What are the 5 most common Pythagorean triples?

The graph of equation y = 6 - x - x² is shown in figure.

And, The value of gradient at x = 2 is, - 5.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ y = 6 - x - x²

Now, The graph of equation y = 6 - x - x² is shown in figure.

Which represent the graph of parabola.

And, The value of gradient at x = 2 is,

⇒ y = 6 - x - x²

⇒ y' (x) = 0 - 1 - 2x

⇒ y' (x) = - 1 - 2x

At x = 2;

⇒ y' (2) = - 1 - 2 × 2

⇒ y ' (2) = - 1 - 4

⇒ y' (2) = - 5

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The amount of fuel used per mile (m) = unit rate = 5.2 gallons per mile.

Initial amount (b) = 0 gallon.

A proportional relationship can be represented as an equation of the form y = mx, where x and y are variables and m is the constant of proportionality, also known as the unit rate

Unit rate (m) = amount of fuel used per mile = 156/30 or 312/60 = 5.2 gallons per mile.

Initial amount (b) = starting value or y-intercept = 0 gallon.

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The required, Jim can drive the truck for approximately 221.51 miles.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

We can use algebra to solve this problem. Let x be the number of miles Jim drove the truck. Then the total cost can be represented as:

15.99 + 0.86x = 206.91

To find the number of miles driven, we can subtract the base fee from both sides of the equation:

15.99 + 0.86x - 15.99 = 206.91 - 15.99

0.86x = 190.92

Finally, we can divide both sides of the equation by 0.86 to find x:

x = 221.51 miles

So, Jim drove the truck for approximately 221.51 miles.

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(a) The angle measurement of first unknown angle is c = 80 degrees

(b) The angle measurement of second unknown angle is y = 110 degrees

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

(a) You can pick pair of starting angles a = 30 degrees and b = 70 degrees

The angle measurement of first unknown angle will be:

a + b + c = 180  (sum of angles in a triangle is 180 degrees)

c = 180 - a - b

c = 180 - 30 - 70

c = 80 degrees

(b) The angle measurement of second unknown angle will be:

y = 180 - b  (sum of angles on a straight line is 180 degrees)

y = 180 - 70

y = 110 degrees

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The area of the triangle below is 34 Square per units. The Option A is correct.

The area of a triangle is total region that is enclosed by the three sides of any particular triangle.  It is equal to half of the base multiplied by the height.

The area of a triangle is given as: Area of triangle= 1/2 * Base of triangle * Height of Triangle where the height is 4 and base is 17

The calculation of our area:

= 1/2 * 17 * 4.

= 34²

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The solution of AB = BC  for A, assuming that A,B and C are square matrices and B is invertible is [tex]A = BCB^{-1}[/tex]

We have to solve the equation

AB = BC , given that these all are square matrices and B is invertible.

Write the required Equation:

 AB = BC

Multiply both sides by inverse of B

The multiplicative inverse of a matrix is the matrix that gives you the identity matrix when multiplied by the original matrix.

Matrix multiplied by an identity matrix, the result is always the same original non-identity (non-unit) matrix, and thus, as explained before, the identity matrix gets the nickname of "unit matrix"

[tex]ABB^{-1} = BCB^{-1}\\AI = BCB^{-1}\\A = BCB^{-1}[/tex]

so the solution of AB = BC is [tex]A = BCB^{-1}[/tex]

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All 4 helpers will be at the clinic on the same day 7 times in 12 weeks.

What is Prime Factorization?

"Prime Factorization" is the process of determining which prime numbers multiply together to get the original number.

To find the number of times in 12 weeks that all 4 helpers will be at the clinic on the same day, we need to find the least common multiple (LCM) of the numbers 4, 6, 2, and 3.

First, we can find the prime factorization of each number:

4 = 2 x 2

6 = 2 x 3

2 = 2

3 = 3

Next, we can find the LCM by taking the highest power of each prime factor that appears in the factorizations:

LCM = 2 x 2 x 3 = 12

Therefore, all 4 helpers will be at the clinic on the same day every 12 days. Since 12 weeks is equivalent to 84 days, we can divide 84 by 12 to get the number of times:

84 ÷ 12 = 7

So, all 4 helpers will be at the clinic on the same day 7 times in 12 weeks.

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Find the difference between the starting and ending values:

    72 - 60 = 12

Divide that difference by the starting value:

    12 ÷ 60 = 0.2

Convert that to a percent:

   0.2 = 20%

The number of teachers increased by 20%.

The key is to divide the difference by the original number, not the ending number.

Divisions of the rectangle will be equal apart from the color Inga assign.

A rectangle is a two-dimensional shape that has four sides and four right angles. The opposite sides are parallel and equal in length. The area of a rectangle can be calculated by multiplying the length of the rectangle by its width.

Here,
Since the rectangles are identical, they would have the same area and thus, the same divided parts. Therefore, the areas of the colored parts would also be equal.

Thus, divisions of the rectangle will be equal apart from the color Inga assign.

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Answer:

the graph of g(x) will be the same shape as the graph of f(x), but shifted downward by 3 units.

Step-by-step explanation:

The functions g(x) = 4(0.5)^x - 3 and f(x) = 4(0.5)^x are both exponential functions with the same base of 0.5 and the same coefficient of 4.

However, the graph of g(x) will be shifted downward by 3 units compared to the graph of f(x), because of the constant subtraction of 3 at the end of the function. This shift will occur for all values of x, meaning that the distance between the two graphs will remain constant as x changes.

In other words, the graph of g(x) will be the same shape as the graph of f(x), but shifted downward by 3 units.

The approximate area of the remaining cardboard would be = 246 cm². That is option B.

To calculate the area of the remaining cardboard = (area of rectangle) - 2(area of circle)

The formula that is used to calculate the area of rectangle = length×width

where length = 14 cm

width = 18cm

area = 14×18 = 252 cm²

The area of the 2 circle formula;

= 2(πr²)

where π = 3.14

r = 2/2 = 1

area = 2(3.14) = 6.28

Area of the remaining cardboard

= 252 cm²- 6.28

= 245.72

= 246 cm²

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Simpson's 1/3rd rule is a method of numerical integration that is used to approximate the value of a definite integral.

It is based on the idea of approximating the area under a curve by dividing it into a series of trapezoids and calculating the area of each trapezoid. The formula for Simpson's 1/3rd rule is:

∫abf(x)dx ≈ (b-a)/6 [f(a) + 4f((a+b)/2) + f(b)]

In this formula, a and b are the limits of integration, and f(x) is the function being integrated. The rule is called the "1/3rd rule" because the coefficient of the middle term is 4/3, which is equal to 1/3 when multiplied by the 3 in the denominator.

To use Simpson's 1/3rd rule, you first need to divide the interval [a,b] into an even number of subintervals. Then, you can apply the formula to each subinterval to get an approximation of the integral over that subinterval. Finally, you can add up the approximations for each subinterval to get an approximation of the integral over the entire interval.

Simpson's 1/3rd rule is a more accurate method of numerical integration than the trapezoidal rule, but it is still an approximation. The accuracy of the approximation depends on the number of subintervals used and the smoothness of the function being integrated.

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The value of complex number |2 - 3i| will be, 3.605

A complex number is one that has the formula a + bi, where I is the imaginary unit and a and b are real numbers. A and b are the real and imaginary halves of a complex number, respectively.

In order to expand the real number system to include answers to polynomial equations that couldn't be solved with just real numbers, complex numbers were first introduced. Many branches of mathematics and science, such as computer science, physics, and engineering, are based on the idea of a complex number.

The absolute value of a complex number "a + bi" can be calculated as the square root of the sum of the squares of its real and imaginary parts:

|a + bi| = √(a² + b²)

In this case, a = 2 and b = -3, so:

|2 - 3i| = √(2 + (-3)²)

          = √(4 + 9)

          = √(13)

          = approximately 3.6055

So, the value of |2 - 3i| is approximately 3.6055.

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Answer:

225

Step-by-step explanation:

(x+y)^2, if x=6 and y=9

Put 6 in place of x and 9 in place of y.

(6+9)^2 According to order of operations, add the 6+9 first.

(6+9)^2

= 15^2

= 225

AB and CD are not parallel lines.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

If the slope of AB and CD are equal then the lines are parallel.

A(-3, 5), B(1, 13), C(4, 2), and D(10, 5)

AB=13-5/1+3

=8/4=2

CD=5-2/10-4

=3/6=1/2

As the slope of lines are different, the lines are not parallel.

Hence, AB and CD are not parallel lines.

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Answer:

0.36

Step-by-step explanation:

and I got this answer by using calculator

The slope in both equations shows the rate of their savings per week, is Adma saves 3$ per week while Shane saves $4 per week.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees. And also it is defined as the rate of change of a function.

Here,
Adam and Shane are competing to see who can save the most money in one month. From the graph, Adam's linear function of saving is given as by slope-intercept form of equation as,
y = 3x + 3

While the linear function for Shane is not given, so we assume the function as y = 4x.

The slope in both equations shows the rate of their savings per week, is Adma saves 3$ per week while Shane saves $4 per week.

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Answer:

If the Esteban's car continues to decrease 20%, by five years the car will be worthless.

20 x 5 is 100. This means that 100%  of the car will have lost its value and will be worthless.

I hope this helps & Good luck <3 !!!

Function transformation rules are a set of rules that can be applied to a basic function in order to transform or modify its graph. These rules include:

1. Vertical translation: adding or subtracting a constant to the function. This shifts the graph up or down without changing its shape.

2. Horizontal translation: replacing x with x + c. This shifts the graph left or right without changing its shape.

3. Vertical scaling: multiplying the function by a constant. This stretches or compresses the graph vertically.

4. Horizontal scaling: replacing x with kx. This stretches or compresses the graph horizontally.

5. Reflection: reflecting the graph across the x-axis or y-axis. This changes the orientation of the graph.

6. Composition: combining two or more functions to create a new function.

These rules allow mathematicians to manipulate and analyze functions in order to better understand their properties and behavior. By applying these rules to a basic function, mathematicians can create a variety of related functions with different features and behaviors.

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To validate a min-heap, you can follow these steps: Start at the root, Check each subtree, Repeat the process recursively, If any node violates the min-heap property, then the heap is not valid.

Start at the root: Verify that the value at the root node is the minimum value in the heap. This is the defining property of a min-heap. Check each subtree: For each subtree, check that the value at the root of the subtree is less than or equal to the values of its child nodes. If this property holds true for all subtrees, the heap is a valid min-heap. Repeat the process recursively: Continue the above steps for each subtree until all nodes have been checked. If any node violates the min-heap property, then the heap is not valid. In that case, you can either rebuild the heap or identify the specific node or subtree that violates the property and fix it. In summary, to validate a min-heap, you need to check that the root node contains the minimum value, and each subtree obeys the min-heap property. You can check the property recursively until all nodes have been verified, and identify any nodes that violate the property for correction.

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a. The median of Otter 2 's data is greater than the median of Otter 1's data. b. The variability in the data for Otter 1 is greater than the variability in the data for Otter 2.

c. Liz can conclude that Otter 2 generaily eats more food.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution.

The median is the value in the middle of a data set, meaning that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median.

The median for A is 25.5 and 26 for B. This implies that B has higher median than A.

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The algorithms are a problem solving tool in Python because it  provides a wide range of built-in algorithms that can be used to solve many common problems.

The Algorithms are a fundamental problem solving tool in Python . An algorithm is a set of instructions that are executed in a specific order to solve a particular problem. In Python, algorithms can be implemented in the form of functions or methods.

So , In addition to the built in algorithms, Python also provides a rich collection of third party libraries that contain various algorithms that can be used to solve complex problems.

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The given question is incomplete , the complete question is

How are algorithms a problem solving tool in Python ?

Answer:

5 weeks

Step-by-step explanation:

Let factory B produce the same amount of shoes as factory A in w weeks.

then,

70+50w = 120+40w

50w - 40w = 120 - 70

10w = 50

w = 50/10

w = 5

Therefore, in 5 weeks factory B will produce the same amount of shoes as factory A will produce in 5 weeks time.

The box plot that represents the data-set is given as follows:

Option B.

From left to right, the five features of the box and whisker plot are listed as follows

The data-set in this problem has 11 elements, hence:

The quartiles are the mean of each half, hence:

Meaning that the second plot is correct.

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Answer:

B. 1/12

Step-by-step explanation:

1/8 × 5/6 = 5/48 × 4/5 = 1/12

Answer:

y=12-5x

Step-by-step explanation:

We know that 12 is our original number so we put that first. X represents the number of hours. And 5 is how much its dropping per hour. Y would be our final answer. If you sub in for x the amount of hours outside and multiply it by 5, that's how many degrees it dropped.

The ratio of SR and ML and ratio of ST , MN are equal ,so they are similar triangles .

What is triangle ?

Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.

In given two triangles,

RST and NLM

In the triangle RST ,

The sum of angles is 180

so,

44  + 15 + S = 180

S =   180 - 59

S = 121

And similarly in the triangle NLM,

N + 121 + 44 = 180

N = 180 - 165

N = 15

Therefore, The values of given angles S and N are 121 , 15 respectively

SR / ML  = 3.61 / 5.415 = 0.667
ST / MN = 9.71 / 14.565 = 0.667

Hence, The ratio of SR and ML and ratio of ST , MN are equal ,so they are similar triangles .

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Answer: Area of path = 1492 m^2 Area of "no path" = 123508 m^2

Step-by-step explanation:

Probably wrong