Question 22 of 30
What is the y-intercept of the line y=1/2x-5?
O A. - 1/2
OB. 5
O C.1/2
OD. -5

Answer:

  h = 10 13/14 units

Step-by-step explanation:

You want the height from the side of length 14 of a parallelogram with side length 17 and height 9.

The area of a parallelogram is the same, no matter which side is used as the "base". This means ...

  A = bh = 17(9) = 14(h)

  h = 17·9/14 = 10 13/14 . . . . units

Answer:

Step-by-step explanation:

-109f

Answer:

36

Step-by-step explanation:

Given:

1/6 of the marbles are red

1/3 of the marbles are blue

There are 18 green marbles in the jar

We can set up the following equations based on the given information:

Number of red marbles = 1/6 * x

Number of blue marbles = 1/3 * x

Number of green marbles = 18

Since the total number of marbles in the jar is "x", we can write the equation for the sum of all the marbles as:

(Number of red marbles) + (Number of blue marbles) + (Number of green marbles) = x

Substituting the values from the given information:

1/6 * x + 1/3 * x + 18 = x

Multiplying through by 6 to eliminate the fraction:

x/6 + 2x/6 + 18 = 6x/6

x + 2x + 108 = 6x

Combining like terms:

3x + 108 = 6x

Subtracting 3x from both sides of the equation:

3x + 108 - 3x = 6x - 3x

108 = 3x

Dividing both sides by 3 to solve for x:

108/3 = 3x/3

36 = x

Answer:

3/8x8/3 = 1    

ur welcome I hoped I helped u answering ur question!!

Answer: 1

Step-by-step explanation:

3/8 * 8/3 just simplifies to 1 because the numerator and denominator will be equal meaning it equals 1.

Neither of the segments is the perpendicular bisector of the other.

To determine which segment is the perpendicular bisector of the other, we need to find the equations of the lines containing each segment and then check if one of the lines is perpendicular to the other and passes through the midpoint of the other segment.

Let's start by finding the midpoint of segment AT. The coordinates of A and T are not given, but we don't actually need them to find the midpoint.

So, the midpoint M of segment AT is:

M = ((AT_x1 + AT_x2)/2, (AT_y1 + AT_y2)/2)

We don't know the actual values of AT_x1, AT_x2, AT_y1, and AT_y2, but we can find their expressions in terms of x using the segment lengths and the coordinates of the endpoints. We have:

AT_x2 - AT_x1 = BT_x2 - AT_x1 = (x + 5) - (2x + 3) = -x + 2

AT_y2 - AT_y1 = BT_y2 - AT_y1 = (BT - AT) = (x + 5) - (2x + 3) = x + 2

Therefore,

AT_x1 = AT_x2 + x - 2

AT_y1 = AT_y2 - x - 2

Now, we can substitute x=2 and the expressions for AT_x1 and AT_y1 into the midpoint formula to find the coordinates of M:

M = ((AT_x1 + AT_x2)/2, (AT_y1 + AT_y2)/2) = ((AT_x2 + 2 - AT_x2)/2, (AT_y2 - 2 - AT_y2)/2) = (1, -1)

So, the midpoint of segment AT is M(1, -1).

Next, let's find the equations of the lines containing segments AT and DT. We can use the point-slope form of the equation of a line, which states that the equation of a line passing through a point (x1, y1) with slope m is y - y1 = m(x - x1).

For segment AT, we have:

m_AT = (AT_y2 - AT_y1)/(AT_x2 - AT_x1) = (x + 2)/(x - 1)

Let's substitute x=2 to find the slope of the line containing segment AT:

m_AT = (2 + 2)/(2 - 1) = 4

So, the equation of the line containing segment AT is:

y - AT_y1 = m_AT(x - AT_x1)

y - (22 + 3) = 4(x - 22 - 1)

y - 7 = 4(x - 5)

y = 4x - 13

For segment DT, we have:

m_DT = tan(m∠ATD) = tan(41x + 8)

Let's substitute x=2 and simplify:

m_DT = tan(82 + 8) = tan(90) = undefined

This means that the line containing segment DT is vertical and its equation is x = DT_x1 = 4*2 + 1 = 9.

Now, we need to check if one of these lines is perpendicular to the other and passes through the midpoint of the other segment.

First, let's check if the line containing segment AT is perpendicular to the line containing segment DT.  We have:

m_AT * m_DT = 4 * undefined = undefined

Since undefined is not equal to -1, the lines are not perpendicular, and we can rule out the possibility that the line containing segment AT is the perpendicular bisector of segment DT.

Next, let's check if the line containing segment DT is perpendicular to the line containing segment AT. We have:

m_AT = 4

So, the slope of the line perpendicular to the line containing segment AT is -1/4. We can use the point-slope form of the equation of a line again:

y - M_y = -1/4(x - M_x)

y - (-1) = -1/4(x - 1)

y + 1 = -1/4x + 1/4

y = -1/4x + 3/4

Now, we need to check if this line passes through point D, an endpoint of segment DT. We can substitute the coordinates of D into the equation of the line and check if the equation holds true:

DT_y1 = 4*2 + 1 = 9

DT_x1 = 9

9 = -1/4*9 + 3/4

9 = -9/4 + 3/4

9 = -6/4

This is not true, so the line containing segment DT does not pass through point D. Therefore, we can conclude that the line containing segment DT is not the perpendicular bisector of segment AT.

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Answer:

Step-by-step explanation:

I think it’s b

The answer depends on the rank of A.

If the rank of A is less than 4, then the dimension of its null space is greater than or equal to 4-rank(A).

If the rank of A is 4, then the dimension of its null space is 0.

The dimension of the null space of a matrix A is given by the number of linearly independent vectors that satisfy the equation A x = 0,

where x is a column vector.

Since A is a 6x4 matrix, the equation A x = 0 represents a homogeneous system of 6 linear equations in 4 unknowns.

The rank-nullity theorem states that the rank of a matrix plus the dimension of its null space equals the number of columns of the matrix. Therefore, we have:

rank(A) + dim(null(A)) = 4

The rank of A is at most 4, since there are only 4 columns.

If the rank of A is 4, then the dimension of its null space is 0, because there are no linearly independent vectors that satisfy A x = 0. On the other hand, if the rank of A is less than 4, then the dimension of its null space is at least 4-rank(A).

Therefore, the smallest possible dimension of null(A) is:

dim(null(A)) = 4 - rank(A).

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The smallest possible dimension of the null space (nul A) for a 6x4 matrix A is 0.

To determine the smallest possible dimension of the null space (nul A) of a 6x4 matrix A, we need to consider the rank-nullity theorem, which states:

dim(A) = rank(A) + dim(nul A)

Here, dim(A) represents the dimension of the matrix A, rank(A) represents the rank of the matrix A, and dim(nul A) represents the dimension of the null space of A.

For a 6x4 matrix A, the dim(A) is 4 since there are 4 columns. The rank(A) represents the number of linearly independent columns, and it can be at most 4 since there are 4 columns.

To find the smallest possible dimension of the null space, we need to maximize the rank(A). In this case, the maximum possible rank(A) is 4. Now, using the rank-nullity theorem:

4 = 4 + dim(nul A)

Solving for dim(nul A), we get:

dim(nul A) = 4 - 4
dim(nul A) = 0

Therefore, the smallest possible dimension of the null space (nul A) for a 6x4 matrix A is 0.

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Answer:

(0, [tex]\frac{1}{2}[/tex] ) , (1, [tex]\frac{5}{4}[/tex] ) , (2, 2 )

Step-by-step explanation:

to determine which points are contained in the graph.

substitute the x- coordinate of each point into the equation and if the value obtained is equal to the y- coordinate of the point then it is contained in the graph.

(0, [tex]\frac{1}{2}[/tex] )

y = [tex]\frac{3}{4}[/tex] (0) + [tex]\frac{1}{2}[/tex] = 0 + [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{2}[/tex] = y- coordinate ← contained in graph

(1, [tex]\frac{5}{4}[/tex] )

y = [tex]\frac{3}{4}[/tex] ( 1) + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{4}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{4}[/tex] + [tex]\frac{2}{4}[/tex] = [tex]\frac{5}{4}[/tex] = y- coordinate ← contained in graph

([tex]\frac{1}{2}[/tex], 0 )

y = [tex]\frac{3}{4}[/tex] ([tex]\frac{1}{2}[/tex] ) + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex] + [tex]\frac{4}{8}[/tex] = [tex]\frac{7}{8}[/tex] ≠ y- coordinate ← not contained in graph

(2, 2 )

y = [tex]\frac{3}{4}[/tex] (2) + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2 = y- coordinate ← contained in graph

Answer:

$10,244.14 after 12 years

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(n*t)

A = the final amount of the investment

P = the principal amount ($4200 in this case)

r = the annual interest rate (8% or 0.08 as a decimal)

n = the number of times the interest is compounded per year (once annually in this case)

t = the number of years the money is invested (12 years in this case)

Substituting the given values into the formula, we get:

A = 4200(1 + 0.08/1)^(1*12)

A = 4200(1.08)^12

A = 4200(2.44140625)

A = $10,244.14 (rounded to the nearest cent)

The possible lengths of each side of the garden is given by the inequality relation 0 ≤ x ≤ 12

Given data ,

Let's assume that the square garden has sides of length x.

To surround the garden, we will need fencing of length equal to the perimeter of the square, which is 4x

The total amount of fencing is at most 52 feet

So , the inequality is

4x ≤ 52

Dividing both sides by 4, we get:

x ≤ 13

Therefore, the possible length of each side of the garden is less than or equal to 13 feet

And , each side of garden should be more than 0 , so

x > 0

Hence , the full inequality representing the possible length of each side of the garden would be 0 < x ≤ 13

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No, 3 is not greater than 5. This is because 5 is larger than 3.

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

3 and 5

No, 3 is not greater than 5. This is because 5 is larger than 3.

In other words, 5 is further to the right on the number line than 3.

We can also say that 5 is the greater number and 3 is the lesser number.

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The main advantage of an independent measures design is that it reduces the risk of order or practice effects and minimizes the influence of individual differences between participant

An independent measures design, also known as a between-subjects design, is a type of research study in which different groups of participants are used for each condition being tested.

In other words, each participant is only exposed to one condition, and the data from each group is analyzed and compared to determine if there are any significant differences between the groups.

The main characteristics of an independent measures design are:

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The values using trigonometric ratios are sinR = 15/17; cosR = 8/17, tanR = 15/8

An equation is an expression that uses mathematical operations to show how numbers and variables are related to each other.

Pythagoras ratio is an equation that shows the relationship between the sides of a right triangle.

To find TR, using Pythagoras:

TR² = TY² + YR²

TR² = 15² + 8²

TR = 17

Trigonometric ratios show the relationship between sides and angles of right triangle.

Hence:

sinR = 15/17; cosR = 8/17, tanR = 15/8

The values are sinR = 15/17; cosR = 8/17, tanR = 15/8

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Sara used 3/5 cup of milk in the recipe. The answer corresponds to option (B) in the given answer choices.

The total amount of liquid used by Sara in the recipe is 1 cup. Out of this 1 cup, Sara used 2/5 cup of vinegar. Therefore, the amount of milk she used would be the difference between the total amount of liquid used and the amount of vinegar used.

Mathematically, we can represent this as:

Amount of milk = Total amount of liquid - Amount of vinegar

Amount of milk = 1 cup - 2/5 cup

Simplifying the expression on the right side, we get:

Amount of milk = 5/5 cup - 2/5 cup

Amount of milk = 3/5 cup

Therefore, Correct option is B.

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Complete question is:

Sara used a total of 1 cup of liquid for a recipe. She used 2/5 cup of vinegar, and the rest of the liquid she used was milk.

How much milk, in cups, did sara use for the recipe?

A) 2/5

B)3/5

C)5/5

D) 1 2/5​

The possible rational zeros of the polynomial function are

±1, ±3, ±9, ±1/2, ±3/2, ±9/2

We have,

To find the possible rational zeros of the polynomial function P(x), we can use the Rational Root Theorem.

According to the theorem,

Any rational zero of a polynomial function with integer coefficients must have the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

In this case,

The constant term is -9, which has factors of ±1, ±3, ±9.

The leading coefficient is 2, which has factors of ±1, ±2.

So the possible rational zeros are:

±1/1, ±3/1, ±9/1, ±1/2, ±3/2, ±9/2

Simplifying the fractions, the possible rational zeros are:

±1, ±3, ±9, ±1/2, ±3/2, ±9/2

Thus,

The possible rational zeros are ±1, ±3, ±9, ±1/2, ±3/2, ±9/2

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If diameter 6 cm and height 16 cm, the volume of the right circular cylinder is 144π cubic cm.

The volume of a right circular cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height. In this case, the diameter is given as 6 cm, so the radius is half of the diameter, which is 3 cm. The height is given as 16 cm.

Substituting these values into the formula, we get:

V = π(3 cm)^2(16 cm)

V = π(9 cm^2)(16 cm)

V = 144π cubic cm

A right circular cylinder is a three-dimensional object with a circular base and straight sides that are perpendicular to the base. The volume of a cylinder is the amount of space that it occupies and is calculated by multiplying the area of the base by the height.

In this case, the base of the cylinder is a circle with radius 3 cm, so its area is π(3 cm)^2 = 9π square cm. The height of the cylinder is 16 cm, so the volume is 9π x 16 = 144π cubic cm.

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For a continuous random variable X, which is uniformly distributed on an interval [4,9], the probability density function of [tex]f_Y( y)[/tex] is equals to

[tex]f_Y( y) =\begin{cases} \frac{2y}{5},\quad 2≤ x ≤ 3 \\ 0, \quad \: otherwise\ \ \end{cases}[/tex]. So, option(5) is correct.

We have a continuous random variable X is uniformly distributed on the interval [4,9]. The PDF is a probability that a random variable acquire a value exactly same or equal to the random variable but in case of CDF, this probability values is less than or equal to the random variable. The probability density function for X is defined as [tex]f_X(x) = \frac{1}{b - a} [/tex] so, we can write it as [tex]f_X ( x) =\begin{cases} \frac{1}{5},\quad 4≤ x ≤ 9 \\ 0, \quad otherwise \\ \end{cases}[/tex].

We have to determine the probability density function [tex]f_Y(y)[/tex]. For this first we have to calculate the cumulative distribution function for f(x) is written as [tex]F_X(x) = \int_{4}^{x} f(x) dx [/tex]

[tex]= \int_{4}^{x} \frac{1}{5} dx [/tex]

[tex]= \frac{1}{5} [ x]_{4}^{x} [/tex]

[tex]F_X(x) = \frac{x - 4}{5}[/tex]

Now, we have, [tex] Y = \sqrt{X}[/tex]

when X = 4 => Y = 2 and X = 9 => Y = 3

Also, X = Y²

Differentiating X = Y² with respect to Y

=> dX = 2Y dY

=> dX/dY = 2Y

Now, pdf of Y is written as [tex]f_Y(y) = f_X(x)|\frac{dX}{dY}| [/tex]

[tex] = \frac{ 1}{5} × 2y[/tex]

[tex]= \frac{ 2y}{5}[/tex]

So, [tex]f_Y( y) =\begin{cases} \frac{2y}{5},\quad 2≤ x ≤ 3 \\ 0, \quad \: otherwise \ \ \end{cases}[/tex]. Hence, required value is [tex]f_Y( y) =\begin{cases} \frac{2y}{5},\quad 2≤ x ≤ 3 \\ 0, \quad \: otherwise \ \ \end{cases}[/tex].

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Complete question:

The above figure complete the question.

Answer:

6.4

Step-by-step explanation:

Answer:

roughly 8.58

Step-by-step explanation:

long division I hope this helps bye !!! have a great day!!! :D

[tex]sin^2(x)[/tex]  can be expressed as [tex](1 - cos(2x)) / 2[/tex] using the power reducing formula.

To express [tex]sin^2(x)[/tex]using the power reducing formula,

we need to recall the following trigonometric identity:
[tex]sin^2(x) = (1 - cos(2x)) / 2[/tex]
Recognize that the question asks for the power reducing formula for sin^2(x).
Recall the trigonometric identity:[tex]sin^2(x) = (1 - cos(2x)) / 2[/tex]
The power reducing formula for [tex]sin^2(x)[/tex] is:[tex](1 - cos(2x)) / 2.[/tex]

The power reducing formula is a trigonometric identity that allows you to express a trigonometric function of a higher power in terms of a trigonometric function of a lower power.

It is most commonly used for reducing the power of the sine and cosine functions.

The power reducing formula for cosine is:

[tex]cos^2(x) = (1 + cos(2x))/2[/tex]

The power reducing formula for sine is:

[tex]sin^2(x) = (1 - cos(2x))/2[/tex]

These formulas can be derived using the Pythagorean identity, which states that [tex]sin^2(x) + cos^2(x) = 1.[/tex]

By solving for either[tex]sin^2(x) or cos^2(x)[/tex] in terms of the other, and then using the double angle formula for cosine[tex](cos(2x) = cos^2(x) - sin^2(x)),[/tex] we can arrive at the power reducing formulas.

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Answer:

a) a square number:64

b) a multiple of 13:65

c) a factor of 186:62

d)the prime number:61,67

For every 100 free throws Chris Paul attempted, he made approximately 93 of them.

We have,

Chris Paul's free throw percentage of 93.4 means that he made 93.4% of his free throw attempts during the 2020-21 season.

In other words, for every 100 free throws he attempted, he made approximately 93 of them.

This is a high free throw percentage and indicates that Chris Paul is a skilled free throw shooter.

Thus,

For every 100 free throws Chris Paul attempted, he made approximately 93 of them.

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For the given problem, The correct answer will be option 2: The IQR of 13 is the most accurate to use, since the data is skewed.

The Interquartile Range (IQR) is a measure of variability that compares the 25th percentile (Q1) to the 75th percentile (Q3) of a dataset (Q3). It is frequently used to describe the distribution or variability of data that may contain outliers or is not regularly distributed.

The data in the histogram is not evenly distributed in this example because there are many donations at the higher end of the scale (16 to 20), resulting in a positively skewed distribution. Using a range of 20, which indicates the difference between the greatest and lowest value in the dataset, may not adequately depict the data's variability since it is significantly impacted by outliers at the extremes.

For the given dataset, IQR can be calculated as:

Arrange the dataset in ascending order:

[tex]5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20[/tex]

Find the median (Q2), i.e. the middle value of given dataset:

Median (Q2) = 15

Find the lower quartile (Q1), which is the median of the lower half of the dataset:

[tex]Q1 = Median of (5, 5, 6, 8, 10) = 6[/tex]

Find the upper quartile (Q3) i.e. median of the upper half of dataset:

[tex]Q3 = Median \;of (15, 18, 20, 20, 20, 20, 20) = 19[/tex]

[tex]IQR = Q3 - Q1 = 19 - 6 = 13[/tex]

Utilizing the IQR of 13, which represents the range between the 25th percentile (Q1 = 6) and the 75th percentile (Q3 = 19), would provide a more accurate measure of variability that is less impacted by outliers at the higher end of the data. It would also offer a better indication of the organization's typical donations because it captures the middle 50% of the data.

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They form a parallelogram because opposite sides of the given points have an equal slope.

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

To prove that the four points (2,1), (-1,-5), (1,5), and (-2,-1) are the vertices of a parallelogram, we need to show that opposite sides are parallel.

First, we can find the slope of the line connecting (2,1) and (-1,-5):

m1 = (1 - (-5)) / (2 - (-1)) = 6/3 = 2

Next, we can find the slope of the line connecting (1,5) and (-2,-1):

m2 = (5 - (-1)) / (1 - (-2)) = 6/3 = 2

Since the slopes are the same, the line segments connecting these points are parallel.

Now, we can find the slope of the line connecting (2,1) and (1,5):

m3 = (5 - 1) / (1 - 2) = -4

Next, we can find the slope of the line connecting (-1,-5) and (-2,-1):

m4 = (-1 - (-5)) / (-2 - (-1)) = 4/3

Since the slopes are different, the line segments connecting these points are not parallel.

However, we can also see that the line connecting (1,5) and (-1,-5) has the same slope as the line connecting (-2,-1) and (2,1), which is:

m5 = (5 - (-5)) / (1 - (-1)) = 10/2 = 5

Therefore, the line segments connecting (1,5) and (-1,-5), and (-2,-1) and (2,1) are parallel.

Since opposite sides are parallel, the four points (2,1), (-1,-5), (1,5), and (-2,-1) form a parallelogram.

Therefore, they form a parallelogram because opposite sides of the given points have an equal slope.

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There is no solution to this system of equations. (option B).

What is equation?

An equation is a mathematical statement which is made by two expressions connected by an equal sign. For example, 3x – 8 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 8.

There is no solution to the given graph of two linear equations or system of linear equations.

From the given graph it is clear that graph of the given two equations shows  two lines that are parallel to each other. They don't meet or intersect each other at any point.

Since no point is on both lines, there is no ordered pair that makes both equations true.

Hence, there is no solution to this system of equations.

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The picture below shows the graph of the inequality of x² ≤ 4

Option B is correct.

In mathematics, an inequality is described as a relation which makes a non-equal comparison between two numbers or other mathematical expressions which is used most often to compare two numbers on the number line by their size.

A graph of inequality denotes that the variables is the set of points that represents all solutions to the inequality.

A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.

Therefore, the correct option is B. x² ≤ 4

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Answer:

All new reflected coordinates

T (-3, 6)

S (-2, 4)

U (-4, 4)

R (-3, 2)

Step-by-step explanation:

This is because the are reflected sideways on x = 1. This works like a mirror or opening a page of a book if that helps visualise it.

The Pythagorean Theorem can be utilized in any situation to establish a connection between the side lengths of the squares and the sort of triangle that results.

Let's use the notation "a, b, and c" to indicate the three squares' side lengths, where "a" stands for the shortest side, "b" for the midpoint, and "c" for the longest side.

The area of the largest square (c), which is created by the hypotenuse of the triangle, is equal to the sum of the areas of the two smaller squares when three squares' sides form an acute triangle.

The areas of the two smaller squares (a and b) formed by the two larger squares (a and b) are equal when three squares have sides that form an obtuse triangle.

If three squares have sides that make a right triangle, then the sum of the areas of the two small squares is equal to the area of the largest square (c) formed by the hypotenuse of the right triangle.

In all cases, the Pythagorean Theorem can be used to determine the relationship between the side lengths of the squares and the type of triangle formed.

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