The greatest common factor(GCF) of LaTeX: x^7,\:x^3,\:x^5\:is\:_{ }__________.

Total Number of Factors for N = (a+1) (b+1) (c+1) is the formula for how many factors there are in total for a given number.

Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.

Total Number of Factors for N = (a+1) (b+1) (c+1) is the formula for how many factors there are in total for a given number.

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Answer:

x ≈ 21.3

Step-by-step explanation:

using the sine ratio in the right triangle

sin80° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{21}{x}[/tex] ( multiply both sides by x )

x × sin80° = 21 ( divide both sides by sin80° )

x = [tex]\frac{21}{sin80}[/tex] ≈ 21.3 ( to 1 decimal place )

Therefore , the solution of the given problem of percentage comes out to be 246 kilometers left for distance to covered.

In mathematics, a percentage is a mathematical ratio that is stated as a portion of 100. Occasionally, the abbreviations "pct.," "percent," and "pt" are also used. However, the percentage symbol "%" is frequently used to represent it. There are no dimensions to the % quantity. Since percentages have a numerator of 100, they are actually fractions. A number must be followed by the cent symbol (%) to denote that it is a percentage. For illustration, you would receive a 75% mark if you answered 75 out of questions on a test correctly.

Here,

Given:

Saed discovered that he had barely traveled 18% of the

distance after driving 54 km.

Therefore, if he traveled 54 kilometers outside of it,

the total distance

=> 100/18 * 54

=> 300 kilometers

Thus , the left distance

=> 300 - 54

=> 246 kilometers

Therefore , the solution of the given problem of percentage comes out to be 246 kilometers left for distance to covered.

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The function that represents the vertical compression of function f(x) = x² by a factor of 1/2 is given as follows:

f(x) = x²/2.

The parent function for this problem is defined as follows:

f(x) = x².

For a vertical compression by a factor of a, the function is multiplied by the constant a with absolute value less than 1, that is:

g(x) = a x f(x), |x| < 1.

The factor of the compression for this problem is of a = 1/2, hence the function that represents the vertical compression of function f(x) = x² by a factor of 1/2 is given as follows:

f(x) = x²/2.

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If the scale factor is a fraction, the shape will be smaller. This is called reduction. Therefore, a 1/2 scaling factor means that the new shape is half of the original shape

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If the scale factor is a fraction, the shape will be smaller. This is the so-called recovery. So a scale factor of 1/2 means that the new shape is half the original shape.

Half scale is 1.

2. It is convenient to imagine that 1 unit on the drawing is equal to 2 units on the object. You can enlarge small objects and draw them on paper 2:

1 scale. This means that the drawing of the object is twice the size of the object itself.

Starting from the top right corner of the paper, draw five parallel diagonal lines towards the bottom left corner.

Step 2 - Create a diagonal cross pattern. ... Step 3 - Put the scales into the diamond shaped box. ...

Step 4 - Draw the scales in the middle part.

A full-size drawing will be 1.

1 (or sometimes 1/1 or "one to one"). A half-sized drawing will be 1.

2. A 10th grade drawing will be 1.

10. A double size drawing will be 2.

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The smallest possible perimeter of an acute triangle with the longest side of 30 inches and two congruent sides is 40.96 inches by applying the triangle inequality theorem.

For an acute triangle, the longest side or hypotenuse must be less than the sum of the other two sides, this is known as the triangle inequality theorem.

Given that the longest side of the triangle measures 30 inches, and the two remaining sides are congruent, we can use the triangle inequality theorem to find the smallest possible perimeter of the triangle.

If we call the length of the other two sides x, then we know that x+x>30, so x>15.

The smallest perimeter is then 2x+30.

The smallest possible perimeter of the triangle, rounded to the nearest hundredth is 40.96 inches.

So the answer is 40.96 in.

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The question is -

The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown. What is the smallest possible perimeter of the triangle, rounded to the nearest hundredth? 40.96 in. 51.22 in. 72.44 in. 81.22 in.

Answer:

Step-by-step explanation:

The integral of x^0.5 from 9 to 1 is approximately 17.3333

An integral is a mathematical concept used to calculate the area under a curve or the total change of a function. It's a fundamental concept of calculus and has many applications in physics, engineering, economics and more.

To evaluate the integral of [tex]\sqrt{x}[/tex] from 9 to 1, we can use the antiderivative method. The antiderivative of [tex]\sqrt{x}[/tex] is (2/3) [tex]x^\frac{3}{2}[/tex], so the definite integral can be evaluated as:

[tex]\int\limits^9_1 {\sqrt{x} } \, dx[/tex] =  [tex]\left \{ {{x=9} \atop {x=1}} \right.[/tex]   (2/3) [tex]x^\frac{3}{2}[/tex]

On substituting the limits we get

(2/3)[[tex]9^\frac{3}{2}[/tex]- 1]

= (2/3)(27) - (2/3)

= 18 - 2/3

= 17.3333

Therefore, the definite integral of x^0.5 from 9 to 1 is approximately 17.3333

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The 2D to 3D conversion process consists of two steps:

A stereo pair is formed by depth estimation of a given 2D image and depth-based rendering of a new image.

A 3D shape is a three-dimensional shape or object that has three dimensions (length, width, and height), as opposed to two-dimensional objects that have only length and width. Other important terms related to 3D geometry are faces, edges, and vertices. Due to its depth, it occupies a certain volume. Some 3D shapes have a base or cross section as a 2D shape. For example, all sides of a cube are squares.

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Based on their percentages, the total number of students in Ridgewood Junior High School is 170.

The percentage refers to the ratio or relative value of a variable or number compared to another.

Percentages are expressed as the product resulting from the multiplication of a quotient (numerator over denominator) by 100.

The percentage of students who brought their lunch = 20%

The number of students who brought their lunch = 34

Since all students either eat from the school cafeteria or bring their launch, the percentage of students who brought their lunch = 80% (1 - 20%).

34 = 20%

The percentage of students in the school = 100% (20% + 80%)

The number of students in the school = 34/20%

= 170

Thus, using percentage ratios, we can conclude that the total number of students in the school is 170.

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If Rhonda drives x miles in a month, she will be paid a total of $2,352 + ($0.55 * x).

We can use the information given to set up a system of equations to find the function that relates the number of miles driven (x) to the total amount paid (y).

Let's call the fixed salary that Rhonda receives each month "s" and the extra money she receives per mile driven "m".

Based on the information given, we know that in July, Rhonda drove 640 miles and was paid a total of $3,502. So, we can set up the following equation:

y = s + (m * 640) = $3,502

And in August, Rhonda drove 820 miles and was paid a total of $3,601. So, we can set up the following equation:

y = s + (m * 820) = $3,601

We can use these equations to solve for "s" and "m".

Subtracting the first equation from the second equation:

$3,601 - $3,502 = s + (m * 820) - s - (m * 640)

$99 = (m * 820) - (m * 640)

$99 = m * 180

m = $0.55

Now we can substitute this value of m back into one of the equations to solve for s

$3,502 = s + (0.55 * 640)

s = $2,352

So the function that relates the number of miles driven (x) to the total amount paid (y) is:

y = $2,352 + ($0.55 * x)

Thus, This means that if Rhonda drives x miles in a month, she will be paid a total of $2,352 + ($0.55 * x).

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Answer:

altitude ≈ 23 cm

Step-by-step explanation:

since the triangle is isosceles then the altitude AD is the perpendicular bisector of BC , so

BD = [tex]\frac{1}{2}[/tex] BC = 7 cm

using Pythagoras' identity in right triangle ABD

AD² + BD² = AB²

AD² + 7² = 24²

AD² + 49 = 576 ( subtract 49 from both sides )

AD² = 527 ( take square root of both sides )

AD = [tex]\sqrt{527}[/tex] ≈ 23 cm ( to the nearest whole number )

then the altitude is approximately 23 cm

The percentage change could be around 50 % as we are doubling the recipe to make 2 pies.

What is percentage ?

percentage can be defined as the product of ratio of given value, total value to the 100.  

Given,

The recipe calls for 4 apples to make a pie.

If I want to double to recipe to make 2 pies,

So,

let the percentage could be x ,

x =( change in value / total value ) * 100

x = (8-4/8)*100

x = 50%

Hence , The percentage change could be around 50 % as we are doubling the recipe to make 2 pies.

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Answer:  x=−4

Step-by-step explanation:

As the value of x(=5) and y(=3) does not satisfies any of the given equation, hence (5,3) is not a solution of the pair of equations 3x−2y=4 and 6x−4y=8

The correct option D

Now, According to the question:

Given,

There are two equation are given as:

3x - 2y = 4

6x - 4y = 8

To check the which of the following is not a solution of the pair of equations ?

A) x = 2 and y = 1

=> 3 × 2 - 2 × 1 = 4

6 - 2 = 4

4 =4

=> 6 × 2 - 4 ×1 = 8

12 - 4 = 8

8 = 8

B) x = 4 and y = 4

=> 3 × 4 - 2 × 4 = 4

12 - 8 = 4

4 =4

=> 6 × 4 - 4 × 4 = 8

24 - 16 = 8

8 = 8

C) x = 6 and y =7

=> 3 × 6 - 2 × 7 = 4

18 - 14 = 4

4 = 4

=> 6 × 6 - 4 × 7 = 8

36 - 28 = 8

8 = 8

D) x = 5 and y = 3

=> 3 × 5 - 2 × 3 = 4

15 - 6 = 4

9 ≠ 4

=> 6 × 5 - 4 × 3 = 8

30 - 12 = 8

12 ≠ 8

As the value of x(=5) and y(=3) does not satisfies any of the given equation, hence (5,3) is not a solution of the pair of equations 3x−2y=4 and 6x−4y=8

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Tony earned $220

Step-by-step explanation:

Tony = n

Jenifer = x

Chris = y

x = 2n - 40

y = n + 60

Write an equation for the total the three waiters earned. Solve for Tony's earnings.

n + x + y = $900

n+2n−40+n+60=900

Step 1: Simplify both sides of the equation.

n+2n−40+n+60=900

n+2n+−40+n+60=900

(n+2n+n)+(−40+60)=900(Combine Like Terms)

4n+20=900

4n+20=900

Step 2: Subtract 20 from both sides.

4n+20−20=900−20

4n=880

Step 3: Divide both sides by 4.

4n/4 = 880/4

n=220

The formula to find the resolution of an image, also known as its pixel density, is Pixels per Inch (PPI) or Pixels per Centimeter (PPCM). This formula is used to determine the number of pixels in a given area of an image.

The higher the PPI or PPCM, the greater the resolution of the image.

To calculate PPI, you need to know the total number of pixels in the image (width x height) and the physical size of the image (width x height in inches or cm). Once you have this information, you can use the following formula: PPI = (pixels / physical size) x (inches/cm).

For example, if an image has a resolution of 1920 x 1080 pixels and is printed at a size of 8 x 6 inches, the PPI would be (1920 x 1080) / (8 x 6) = 240 PPI.

In conclusion, PPI or PPCM is the formula used to find the resolution of an image, also known as its pixel density. It is calculated by dividing the total number of pixels in the image by its physical size and multiplying it by inches/cm.

The higher the PPI or PPCM, the greater the resolution of the image. It is important to consider the PPI or PPCM when choosing an image to print or display in order to ensure that it will be of high quality and have a high resolution.

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The hike between the pictures will be 22.32 miles.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that along a hike, Jon takes 6 pictures. He takes 1 picture at equal distances along the 3.72-mile trail.

The hike will be calculated as:-

Hike = 6 x 3.72

Hike = 22.32 miles

Hence, the hike will be 22.32 miles between the pictures.

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Answer

The answer is (m = 9)

Step-by-step explanation:

Rearrange terms = Step 1

0.4(20-10m) = 2.5 - 2m-12.5

0.4(-10m+20) = 2.5 - 2m - 12.5

Step 2 = Combine multiplied terms into a single fraction

Step 3 = Distribute

Step 4 = Subtract the numbers

Step 5 = Rearrange terms

Step 6 = Add 2m to both sides

Step 7 = Simplify

Step 8 = Multiply all terms by the same value to eliminate fraction denominators

Step 9 = Cancel multiplied terms that are in the denominator

Step 10 = Multiply the numbers

Step 11 =Subtract 40 from both sides

Step 12 = Simplify

Step 13= Divide both sides by the same factor

Last but not least is Simplify

Hope it helped:)

10 is the standard deviation of the possible outcomes.

It is a branch of mathematics that deals with the occurrence of a random event.

Given a  a binomial trial has a probability of success of 0.2, and 500 trials are performed

We need to find the standard deviation of the possible outcomes

To find the standard deviation of this binomial distribution, first find the variance by the formula:

= Number of trials x probability of success x ( 1 - probability of success )

= ( 500 x 0. 2 x ( 1 - 0. 2))

= 100

The standard deviation would be:

= √(Variance )

= √(100)

= 10

Hence, 10 is the standard deviation of the possible outcomes.

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This system has no solution because the two equations are not consistent.

An equation is a statement that asserts the equality of two expressions. For example, the equation "2x + 3 = 7" asserts that the value of the expression "2x + 3" is equal to the value of the expression "7".

A system of linear equations is a set of two or more linear equations that are to be solved simultaneously. Linear equations are equations in which the highest degree of the variable is 1. For example, the equations "2x + 3y = 7" and "x - 4y = 2" are both linear equations, and solving them together forms a system of linear equations. These systems can be represented graphically by straight lines in a two-dimensional coordinate system, and the solution of a system of linear equations is the point or points of intersection of the lines.

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The value of is dx/dt = 0.95, when x = 12 and y =5.

Pythagoras' Theorem states that the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.

Given:

dz/dt = 1,

dx/dt = 3(dy/dt)

So, dy/dt = 1/3 (dx/dt)

According to the Pythagoras theorem -

z² = x² + y²

Differentiating both sides we get

d/dt (z²) = d/dt (x² + y²)

2z dz/dt = 2x dx/dt + 2y dy/dt

z dz/dt = x dx/dt + y dy/dt

Substituting the value of  dy/dt -

z dz/dt = x dx/dt + y/3 (dx/dt)

z dz/dt = dx/dt (x + y/3)

dx/dt = (z dz/dt)/(x + y/3).....(1)

So, when x = 12 and y = 5, the value of z -

z = √[(12)² + (5)²]

z = √(144+25)

z = √169

z = 13

Substituting the value of x, y, z and dz/dt in equation (1), we get

dx/dt = (13 × 1)/(12 + 5/3)

dx/dt = 13 / 41/3

dx/dt = (13 × 3)/41

dx/dt = 39/41

Hence, the value of dx/dt = 0.95.

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The feet of wiring that are still on the truck at the end of the second day is 629 feet.

Arithmetic operations implies solving a given question by addition, subtraction, division or multiplication as required in the question.

From the given question, total feet of copper wire at the start of the first day is 600 feet.

During the first day,

the total length of wire used = 100 + 82 + 25 + 40

                                      = 247

Total length of copper used in the first day is 247 feet.

Length of copper wire remaining at the end of the first day = 600 - 247

                                                          = 353 feet

He purchased 400 feet of the wire so that;

total length of wire = 353 + 400

                                = 753 feet

the total length of wire used the second day = 41 + 39 + 44

                                                = 124 feet

Total length of copper wire left after the second day = 753 - 124

                                                            = 629 feet

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Answer:-2.3,11.,11.,-0.25 or  x2 - 10x - 25- -5

Step-by-step explanation:

u just go in a TI-nspire CX calculator and type in in how it looks

A function called f is defined by the notation y=f(x). This should be understood as "y is a function of x." The input value, or independent variable, is represented by the letter x. The dependent variable or output value is denoted by the letter y, or f(x).

A relation between a collection of inputs and outputs is known as a function.

A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Each function has a range, codomain, and domain.

The usual way to refer to a function is as f(x), where x is the input.

A function is typically represented as y = f. (x).

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

Hence, A function called f is defined by the notation y=f(x). This should be understood as "y is a function of x." The input value, or independent variable, is represented by the letter x. The dependent variable or output value is denoted by the letter y, or f(x).

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The coordinates of the points after dilation is S'(-20,10), T'(16,-12), U(-4,-4), and V'(-12,-4).

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.

Given that the scale factor is 4. The coordinates of the points after dilation is,

S(-5,2) = S'(-5 x 4 , 2 x 4) = S'(-20, 8)

T(4,-3) = T'(4 x 4, -3 x 4 ) = T'(16, -12)

U(-1,-1) = U'(-4,-4)

V(-3,-1) = V'( -3 x 4, -1 x 4 ) = V'(-12,-4)

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a) The air pressure at sea level is given by the formula when n = 0, so P = 1013 × 0.887 = 900.71 millibars.

b) To find the percentage decrease in air pressure for each kilometre above sea level, we can use the formula for percentage change:

(New Value - Original Value) / Original Value * 100

Air pressure, also known as atmospheric pressure, is the force exerted on a surface by the weight of the air above it. Air pressure is typically measured in units such as millibars (mb) or inches of mercury (inHg). It plays an important role in weather patterns and can affect things like airplane flight and altitude sickness.

Sea level refers to the average level of the surface of the ocean. It is used as a reference point for measuring elevation, and for measuring air pressure at a specific location. At sea level, the air pressure is approximately 1013 millibars or 29.92 inches of mercury (inHg). Air pressure decreases as the altitude increases above sea level.

The new value is P = 1013 × 0.887^n and the original value is P = 1013 (at sea level)

So, the percentage decrease in air pressure for each kilometre above sea level is:

(1013 × 0.887^n - 1013) / 1013 * 100 = (-0.113n) * 100 = -11.3n %

So, the air pressure decreases by -11.3 % for each kilometre above sea level.

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Answer:

Step-by-step explanation:

6-2^x=1

-2^x+6=1

-2^x+6-6=1-6

-2^x=1-6

-2^x=-5

x=-5