What is called prime factorization method?

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

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

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A graph is a visual representation of data, showing relationships between different variables or values.

Graphs are often used to represent a function, which is a set of inputs and outputs. A function is a relationship between two variables, where the output of the function depends on the input. In a graph, the input is represented on the x-axis, and the output is represented on the y-axis.

The first graph pictured is a linear function, which is a function that can be expressed as a straight line. This linear graph has a positive slope, meaning that as the input increases, so does the output. This graph represents a linear function because the output can be determined by the input, which is expressed as an equation in the form of y = mx + b.
The second graph pictured is a quadratic function, which is a function that can be expressed as a parabola.

This graph also has a positive slope, meaning that as the input increases, so does the output. This graph represents a quadratic function because the output can be determined by the input, which is expressed as an equation in the form of y = ax2 + bx + c.
Both of these graphs represent functions because they show a relationship between the input and output of a given data set. The input values are shown on the x-axis and the output values are shown on the y-axis, and these values can be used to determine the equation for the function.

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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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The triangle that have the same shape but not the same size are similar triangles

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

If the respective sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are comparable (or proportion). Triangles that are similar will have the same form but may not be the exact same size.

Two triangles are said to be similar if their corresponding angles are equal. Equiangular triangles are what they are called. Two equiangular triangles were the subject of a significant finding made by the well-known Greek mathematician Thales. He applied the Basic Proportionality Theorem, sometimes known as the Thales Theorem, as a conclusion.

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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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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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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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Answer:

Step-by-step explanation:

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 )

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:-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

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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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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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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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 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 standard form of the equation y = 3x + 10 is -3x +y = 10.

To accomplish the given equation and bring it in the standard form for our problem, we first arrange it in standard form and then apply a little algebra to subtract 3x from both sides of the equation.

Given,

y = 3x + 10

Subtract 3x from each side.

Simplify: y - 3x = 3x + 10 - 3x.

y - 3x = 10

The x word should be placed first in the left-hand side arrangement.

-3x + y = 10

We discover that y = 3x + 10 is written as -3x + y = 10.

Ax + By = C is the equation of a line in its standard form, where A, B, and C are constants. There are several possible ways to express a line's equation, and if we are given a line that isn't in standard form, we can apply a little algebra to change the equation.

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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 rise is 231 feet 10 inches if the horizontal run of the roof is 15 feet 34 inches.

Let us assume that x represents the rise and y represents the run,

According to the given problem,

x= 15 feet 34 inches

Converting feet into inches,

we know, 1 feet = 12 inches

so, 15 feet 34 inches = 15*12+34 = 214 inches

Now finding the rise in terms of x and y,

13 = y/x

substituting the value of x and solving for y:

13 = y/214

y = 13*214

y = 2782 inches

Converting inches into feet,

2782 inches = 2782/12 = 231 feet 10 inches

Thus, The rise is 231 feet 10 inches if the horizontal run of the roof is 15 feet 34 inches.

Correct question: You’re on a residential construction team doing roofing. The pitch of a roof is 13 rise over run. Find the rise if the horizontal run of the roof is 15 feet 34 inches.

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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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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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Graph for Domain : 1 ≤ x ≤ 3 ; Range : 2 ≤ y ≤ 7 is attached below:

A graph is a kind of a chart where data are plotted as variables across the coordinate.

Given,

Domain : 1 ≤ x ≤ 3

Range : 2 ≤ y ≤ 7

value of y should be 2 to 7.

value of x should be 1 to 3.

Hence, following is the graph that satisfy

Domain : 1 ≤ x ≤ 3

Range : 2 ≤ y ≤ 7

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Remember that to dilate something in the coordinate plane, multiply each coordinate by the scale factor. For this dilation, the mapping will be ( x , y ) → ( 1.5 x , 1.5 y )

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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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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

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:  x=−4

Step-by-step explanation: