how to find the perimeter of a right angled triangle by only its hypotenuse

The approximate arc length is 56.52mm.

What is an arc length?

The distance between two places along a segment of a curve is known as the arc length. Curve rectification is the process of measuring the length of an irregular arc section by simulating it with connected line segments. There are a finite number of segments in the rectification of a rectifiable curve.

Here, we have

Given: A bicycle wheel has a radius of 225 mm and has 25 equally spaced spokes.

To solve this question, we have to use the formula of the length of an arc which is given as

L = θ/360 * 2πr

To find the angle between each spoke, let's divide 360 by 25

θ = 360/25

θ = 14.4

Now that we have the value of the angle, let's substitute it and solve for the length of the arc.

L = 14.4/360 * 2(22/7)(225)

L = 56.52mm

Hence, the approximate arc length is 56.52mm.

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The label covers approximately 4,800 square centimetres of the wheel of cheese.

What is the lateral surface area of a cylinder?

The lateral surface area of a cylinder can be found using the formula:

L = 2πrh

where L is the lateral surface area, r is the radius of the cylinder, and h is the height of the cylinder.

In this case, we need to find the lateral surface area of the wheel of cheese, so we can use the given radius of 30 centimetres and height of 20 centimeters to calculate:

L = 2 x (22/7) x 30 x 20

L = 4,800 square centimetres

This is the total surface area of the cylindrical-shaped wheel of cheese. However, the label does not cover the circular top and bottom, so we need to subtract their areas from the total surface area to find the area covered by the label.

The area of a circle can be found using the formula:

A = πr²

where A is the area of the circle, and r is the radius of the circle.

In this case, we have two circles (top and bottom), so the total area of the circles that are not covered by the label is:

2 x (22/7) x 30²

= 56,400/7 square centimeters

Subtracting this from the total surface area, we get:

4,800 - 56,400/7

= 33,600/7 square centimeters

= 4,800 square centimeters (rounded to the nearest whole number)

Therefore, the label covers approximately 4,800 square centimeters of the wheel of cheese.

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The equation will be;

c = 20 + 4x

Linear equations are equations of the first order. When a linear equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can also have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on. An equation is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line.

A linear equation that will find the cost c to have a name containing x letters will be;

c = $20 + 4x

where c = cost

$20 = basic fee

x = number of letters

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Answer:

HI

The scale fact from the smaller to the larger is 3.  The scale factor from the larger to the smaller is 1/3

Step-by-step explanation:

P(B A)=P(B)

Step-by-step explanation:Given situation that two events occurred event A and event B event A has already occurredtherefore, there is no relationship between them event A and event B since, the probability of B does not depend on any activity of A therefore, P(B A)=P(B)

The probability that event B occurs, given that event A has already occurred is P(A) = P(A ∩ B) / P(B | A).

An event is the outcome of a chance experiment or a collection of similar outcomes.

As the sample space is a collection of all potential outcomes of a random experiment, it might be defined as every subset of that space.

When the event B is dependent on event A,

P(A ∩ B) ≠ P(A) x P(B)

When the event A comes before event B. So, the probability of B given A:

P(B | A) = P(A ∩ B) / P(A)

P(A) = P(A ∩ B) / P(B | A)

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The angle AED of arc AD of the circle is calculated to be equal to 8100/πr

We shall use the formula:

arc length = (arc angle/360) × 2 × π × radius

where arc angle is measured in degrees and radius is the distance from the center of the circle to the point on the circle where the arc begins.

If AD = 45 and r the radius, we evaluate the arc angle m ∠AED as follows:

(arc angle/360°) × 2 × π × r

by cross multiplication;

arc angle AED = (360 × 45)/2πr

2 can divide 360° to give;

arc angle AED = (180 × 45)/πr

arc angle AED = 8100/πr

Therefore, the angle AED of arc AD of the circle is calculated to be equal to 8100/πr

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For the linear equation 3x + y = 9 we have:

Here we want to find the two intercepts for the linear equation:

3x + y = 9

First, the x-intercept is the point that we get when we evaluate on y = 0.

3x + 0 = 9

3x = 9

x = 9/3

x = 3

Then we get: x-intercept (3, 0)

And for the y-intercept we need to evaluate in x = 0.

3*0 + y = 9

y = 9

Then the y-intercept is (0, 9).

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After solving the system of equations, we found that the number of small chairs is 53 and the number of large chairs is 45.

What is meant by the system of equations?

A set of equations with a finite number of solutions is referred to as a system of equations. A system of equations in algebra consists of two or more equations and looks for common answers to the equations. A group of equations that are all satisfied by the same set of variables are referred to as a system of linear equations.

Given,

  Cost of material for small chair = $10

Cost of material for large chair = $15

The selling price for a small chair = $22

The selling price for a large chair = $51

The total money spent on materials = $305

Designer makes 8 more small chairs than large chairs.

If the number of large chairs = t  and the number of small chairs =  s

Using the given equations, we can write the following system of equations.

10s + 15t = 305

s - t = 8

Now we make the coefficient of s in both equations the same.

Multiply 10 in the second equation.

10s + 15t = 305

10s - 10t = 80

Subtracting,

5t = 225

t = 45

s = 8 + t = 45 + 8 = 53

Therefore after solving the system of equations, we found that the number of small chairs is 53 and the number of large chairs is 45.

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Answer:

76

Step-by-step explanation:

(16x3)+28

Its 16x3 because there's 3 half hours in 1.5hrs  

The sequence will be aₙ=$1250-118ⁿ⁻¹ where n= place at which a bowler finished.

What exactly is a sequence?

A sequence is a collection of numbers that follows pattern. Olivia, for example, has been offered a position with a beginning monthly pay of $1000 and a yearly raise of $500. To figure out her monthly pay for the first three years? The prices will be $1000, $1500, and $2000. Note that Olivia's income over a number of years creates a sequence as they follow a pattern where the numbers increase by $500 each time.

Now,

given award money for 1, 2, 3 places is given as $1250, $1132 and $1014

that means for the sequence, first term is 1250 and difference between the next terms will be 118 (less)

So, the sequence will be aₙ=$1250-118ⁿ⁻¹

where

n=place at which a bowler is placed.

Hence,

           The sequence will be aₙ=$1250-118ⁿ⁻¹.

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The simplified value of the expression is [a² + b² - 2ab]/[2a²b² - ab³ - a³b]

From the question, we have the following parameters that can be used in our computation:

1/(b² - ab) - 1/(ab - a²)

Take the LCM of the expression

So, we have the following representation

[ab - a² - b² + ab]/[(b² - ab)(ab - a²)]

Evaluate the like terms

So, we have the following representation

[2ab - a² - b²]/[(b² - ab)(ab - a²)]

Open the bracket

[a² + b² - 2ab]/[2a²b² - ab³ - a³b]

Hence, the solution is [a² + b² - 2ab]/[2a²b² - ab³ - a³b]

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The solution is, the equation is y=2/3x.

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.

A diagram representing a system of connections or interrelations among two or more things by a number of distinctive dots, lines, bars, etc.

here, we have,

so the line is in slope intercept form

y=mx+b, m=slope and b=y intercept

we know the slope so just solve for b

y=2/3x+b

subsitute

3 for x and 2 for y

2=2/3(3)+b

2=2+b

subtract 2 from both sdies

0=b

so the equaiton is

y=2/3x+0 or just simply

y=2/3x

here is the graph

just input values for x and get y values exg

x=3 y=2

x=6 y=4

x=0 y=0

x=-3 y=-2

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Answer:

Let's call the number of students at the college "x". Then, the number of faculty/staff is 3 times that number, or 3x. The total number of people at the college is the sum of the students and faculty/staff, which is x + 3x = 4x.

According to the problem, the ratio of faculty/staff to students is 3 to 13, so we can write an equation:

3x / x = 3 / 13

To find the number of students, we can solve for x:

4x = 4000

x = 1000

So, there are 1000 students at the college.

(a) The union set is AUB'={f, k, m, x, y}.

(b) The union set is A'UB'={q,k, x, y}.

The union of two sets is also a set. This set contains all the elements of both two sets.

The universal set is U= {f, k, m, q, x,y} and two subsets are A={f, k, m, y} and B = {f, m,q}.

(a)

B' is the complementary set of B. So, find the elements of B'=U-B.

B'= {f, k, m, q, x,y}-{f, m,q}

={k, x,y}

Now, find the union set AUB'.

AUB' ={f, k, m, y}U{k, x,y}

={f, k, m, x, y}

Therefore, the required answer is AUB'={f, k, m, x, y}.

(b)

Also, A' is the complementary set of A. So, find the elements of A'=A-B.

A'= {f, k, m, q, x,y}-{f, k,m, y}

={q,x}

Now, find the union set A'UB'.

A'UB' ={q,x}U{k, x,y}

={q,k, x, y}

Therefore, the required answer is A'UB'={q,k, x, y}.

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By using the continuous interest formula, we get 8.54 years that the amount will take to double itself.

The continuous interest formula is used to calculate the future value of a compound interest investment. It is written as follows:

Future Value = Principal × [tex](1 + r)^{n}[/tex]

where Principal is the original investment, r denotes the yearly interest rate, and n denotes the number of compounding periods.

The continuous interest formula is used to compute the future worth of an investment given its current value, yearly interest rate, number of times the interest is compounded each year, and number of years held.

In the given question,

A = A_0[tex]e^{rt}[/tex]

2A_0 = A_0[tex]e^{rt}[/tex]

2 = [tex]e^{rt}[/tex]

ln(2) = rt

t = [tex]\frac{2}{r}[/tex]

t = [tex]\frac{2}{0.08}[/tex]

t = 8.54 years

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Answer:

14v-2

Step-by-step explanation:

1. distribute

2. combine like terms

see photo for more information

The domain of f(x) is equal to the range of inverse function g(x).

What are inverse functions?

A function from a set X to a set Y in mathematics assigns each element of X the exact same number of elements from Y. A function's inverse function reverses the action of a function or f. If and only if the function is bijective, the inverse of f is true.

Given two functions f(x) and g(x).

It is also said that g(x) is the inverse of f(x).

One of the properties of inverse functions is that only one-to-one functions are inverse. If g is equal to f's inverse, then f is equal to g's inverse.

Both f and g are one-to-one functions if they are the inverses of one another.

f and g are inverses of each other if (fog)(x) = x, x ∈ the domain of g.

The range of g equals the domain of f, and the domain of f equals the range of g.

Therefore the domain of f(x) is equal to the range of inverse function g(x).

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Answer: The correct system of linear inequalities that represents this situation is:

X + Y ≤ 32 (to represent the maximum number of hours you can work)

7X + 8Y ≥ 256 (to represent the minimum amount of money you need to earn)

X ≥ 0, Y ≥ 0 (to represent that you can only work a non-negative number of hours at each job)

Where X represents the number of hours you spend tutoring and Y represents the number of hours you spend babysitting. The first inequality represents the maximum number of hours you can work, and the second inequality represents the minimum amount of money you need to earn. The last two inequalities represent that you can only work a non-negative number of hours at each job.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve the equation (3x + 20)^2 = 125 using the square root method, we start by taking the square root of both sides:

√[(3x + 20)^2] = √125

3x + 20 = ± 5

Next, we subtract 20 from both sides:

3x = -20 ± 5

Finally, we divide both sides by 3:

x = -8 or x = 3/3

So, the two solutions to the equation (3x + 20)^2 = 125 are x = -8 and x = 1. These solutions are in radical form and are already simplified.

Conclusions drawn from a sample of 50 monarch butterflies tagged from one location in California may not be entirely true for all monarch butterflies.

A sample is a subset of data drawn from a larger population by a researcher using a predetermined selection process. These components are referred to as sample points, sampling units, or observations.

The sample size is relatively small compared to the entire population of monarch butterflies. Additionally, the sample is only taken from one location, so the results may not be representative of the entire migration pattern.

The monarch butterfly is known to have a wide geographic range, migrating across North America, and covering a distance of thousands of miles during their annual migration. Thus, to make conclusions that apply to the entire population of monarch butterflies, a more comprehensive and representative sample size from various locations along their migration route would be needed.

In scientific research, it is essential to have a large and representative sample size to minimize the margin of error and to obtain accurate results. Therefore, a larger sample size and a more diverse geographical representation would provide a better understanding of the migration patterns of monarch butterflies.

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Based on the information provided, the passage that explains the citation is "The outcome...is situational irony..." (option A).

When you cite information from other sources or authors, there are three elements that should be included:

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Answer: 71/7

Step-by-step explanation:

I like this problem a lot!

Let the shorter leg length be x:

then the longer leg length is 3x - 9

the hypotenuse length is (3x - 9) + 2 = 3x - 7

Perimeter of Triangle = Sum of all 3 sides of a triangle

24 = x + (3x - 9) + (3x - 7)

24 = 7x - 16

40 = 7x

.: x = 40/7

.: hypotenuse = 3x - 7 = (120/7) - 7 = 71/7

Done!

A transformation rule, if applied to a polygon on a coordinate grid, which does not preserve congruence include the following: C. (x, y) → (3x, 3y).

In Geometry, dilation simply refers to a type of transformation which changes the size of a geometric figure and the location of its points based on the scale factor, but not its shape.

Generally speaking, a dilation is not a rigid transformation because it can preserve angle measure, orientation, perpendicular lines, betweenness of points, parallel lines, and collinearity in any geometric figure.

In conclusion, we can reasonably infer and logically deduce that dilations does not preserve congruence.

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Answer:

y = 4x + 32

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 4x ← is in slope- intercept form

with slope m = 4 and y- intercept = 0

• Parallel lines have equal slopes , then

y = 4x + c ← is the partial equation

to find c substitute (- 8, 2 ) into the partial equation

2 = 4(- 8) + c = - 32 + c ( add 32 to both sides )

34 = c

y = 4x + 32 ← in slope- intercept form

When we are given the value of the explanatory variable, we can use the least-squares regression line to predict the value of the outcome variable.

The least square method is the process of finding the best-fitting curve or line of best fit for a set of data points by reducing the sum of the squares of the offsets (residual part) of the points from the curve. During the process of finding the relation between two variables, the trend of outcomes is estimated quantitatively. This process is termed as regression analysis. The method of curve fitting is an approach to regression analysis. This method of fitting equations that approximates the curves to give raw data is the least squares.

It is quite obvious that the fitting of curves for a particular data set is not always unique. Thus, it is required to find a curve having a minimal deviation from all the measured data points. This is known as the best-fitting curve and is found by using the least-squares method.

When we are given the value of the explanatory variable, we can use the least-squares regression line to predict the value of the outcome variable.

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The coordinates of point C in the given right triangle ABC is (2, 2√3-2)

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

Given that, triangle ABC is a 30°-60°-90° triangle, where two vertices are A(-4, -2) and B(4, -2).

Now, AB=4-(-4)=8

AC=AB×sin60°= 8×√3/4√3

In right triangle ACD

AD=AC×cos30°

= 4√3×√3/2

= 6

Xc=6-4=2

Yc=AC×sin30°-2

= 4×3×1/2-2

= 2√3-2

The coordinates of point C(2, 2√3-2)

Therefore, coordinates of C(2, 2√3-2).

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To get an 85 average, Laurence needs a score of 25 on his upcoming biology exam.

We can use the formula for the average (or mean) of a series of variables to determine Laurence's next biology test score in order to achieve an average of 85:

Average = (sum of values) / (number of values)

The total of Laurence's marks on the first four biology exams can be calculated using the following formula:

Sum of scores = 87 + 80 + 75 + 85

= 327

We need the total of all five scores to be 85 x 5 = 425 in order to obtain an average of 85 for five tests.

Therefore, We need the total of all five scores to be 85 x 5 = 425 in order to obtain an average of 85 for five tests.

By deducting Laurence's first four scores from the desired total of all five scores, and dividing the result by one (the number of scores left), we can get the score that Laurence has to achieve in his next biology exam:

Next score = (sum of all five scores) - (sum of first four scores)

= (85 x 5) - 327

= 25

Therefore, To get an 85 average, Laurence needs a score of 25 on his upcoming biology exam.

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Answer:B

Step-by-step explanation:

Answer:

5/6

Step-by-step explanation: