Why are rigid transformations important?

The HCF and LCM are Highest common factor and Least common multiple respectively

What is HCF and LCM?

The Greatest Common Divisor GCF or the Highest Common Factor HCF is the highest number that divides exactly into two or more numbers. It is also expressed as GCF or HCF

Least Common Multiple (LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers

Product of HCF x LCM = product of two numbers

Given data ,

Let the two numbers be A and B

The value of A is A = 160

The value of B = 252

HCF is the product of common prime factors

So , Prime Factorization of 160: 2 x 2 x 2 x 2 x 2 x 5

And , Prime Factorization of 252: 2 x 2 x 3 x 3 x 7

So , HCF = 2 x 2 = 4

Now, finding LCM of 160 and 252

LCM is the product of all factors of both numbers

Prime Factorization of 160: 2 x 2 x 2 x 2 x 2 x 5

Prime Factorization of 252: 2 x 2 x 3 x 3 x 7

LCM= 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7

LCM= 10080

Now , the product of HCF x LCM = product of two numbers

160 x 252 = 40320

4 x 10080 = 40320

Hence , the HCF and LCM are solved

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The common multiple of 5y²- 45 and y + 3 is (y + 3).

For any two or more expressions, if any one of their factors is common in all of them, then that factor is said to be the common multiple of those expressions.

The given expressions are 5y²- 45 and y + 3

On factorizing them, we get

5y²- 45 = 5(y² - 9)

⇒ 5(y² - 3²)

From he binomial formula a² - b² = (a + b)(a - b), we can write

5y²- 45 = 5(y + 3)(y - 3)

Now, the second expression has no further simplification. The expression is itself a factor for it.

So, we can write their factors as

5y²- 45 = 5 × (y + 3) × (y - 3)

y - 3 = 1 × (y - 3)

From this, (y - 3) is the only factor that is a common factor for both the expression.

So, (y - 3) is the common multiple for the given expressions.

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Latitude lines always have an equal distance between them, however longitude lines are separated from one another at the equator and come together at the poles. Longitude and latitude lines near the equator are equal in distance, with one degree covering 111 kilometers (69 miles).

Latitude lines are always equally spaced apart because they are always parallel to one another. Never do latitude lines converge or intersect. Distances north or south of the equator are measured by lines of latitude.

How do longitudes work?

Distance east or west of the prime meridian is measured by longitude. Meridians, which are also known as lines of longitude, are fictitious lines that divide the globe. They measure the distance either east or west, running from pole to pole from north to south. The units of longitude are degrees, minutes, and seconds.

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A discontinuity in mathematics is when a function is not well defined

As earlier defined, discontinuity deals with a function that is not well defined.  

Different functions have different discontinuity depending on the function

Good examples of discontinuity include

y=1/x this is a discontinuous function.

x=0 is also a discontinuous function as it is not well defined. because there is no value for y

The function TanA is a discontinuous function because it is not well defined.

Other discontinuities include

y=5п/3,  9п/4, 6п8, 4п/3

All these are discontinuous functions

In conclusion, a  discontinuity in mathematics is when a function is not well defined

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The weight of the package is 15 pound.

What is an linear equation?

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.

Given that the fees for sending a package by media mail

For first pound : $2.41

For the next six pounds: $0.41 per pound

For additional pound: $0.39 per pound

The cost of first 7 pounds is = $(2.41 + (0.41 × 6)) =$4.87

$4.87 < $7.99. Thus the weight of the package is more than 7 pounds

Assume that, the weight of the package is (7 + x) pound.

The fee for (7 + x) pounds package is $(4.87 + 0.39x)

According to the question:

4.87 + 0.39x = 7.99

Subtract 4.87 from both sides:

0.39x = 3.12

Divide both sides by 0.39

x = 8

The weight of the package is (8 + 7) = 15 pounds.

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Answer:

580-80=500×6.5=3250 its ans iit

For the shaded region given in the diagram the area is obtained as 50.2 cm². The correct option is (A).

A circle is a geometric shape, all of which points are equidistant from a fixed point called as the center.The center of the circle does not lie on it. The angle subtended by the semicircle on its any point is always a right angle.

The diameters of the external and internal circle are 10 cm and 6 cm.

Then, the radius are given as 10/2 = 5 cm and 6/2 = 3 cm

Now, area of the shaded region is given as follows,

Area of external circle - Area of internal circle

= π × 5² -  π × 3²

= 16π

= 50.2

Hence, the area of the shaded region is given as 50.2 cm².

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A collection of numbers, variables, and mathematical operations is referred to as an expression. The  expression is -2/5- 4/3P and 2/5+4/3P

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation .A collection of numbers, variables, and mathematical operations is referred to as an expression.

Given,

-4/3p - 2/5

= -20p - 6/15

= 2(10 p +3)/15

A mathematical expression is a sentence that includes numbers, variables, or both. The equal symbol is never used in expressions. Here are a few phrases as examples. A mathematical statement stating the equality of two expressions is known as an equation.

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Answer:

y-intercept = (0,6)

slope = -2

Step-by-step explanation:

⭐What is the slope of a line?

⭐How can we find the slope of a line?

To find the slope, pick two coordinates you see on the line, substitute them into the slope formula, and solve for the slope!

I am choosing the coordinates (0,6) and (3,0), but you can choose any 2 coordinates that you see on the line.

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m = \frac{0-6}{3-0}\\m = \frac{-6}{3}\\m = -2[/tex]

∴ The slope of the line is -2.

⭐ What is the y-intercept of a line?

⭐How do we find the y-intercept of a line?

When x=0, y=6

∴ The y-intercept of the line is (0,6)

If 800g:1kg is equal to 1:n then the value of n is 1/8.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

800g : 1kg = 1 : n

This can be written as,

800g/1kg = 1/n

Cross multiply.

n = 1kg/800g

[ 1 kg = 1000g ]

n = 1000g/8000g

n = 1/8

Thus,

The value of n is 1/8.

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Sandra sets the speed to 69 miles per hour. The equation that express how many hours it will take her to drive m miles is: h = m/69.

Speed or velocity 69 miles per hour means: in 1 hour she will travel 69 miles

69 miles need 1 hour

1 miles need 1/69 hours

m miles need m x 1/69 hours.

If h is the amount of time need to take her to drive m miles, then:

h = m x 1/69 = m/69 hours

We can also solve the problem, using formula:

s = vt

Where:

s = distance

v = speed = 69 mph

t = time

In the given problem, the distance is m, hence s = m, and t = h

Hence,

t = s/v

h = m/69

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Answer: a) The equation of the least-squares regression line is y = -1.66x + 78.83. b) Residual =  7.11 inches. c) The residual is the deviation of a data point from the fitted regression line. In this case, the residual is 7.11 inches, indicating that the player who wears a size 9 and is 71 inches tall is taller than what would be expected based on the trend in the data.

Step-by-step explanation:

What is the least square regression and residual?

Least squares regression is a statistical method that is used to find the line of best fit for a set of data points. It involves finding the line that minimizes the sum of the squares of the differences between the actual data points and the predicted values on the line. The residual is the difference between the actual data point and the predicted value on the line.

Part A: The equation for the least-squares regression line can be found by using the following formula: y = bx + a

To find the values for a and b, we need to calculate the following values:

x: the mean of the shoe sizes,

y: the mean of the heights.

S x y: the sum of the products of the differences between the shoe sizes and x and the differences between the heights and y.

S x x: the sum of the squares of the differences between the shoe sizes and x.

X = (7+10+12+8+9.5+10+11.5+12.5+13.5+10) / 10 = 10.5

Y = (64+69+72+67+69+70+75+73+71+68) / 10 = 69.4

To find S x y and S x x, we use:

S x y = ∑(x - x)(y - y)

S x x = ∑(x - x)^2

Inserting the values from the table, we get:

S x y =-47.5

S x x = 28.5

Using values, we can calculate the slope and y-intercept of the least-squares regression line:

b = S x y / S x x = -47.5 / 28.5 = -1.66

a = y - bx = 69.4 - (-1.66)(10.5) = 78.83

So the equation of the least-squares regression line is y = -1.66x + 78.83

Part B: We can use the equation for the least-squares regression line to determine the residual for a player who wears a size 9 and is 71 inches tall. We calculate the player's height using the size 9 into the equation:

y=-1.66x+78.83=63.89 inches.

The residual is then calculated by deducting the expected height from the actual height: 7.11 inches =71- 63.89 inches.

Part C: The residual is the variation between the dependent variable's actual value (height) and its anticipated value according to the least-squares regression line. The athlete in this instance, who wears a size 9 and is 71 inches tall, is taller than what might be anticipated based on the trend in the data, according to the residual of 7.11 inches.

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The equation of the least-squares regression line is y = -1.66x + 78.83. b) Residual =  7.11 inches.

What is the least square regression and residual?
Least squares regression is a statistical method that is used to find the line of best fit for a set of data points. It involves finding the line that minimizes the sum of the squares of the differences between the actual data points and the predicted values on the line. The residual is the difference between the actual data point and the predicted value on the line.

Part A: The equation for the least-squares regression line can be found by using the following formula: y = bx + a
To find the values for a and b, we need to calculate the following values:
x: the mean of the shoe sizes,
y: the mean of the heights.
S x y: the sum of the products of the differences between the shoe sizes and x and the differences between the heights and y.
S x x: the sum of the squares of the differences between the shoe sizes and x.
X = (7+10+12+8+9.5+10+11.5+12.5+13.5+10) / 10 = 10.5
Y = (64+69+72+67+69+70+75+73+71+68) / 10 = 69.4
To find S x y and S x x, we use:
S x y = ∑(x - x)(y - y)
S x x = ∑(x - x)^2
Inserting the values from the table, we get:
S x y =-47.5
S x x = 28.5
Using values, we can calculate the slope and y-intercept of the least-squares regression line:
b = S x y / S x x = -47.5 / 28.5 = -1.66
a = y - bx = 69.4 - (-1.66)(10.5) = 78.83
So the equation of the least-squares regression line is y = -1.66x + 78.83
Part B: We can use the equation for the least-squares regression line to determine the residual for a player who wears a size 9 and is 71 inches tall. We calculate the player's height using the size 9 into the equation:
y=-1.66x+78.83=63.89 inches.
The residual is then calculated by deducting the expected height from the actual height: 7.11 inches =71- 63.89 inches.
Part C: The residual is the variation between the dependent variable's actual value (height) and its anticipated value according to the least-squares regression line. The athlete in this instance, who wears a size 9 and is 71 inches tall, is taller than what might be anticipated based on the trend in the data, according to the residual of 7.11 inches.

c) The residual is the deviation of a data point from the fitted regression line. In this case, the residual is 7.11 inches, indicating that the player who wears a size 9 and is 71 inches tall is taller than what would be expected based on the trend in the data.

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The equation of the perpendicular line is y = -0.5x + 6.5

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

y = 2x - 6

Also, from the question;

We have the following points

Point = (5, 4) i.e.  (x, y) = (5, 4)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 2

This means that the slope is 2

The slopes of perpendicular lines are opposite reciprocals

This means that the slope of the other line is -1/2

The equation of the line is then calculated as

y = m(x - x₁) +y₁

Where

m = -1/2

(x₁, y₁) = (5, 4)

So, we have

y = -1/2(x - 5) + 4

Evaluate

y = -0.5x + 6.5

Hence, the line has an equation of y = -0.5x + 6.5

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A postulate is an unsupported assertion that is taken to be true. A provable true assertion is referred to as a theorem.

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For a given function f, it is linear if the function has a constant slope and it doesnot contain the power of x greater than 1.

An association between each element of a non-empty set A and at least one element of a different non-empty set B is called a function. The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.

A function which is also linear, represents a straight line in the graph. The graphs to the linear functions are straight lines which have constant slope throughout the graph.

A function f is referred to as linear if it meets both of the following criteria:

The slope of the function is constant. This indicates that the slope of the line is constant, independent of the value of x that you enter into the function.

There are no powers of x bigger than 1 in the function. This indicates that there are no terms in the function that have x2, x3, etc.

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Answer:

28 apples

Step-by-step explanation:

29 - 1 = 28 apples

Answer:

28apples

Step-by-step explanation:

simple:29-1

hope this helps

1, 2, 4, 8, and 16 are the components that make up 16. Similarly, the negative components of 16 are -1, -2, -4, -8, and -16. factors of 16: 1, 2, 4, 8, and 16.

The natural number 16 (or sixteen) comes after the number 15 and before the number 17. Since 42 = 4 4 is a square number, the number 16 is both a composite and a square. It has precisely five correct divisors, making it the lowest number. These are 1, 2, 4, and 8. The numbers 16 and 60 sound remarkably similar in English speech, which might lead to confusion.

There are three factor pairs of 16:

1 × 16 = 16.

2 × 8 = 16.

4 × 4 = 16.

1, 2, 4, 8, and 16 are the 16 factors. Likewise, the unfavorable factors of 16 are -1, -2, -4, -8, and -16. 1, 2, 4, 8, and 16 make up the number 16.

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On observing the provided question we can say that - the function f(x) = [tex]a^x[/tex] is Domain: (−∞,∞) or all real numbers

Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.

The answer to the question is that all real numbers or (−∞,∞)

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By drawing a mirror line across the center of a shape and examining if both halves are the same, you may determine whether it is symmetrical.

When anything has two identical parts, it is symmetrical. In other terms, symmetry is the presence of identical pieces facing one another or revolving around an axis.

But what attributes give a shape symmetry? A symmetrical shape has an identical side on the side, also known as symmetry. When mirrored, rotated, or translated, symmetrical shapes retain their original appearance. The four main subcategories of symmetry are translation, rotation, reflection, and glide reflection. However, the primary type of symmetry in mathematics taught in schools is reflectional symmetry, commonly referred to as mirror symmetry or line symmetry.

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Therefore , the kids can able to sings alphabets ABC by the age of 2 and by age of 4 children frequently know every letter of the alphabet .

In alphabet, set of graphs, or characters, used to represent the phonemic structure of a language .The characters are often placed in a specific order, or sequence, in most alphabets (e.g., A, B, C, etc.).

Here,

By the age of two, children can sing or say out loud the "ABC" song and begin to recognise some letters.

By the age of three, children may recognise around half of the alphabet's letters and begin to associate letters with their sounds.

(S makes the sound /s/.)

Most kids are familiar with all 26 letters of the alphabet and their order by the time they are four years old.

Therefore , the kids can able to sings alphabets ABC by the age of 2 and by age of 4 children frequently know every letter of the alphabet .

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Children can begin to sing the alphabet by the time they are two years old.

The phonemic structure of a language is represented by an alphabet, which is a system of graphs or symbols. In most alphabets, the characters are frequently arranged in a certain order, or sequence (e.g., A, B, C, etc.).

There are 26 alphabets named from A to Z.

By the time they turn two, kids can sing or say the "ABC" song aloud and start to recognize some letters.

Around half of the alphabet's letters may be recognized by three-year-old, and they are starting to connect letters with sounds.

By the time they are four years old, the majority of children are familiar with all 26 letters of the alphabet and their placement.

As a result, children can begin to sing the alphabet by the time they are two years old, and by the time they are four, many of them are already familiar with all 26 letters.

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Step-by-step explanation:

To multiply 17m 25cm by 24, you need to first convert the units of measurement to a common unit, such as meters or centimeters.

17m 25cm can be written as 17.25 m, since 1 meter is equal to 100 centimeters. Therefore, to multiply 17.25 m by 24, you can simply perform the calculation as follows:

17.25 m * 24 = 413 m

This means that the result of the multiplication is 413 meters.

Alternatively, you could express the result in centimeters by performing the calculation as follows:

(17 m * 100 cm/m) + (25 cm * 24) = 1700 cm + 600 cm = 2300 cm

This means that the result of the multiplication is 2300 centimeters.

Answer:

25

Step-by-step explanation:

(60+15)/3-2(4)+2^3

75/3 -2 x4 + 2^3

75/3 - 8 +2^3

75/3 - 8 +8

75/3

25

According to the 90° clockwise rotation, the new coordinate of the quadrilateral D' is (3, -2)

Quadrilateral

Quadrilateral refers a closed shape and a type of polygon that has four sides, four vertices and four angles.

If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’.

Here we need to find the coordinate of D'.

In order to find the new coordinates, first we have to identify the current coordinates of the quadrilateral.

While we looking into the graph, we have identify the point of

A (0,0), B(-4, 3), C(1,5) and D(2,3)

Now, we have to use the rule of clockwise 90° rotation, states that to rotate the figure 90 degrees clockwise about a point, every point(x , y) will rotate to (y, -x).

According to this rule, the new coordinates are written as,

A(0,0) = A'(0,0)

B'(-4,3) = B'(-3,-4)

C(1,5) = C'(5, -1)

D(2,3) = D' (3, -2)

Therefore, the new coordinate of D' is (3, -2).

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The mass of 60,000 molecules of methane is 1.62 × 10⁻¹⁸ g

what is mass of molecule ?

Watch your pronunciation. pronounced "muh-LEH-kyoo-ler mas" the total atomic mass of every atom in a molecule, calculated using a scale with hydrogen, carbon, nitrogen, and oxygen having atomic masses of 1, 12, 14, and 16, respectively.

solution:

The mass of one methane molecule should be "2.7 × 10⁻²³ gram" instead of "27 × 10⁻³ grams".

Mass of 60,000 molecules of methane

= (2.7 × 10⁻²³ g) × 60,000

= 1.62 × 10⁻¹⁸ g

Therefore,The mass of 60,000 molecules of methane is 1.62 × 10⁻¹⁸ g

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In mathematics, a discontinuity is a point or set of points at which a function or curve is not defined, or is not "well-behaved," meaning it exhibits some kind of sudden or unexpected change in behavior.

Discontinuities can occur in functions or curves of all types, including functions of one variable, functions of several variables, and geometric curves.

There are several types of discontinuities that can occur in a function. For example, a function may have a jump discontinuity, which occurs when the function has a finite limit from one side but a different finite limit from the other side at a given point.

In all, the presence of discontinuities in a function can make it more difficult to analyze or work with, as the behavior of the function may not be predictable at these points.

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Answer:

7.62

Step-by-step explanation:

Simplify the following:

7 + 6/10 + 2/100

Express 6/10 in its lowest form by cancelling out gcd(6, 10) = 2 from the numerator and denominator. 6/10 = (2×3)/(2×5) = 3/5:

7 + 3/5 + 2/100

Express 2/100 in its lowest form by cancelling out gcd(2, 100) = 2 from the numerator and denominator. 2/100 = (2×1)/(2×50) = 1/50:

7 + 3/5 + 1/50

Put 7 + 3/5 + 1/50 over the common denominator 50. 7 + 3/5 + 1/50 = (50×7)/50 + (10×3)/50 + 1/50:

(50×7)/50 + (10×3)/50 + 1/50

50×7 = 350:

350/50 + (10×3)/50 + 1/50

10×3 = 30:

350/50 + 30/50 + 1/50

350/50 + 30/50 + 1/50 = (350 + 30 + 1)/50:

(350 + 30 + 1)/50

| 3 | 5 | 0

| | 3 | 0

+ | | | 1

| 3 | 8 | 1:

Answer: |

| 381/50

A graph of the distance and time data for distance traveled by this train is shown in the image attached below.

In Mathematics, a scatter plot is sometimes referred to as scatter chart and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting data points showing any association or correlation between the data set.

In this scenario, the time (in hours) would be plotted on the vertical axis (x-axis) of the scatter plot while the distance (in kilometers) would be plotted on the horizontal axis (y-axis) of the scatter plot by using an Excel worksheet.

From the scatter plot (see attachment) which models the relationship between the distance (in kilometers) and time (in hours), a linear equation for the line of best fit or trend line is y = 99.43x + 11.43.

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To round to the nearest meter, use the units place and round to the nearest whole number. At the moment, we have a two in place of a one.

It is two divisions or two tenths of a mile short of the halfway point. Therefore, seven centimeters are the closest centimeters.

To figure out how to round, we look to the right, at the unit in the tens place.

Let x represent the unknown, which is the building's height.

level of post = level of the structure

level of the shadow level of the shadow

3.3 m = x

1.78 m 49. 75 m Find the solution for x: (3.3 m) (49.75 m) = x 1.78 m = x The building is 92 meters high, rounded to the nearest meter.

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There are totally 4 terms in the given polynomial

We have a polynomial given by -x³+4x² +7x − 2

Algebraic expressions with coefficients and variables make up polynomials. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.

Since there are 4 terms with either an addition or a subtraction performed between them, the total number of terms is given by 4.

Those 4 terms are -x³ ,4x²,7x,−2

Therefore, there are totally 4 terms in the given polynomial.

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