In this case, since Erica babysits for 8 hours.

To calculate the total number of hours Erica works in a week, we need to consider the number of days she babysits and the number of hours she works per day. Erica babysits for 8 hours per day. Therefore, we can use the equation

Total Hours Worked = Number of Days x Hours per Day

To calculate the total number of hours she works in a week. We can substitute these values into the equation:

Total Hours Worked = 1 x 8 = 8 hours.

This means that Erica works a total of 8 hours per week when she babysits for 8 hours.

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Answer:  5

Step-by-step explanation:

The graph represents a proportional relationship is a false statement.

Based on the graph, it appears to represent a linear relationship, where there is a constant rate of change between the two variables. However, it is not possible to determine if it represents a proportional relationship without knowing the specific context of the data being plotted.

If the variables represented in the graph have a proportional relationship, then the graph should be a straight line that passes through the origin (0,0). This is because in a proportional relationship, as one variable increases, the other variable increases or decreases in proportion to the change in the first variable. Therefore, the ratio between the two variables should remain constant.

If the graph in this example does not pass through the origin, then it is likely that the relationship between the variables is not proportional.

As sufficient data is not provided so this statement is false.

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Answer:The surface area of rectangular prism is 166 m².

Step-by-step explanation:

Given that,

length l= 4 m

Width b= 5 m

Height h=7 m

Using the formula of surface area of rectangular prism

We substitute the value into formula

Hence, The surface area of rectangular prism is 166 m².

With little knowledge of the square shape, we know that the area of the shaded region is (B) x² - 2y².

A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles.

It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.

As we previously stated, a square is nothing more than a rectangle with equally long neighboring sides.

The area of a rectangle is therefore expressed as Area = Length Breadth.

So, according to the given figure:
The area of the shaded region would be:

x² - y²

But as we know that 2 triangles make up 1 small square, so the formula can be molded as:

x² - 2y²

Therefore, with little knowledge of the square shape, we know that the area of the shaded region is (B) x² - 2y².

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Answer:

C and D

Step-by-step explanation:

The expressions that are equivalent to 5x are:

None of the other expressions listed are equivalent to 5x.

Thus, the two factors of quadratic expressions found after factorization are 2 and 3.

Factorization is the technique of expressing a given statement as the product between two or more components. The sum of the greatest common factors of the integer coefficients and the same letters with the smallest powers yields the greatest common factor for two or more monomials.

Given quadratic expressions:

=  x² - 5x + 6

To factorize the expression, find the factors of 6 such that on addition it becomes -5.

= x² - 3x - 2x + 6

Taking x common from first two terms and -2 from last two terms.

= x(x -3) -2(x - 3)

Taking (x - 3) common.

= (x - 3)(x - 2)

x -3 = 0

x = 3

and, x - 2 = 0

x = 2

Thus, the two factors of quadratic expressions found after factorization are 2 and 3.

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Complete question:

Factorize quadratic expressions:  x² - 5x + 6

Step-by-step explanation:

Perhaps you entered your question incorrectly

maybe you meant

x^2 -x + 6     THIS factors to

(x-3)(x+2)     <=====if you multiply this out, you will see = x^2 -x+6

Are you familiar with the Quadratic Formula ?

   for this Quadrtatic     a = 1      b = -1      c = 6

    if you plug these numbers into the Quadratic Formula you get the roots:

            x = 3   and x = -2

       then you know the quadratic is   (x-3)(x+2)

The possible unit rate for Josh is 2.91 minutes per mile. However, keep in mind that this is just one possible rate and there could be other values that satisfy the conditions given in the problem.

Unit rate is a rate that is simplified to have a denominator of 1.

In other words, it is a ratio that compares two measurements with one of the measurements set to 1.

For example, if a car travels 100 miles in 2 hours, the unit rate for the car's speed would be 50 miles per hour.

Kody's unit rate can be found by dividing the time taken by the distance covered:

Unit rate = Time / Distance = 80 minutes / 35 miles = 2.29 minutes per mile (rounded to two decimal places).

To find a possible unit rate for Josh, we can use the fact that he rode at a faster rate per mile than Kody. Let's say that Josh's unit rate is x minutes per mile. Since he rode for 102 minutes, we can set up the following equation:

35 miles x (minutes per mile) = 102 minutes

Solving for x, we get:

x = 102 minutes / 35 miles = 2.91 minutes per mile

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A deep appreciation for the natural world and a desire to contribute to advancing scientific knowledge is essential for pursuing a career in astronomy.

Astronomers require a combination of scientific attitudes to excel in their work. To begin with, they need to be curious and passionate about exploring the unknown universe. They should also have a strong sense of patience, persistence, and attention to detail, given that astronomical observations can take a long time to produce results. A capacity for critical thinking, creativity, and problem-solving is also crucial in analyzing and interpreting data, developing theories, and testing hypotheses. Additionally, astronomers must be skilled in communication, as they often collaborate with colleagues, present their findings to the scientific community and the public, and engage in public outreach and education efforts.

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Answer:

To find the equation of the linear function, we need to first determine its slope, which is the rate of change of the function with respect to its input. We can use the slope formula: slope = (change in y) / (change in x) Using the two given points, we have: slope = (30 - 24) / (6 - 4) = 3 Now that we know the slope, we can use the point-slope form of the equation of a line to find the equation of the function: y - y1 = m(x - x1) where m is the slope, and (x1, y1) is one of the given points. Let's use the point (4, 24): y - 24 = 3(x - 4) Expanding and simplifying, we get: y = 3x -

We can conclude that 10% of the football players complete their degree in five years.

How to investigate the university's claim?

To investigate the university's claim, we can set up a hypothesis test.

Null hypothesis: The proportion of football players who complete their degree in five years is 0.9.

Alternative hypothesis: The proportion of football players who complete their degree in five years is less than 0.9.

We can use a one-tailed binomial test to test this hypothesis. The test statistic is the number of football players who received their degree in our sample of 20. Under the null hypothesis, this follows a binomial distribution with n=20 and p=0.9.

We can calculate the probability of observing 14 or fewer football players receiving their degree if the true proportion is 0.9:

P(X ≤ 14) = Σ P(X = i) for i = 0 to 14

= binom.cdf(14, n=20, p=0.9)

≈ 0.001

This means that the probability of observing 14 or fewer football players receiving their degree in a random sample of 20, if the true proportion is 0.9, is only 0.001.

If we use a significance level of 0.05, this means we reject the null hypothesis if the p-value is less than 0.05. Since our p-value is much smaller than 0.05, we can reject the null hypothesis and conclude that the proportion of football players who complete their degree in five years is less than 0.9.

Therefore, based on the given sample, we cannot conclude that 90% of the football players complete their degree in five years.

So, we can conclude that 10% of the football players complete their degree in five years.

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We can conclude that 10% of the football players complete their degree in five years.

To investigate the university's claim, we can set up a hypothesis test.

Null hypothesis: The proportion of football players who complete their degree in five years is 0.9.

Alternative hypothesis: The proportion of football players who complete their degree in five years is less than 0.9.

We can use a one-tailed binomial test to test this hypothesis. The test statistic is the number of football players who received their degree in our sample of 20. Under the null hypothesis, this follows a binomial distribution with n=20 and p=0.9.

We can calculate the probability of observing 14 or fewer football players receiving their degree if the true proportion is 0.9:

P(X ≤ 14) = Σ P(X = i) for i = 0 to 14

= binom.cdf(14, n=20, p=0.9)

≈ 0.001

This means that the probability of observing 14 or fewer football players receiving their degree in a random sample of 20, if the true proportion is 0.9, is only 0.001.

If we use a significance level of 0.05, this means we reject the null hypothesis if the p-value is less than 0.05. Since our p-value is much smaller than 0.05, we can reject the null hypothesis and conclude that the proportion of football players who complete their degree in five years is less than 0.9.

Therefore, based on the given sample, we cannot conclude that 90% of the football players complete their degree in five years.

So, we can conclude that 10% of the football players complete their degree in five years.

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The area of the rectangle is [tex]$\sqrt{20} \times \sqrt{5} = \sqrt{100} = 10$[/tex] square units. Thus, the answer is option D: 10 square units.

What is area of rectangle?

The area of a rectangle is the measure of the region enclosed by its sides, and is calculated by multiplying the length and the width of the rectangle. The unit of area is typically expressed in square units, such as square meters (m²) or square feet (ft²).

The area of rectangle can be calculated using the distance formula to find the length and width of the rectangle, and then multiplying them. Let A(2,1), B(1,3), C(5,5), and D(6,3) be the coordinates of the rectangle's vertices.

The distance between A and B is [tex]\sqrt{(1-2)^2 + (3-1)^2} = \sqrt{1+4} = \sqrt{5}$.[/tex]

The distance between B and C is [tex]\sqrt{(5-1)^2 + (5-3)^2} = \sqrt{16+4} = \sqrt{20}$.[/tex]

So, the length of the rectangle is [tex]\sqrt{20}$ units.[/tex]

The distance between A and D is [tex]\sqrt{(6-2)^2 + (3-1)^2} = \sqrt{16+4} = \sqrt{20}$.[/tex]

The distance between C and D is [tex]\sqrt{(6-5)^2 + (3-5)^2} = \sqrt{1+4} = \sqrt{5}$.[/tex]

Therefore, the width of the rectangle is [tex]\sqrt{5}$ units.[/tex]

Hence, the area of the rectangle is [tex]$\sqrt{20} \times \sqrt{5} = \sqrt{100} = 10$[/tex] square units. Thus, the answer is option D: 10 square units.

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The domain of a function refers to the set of all values of the independent variable (usually denoted by x) for which the function is defined.

For the function f(x) = 2, the expression is defined for all real values of x. Therefore, the domain of f(x) is all real numbers.

If the function was f(x) = 2 / (x - 9), then the expression is undefined for x = 9. Therefore, the domain of f(x) would be all real numbers except 9.

If the function was f(x) = 2 / (x - 3)(x + 3), then the expression is undefined for x = 3 and x = -3. Therefore, the domain of f(x) would be all real numbers except 3 and -3.

If the function was f(x) = sqrt(2x - 5), then the expression is only defined for values of x that make the argument of the square root non-negative. Therefore, the domain of f(x) would be all real numbers such that 2x - 5 >= 0, which simplifies to x >= 5/2.

Therefore, without more information about the function, it is impossible to determine its domain.

Answer:

I think second one is the answer

Step-by-step explanation:

if a number is raised to a negative power u put 1 as the numerator and the number with a positive power and for p3 it stays the same

Answer:

[tex]\frac{p^3}{n^6}[/tex]

Step-by-step explanation:

using the rule of exponents

[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

given

[tex]n^{-6}[/tex] p³

= [tex]\frac{1}{n^{6} }[/tex] × p³

= [tex]\frac{p^3}{n^6}[/tex] ( with positive exponents )

Option D is incorrect because it gives a value that is not consistent with the scatter plot and the line of fit. The correct answer is: The y-intercept is 40.98. The machine starts with 40.98 ounces of diet soda.

In the context of a graph, the y-intercept is the point where a straight line or curve intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is equal to zero. Mathematically, it is the value of y when x = 0 in the equation of the line or curve. The y-intercept is also known as the initial value or starting point of the graph. It is often denoted as (0, b), where b is the y-coordinate of the intercept point.

The y-intercept of the line of fit represents the starting point of the relationship between the two variables, in this case, the amount of diet soda in the machine and the time after the machine is filled. Therefore, the y-intercept value of 40.98 means that the machine starts with 40.98 ounces of diet soda when it is filled.

Option A is incorrect because the y-intercept is a starting value, and it does not represent a rate of change.

Option B is also incorrect because it suggests that the machine loses 4.8 fluid ounces of diet soda every hour, which is not what the y-intercept represents.

Option D is incorrect because it gives a value that is not consistent with the scatter plot and the line of fit.

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Answer:

B) 4 cubes

Step-by-step explanation:

V = s³

[tex] s = \sqrt[3]{V} [/tex]

[tex] s = \sqrt[3]{64} [/tex]

[tex] s = 4 [/tex]

Answer:

C.)

Step-by-step explanation:

1.) First find the slope of the perpendicular line. The slope of the perpendicular line is the number that when multiplied by the slope of the initial line, you get -1. The slope of the line is 3/8, and -8/3 * 3/8 is -1, therefore -8/3 is the slope of the new line.
2.) Now, since we have a slope if you look at the options, there is only one option with the slope -8/3, which is option C.).

To fill up the blanks such that each rectangle has the same area, we could assign the following numbers:

1. First two upper boxes in the first rectangle 2 and 4. The side box, 3.

2. For the two upper boxes in the second rectangle, we could assign the numbers, 10 and 8.

To find the area of a rectangle, you should multiply the length of the rectangle by its width. So, for the first rectangle, the sum of the length will be 6 and this will be multiplied by the width, which is 3.

Also, for the second rectangle, we could sum up the length to be 10 + 8 which is 18. If multiplied by 1, the result of the area will be 18.

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The calculated value of the equation of the circle in standard form is: (x - 4)^2 + (y - 1)^2 = 9

The equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

In this case, the center of the circle is (4, 1) and the radius is 3.

So we can plug in these values to get:

(x - 4)^2 + (y - 1)^2 = 3^2

Simplifying and expanding, we get:

(x - 4)^2 + (y - 1)^2 = 9

So the equation of the circle in standard form is: (x - 4)^2 + (y - 1)^2 = 9

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The cost of making a 5-minute international call using the given international calling plan is $2.25.

To calculate the cost of making a 5-minute call using unitary method, we need to determine the cost per minute of the call, and then multiply it by the number of minutes.

Given that the international calling plan charges 45 cents per minute or fraction of a minute, we can say that the cost per minute is 45 cents.

Using the unitary method, we can determine the cost of 1 minute of the call as follows

1 minute = 45 cents

5 minutes = 5 x 45 cents = 225 cents

= $2.25

Therefore, the cost of making a 5-minute call is $2.25

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Point E: (7, 3), Point F: (1, 3), Point G: (1, -2) and Point H: (7, -2) are the coordinates of each point.

To translate a point in the (x, y) coordinate plane, we add the translation distances to the x-coordinate and the y-coordinate of the point.

For each point in the quadrilateral EFGH, we can apply this translation as follows:

Point E: (4, 5) + (3, -2) = (7, 3)

Point F: (-2, 5) + (3, -2) = (1, 3)

Point G: (-2, 0) + (3, -2) = (1, -2)

Point H: (4, 0) + (3, -2) = (7, -2)

Therefore, after the translation of 3 units right and 2 units down, the coordinates of the points in quadrilateral EFGH are:

Point E: (7, 3)

Point F: (1, 3)

Point G: (1, -2)

Point H: (7, -2)

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Answer:

3`1

Step-by-step explanation:

Answer: 12 inches

Step-by-step explanation:

The 20 inches is the hypotenuse whereas 16 inches is the height of the triangle respectively.

So,

let keep the paper's length as x inches.

20² = 16² + x²

x² = 20² - 16²

x = [tex]\sqrt{20^{2}-16^{2} }[/tex]

x = 12

I am not sure if this is right because i have never done a sum in inches before but  I hope this helps sorry if it is not right.

to find two values for x that make an inequality true, we can choose values that satisfy the inequality, while to find two values that make it false, we can choose values that do not satisfy the inequality.

How to solve inequality?

A. x+3>70

To make this inequality true, we can choose x = 67 or x = 100. For x = 67, we have 67 + 3 > 70, and for x = 100, we have 100 + 3 > 70. To make the inequality false, we can choose x = 68 or x = 69. For x = 68, we have 68 + 3 < 70, and for x = 69, we have 69 + 3 < 70.

B. x+3<70

To make this inequality true, we can choose x = 0 or x = 1. For x = 0, we have 0 + 3 < 70, and for x = 1, we have 1 + 3 < 70. To make the inequality false, we can choose x = 67 or x = 100. For x = 67, we have 67 + 3 > 70, and for x = 100, we have 100 + 3 > 70.

C. -5x<2

To make this inequality true, we can choose x = 0 or x = -1/5. For x = 0, we have -5(0) < 2, and for x = -1/5, we have -5(-1/5) < 2. To make the inequality false, we can choose x = -2 or x = 1/5. For x = -2, we have -5(-2) > 2, and for x = 1/5, we have -5(1/5) > 2.

D. 5x<2

To make this inequality true, we can choose x = 0 or x = 1/5. For x = 0, we have 5(0) < 2, and for x = 1/5, we have 5(1/5) < 2. To make the inequality false, we can choose x = -2 or x = -1/5. For x = -2, we have 5(-2) > 2, and for x = -1/5, we have 5(-1/5) > 2.

In summary, to find two values for x that make an inequality true, we can choose values that satisfy the inequality, while to find two values that make it false, we can choose values that do not satisfy the inequality.

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To find the sale price, we need to apply the discount to the original price:

Discount = 30% = 0.30

Original price = $50

Discount amount = Discount x Original price

= 0.30 x $50

= $15

Sale price = Original price - Discount amount

= $50 - $15

= $35

Therefore, the sale price after a 30% discount on an original price of $50 is $35.

Answer:

$35

Step-by-step explanation:

70% of 50 is 35

The appropriate test to compare one sample to another sample to see if one is greater than another in some way is called a "two-sample hypothesis test."

In a two-sample hypothesis test, the null hypothesis states that there is no significant difference between the means of the two samples, while the alternative hypothesis states that there is a significant difference between the means.

The specific type of test used depends on several factors, including the type of data being compared, the sample sizes, and the level of significance desired. Commonly used tests include the t-test, z-test, and ANOVA.

It is important to choose the appropriate test for the data being analyzed to ensure accurate results and conclusions.

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Open circle and move to the left.

The tangent line and the radius are perpendicular. and the value of x is 8

The correct answer is B. The tangent line and the radius are perpendicular.

In a circle, the tangent line at a point on the circle is perpendicular to the radius drawn to that point. This is a fundamental property of circles.

The value of x is calculated as

9 * x = 12 * 6

So, we have

9x = 72

Divide

x = 8

Hence, the value of x is 8

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In 1960, the percentage of black students attending integrated schools in the South was approximately 2%.

Brown v Board of Education was a landmark decision in 1954 that declared segregation in public schools unconstitutional. However, it took several years for this decision to be implemented in Southern states, and in 1960, only 2% of black students in the South attended integrated schools. This highlights the resistance to desegregation in Southern states and the slow pace of change. It also underscores the ongoing struggles for civil rights and the continued efforts to address systemic racism in education and other aspects of American society.

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