The triangles are similar. Find the value of the variable.

Answer:

n + 2 + 3m

Step-by-step explanation:

[tex]\frac{1}{2} (2n+4+6m) = (\frac{1}{2}*2n)+(\frac{1}{2}*4)+(\frac{1}{2}*6m)\\ =n+2+3m[/tex]

The equation of perpendicular line that bisects the line segment is y = - (1 / 3) · x + 4 / 3.

In this problem we must determine the equation of the line that is perpendicular to a line segment and partitions the line segment in two parts of equal length, it happens when the perpendicular line passes through the midpoint of the line segment.

The equation of the line in explicit form is shown below:

y = m · x + b

Where:

In addition, two lines are perpendicular to each other when the following relationship is observed:

m · m' = - 1

Where:

Besides, the slope of a line can be determined by secant line formula:

m = Δy / Δx

Where:

And lastly, the midpoint of a line segment is determined by this formula:

M(x, y) = 0.5 · A(x, y) + 0.5 · B(x, y)

First, find the midpoint of the line segment:

M(x, y) = 0.5 · (3, 7) + 0.5 · (- 1, - 5)

M(x, y) = (1.5, 3.5) + (- 0.5, - 2.5)

M(x, y) = (1, 1)

Second, determine the slope of the line related to line segment:

m = (- 5 - 7) / (- 1 - 3)

m = (- 12) / (- 4)

m = 3

Third, calculate the slope of the perpendicular line:

3 · m' = - 1

m' = - 1 / 3

Fourth, find the intercept of the equation of perpendicular line:

b = y - m · x

b = 1 - (- 1 / 3) · 1

b = 1 + 1 / 3

b = 4 / 3

Fifth, write the equation of perpendicular line:

y = - (1 / 3) · x + 4 / 3

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The perimeter of a particular form is equal to the sum of its sides, hence the scale factor indicates that the perimeter of Figure A is 122.50 units.

What is perimeter?
A boundary is a closed path that encompasses, encircles, or delimits a two-dimensional shape or a one-dimensional length. A circle's or an ellipse's perimeter is its outermost portion. Numerous applications in real life involve the perimeter calculation. The radius of a shape's edge is known as the perimeter. By summing the lengths of the sides of various forms, discover how to calculate the perimeter. By multiplying the lengths of the sides, one can always get a shape's perimeter. The area surrounding an object is called its perimeter. An enclosed garden is one example at your home. The distance around anything is called its perimeter. A 200-foot fence will be needed for a yard that is 50 feet by 50 feet.

Ratio factor of  A to B = 7:2

Proportion between the perimeters = 7/2

We now understand that a shape's perimeter equals the sum of all its sides. Consequently, using the values from the provided figure, enter the following expression:

A1 / 9+5+9+12 = 7/2

A1 = (7*35)/2

A1 = 122.50 units.

The perimeter of a particular form is equal to the sum of its sides, hence the scale factor indicates that the perimeter of Figure A is 122.50 units.

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No, the square root of 1 is 1, but 1 is not equal to the square root of 1. The square root of a number, represented by the symbol √, is a value that, when multiplied by itself, gives the original number.

For example, the square root of 4 is 2, because 2 x 2 = 4. In the case of 1, the square root is also 1, because 1 x 1 = 1.

In mathematics, the square root of a number is always non-negative, real number. It is positive for positive numbers and zero for zero. So, in short, the square root of 1 is 1, but 1 is not equal to the square root of 1. It is just a value that gives 1 when multiplied with itself.

It's important to note that the square root is not a number but an operator, an action which you perform on a number. The square root of a number is a value that, when multiplied by itself, gives the original number.

In this case, the square root of 1 is 1, which means that 1 multiplied by 1 is 1.

Also, it's worth mentioning that there are two types of square roots: principal square root and non-principal square roots. Principal square root is the positive value of the square root and non-principal square roots are the negative value of the square root.

In this case, the square root of 1 is 1, which is the positive value of the square root.

In conclusion, the square root of 1 is 1, and it is the positive value of the square root, but 1 is not equal to the square root of 1, as the square root is a value that gives the original number when multiplied by itself.

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Polygonal Modeling: a type of 3D modeling that uses points, lines, and polygons to create a 3D object. NURBS Modeling: a type of 3D modeling that uses mathematical equations to create smooth curves and surfaces. Subdivision Modeling: a type of 3D modeling that uses subdivision surfaces to create smooth, organic shapes.

1. Polygonal Modeling: This type of 3D modeling uses points, lines, and polygons to create a 3D object. The polygons are connected together to create the 3D shape, and then textures and colors can be applied to the shape. This type of modeling is often used to create characters and environments for video games and animations.

2. NURBS Modeling: NURBS stands for Non-Uniform Rational B-Splines. This type of 3D modeling uses mathematical equations to create smooth curves and surfaces. NURBS modeling is often used for creating organic shapes such as cars and furniture.

3. Subdivision Modeling: Subdivision modeling is a type of 3D modeling that uses subdivision surfaces to create smooth, organic shapes. This type of modeling is often used for creating characters and creatures for video games and animations.

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Each friend will get 48 books. The solution is obtained using arithmetic operations.

What are arithmetic operations?

There are four basic operations which are listed as follows:

Now, Tara has 3 boxes of books and each box contains 48 books.

So, the total books that Tara has is equal to 3×48= 144.

Thus, Tara has total 144 books.

Tara divides the books among 3 friends.

So, the number of books that each friend will get is equal to 144÷3= 48

Hence, each friend of Tara will get 48 books.

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Answer:

1/2

Step-by-step explanation:

6 x __ = 3

We divided by 6 into both sides

x  = 3/6 = 1/2

So, the missing number is 1/2

The number of solutions which the system of equations has is: A. no solution.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data point (0, 4), a linear equation of the first line can be calculated in slope-intercept form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 4 = (5 - 4)/(3 - 0)(x - 0)

y = x/3 + 4

For the second line, we have:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 1 = (1 + 1)/(6 - 0)(x - 0)

y = x/3 + 1

In conclusion, the system of linear equations has no solution because it represents parallel lines.

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By using the ratio formula, the number of doughnuts that will be consumed of 8 students in the time period of 9 minutes is 24 doughnuts.

The ratio formula compares the connection between two quantities or numbers. In this case, we are given that:

2 students can eat 4 doughnuts in 6 minutes

By using the ratio formula, 1 student can eat = 4/2 = 2 doughnuts in 6 minutes

It takes an average student about 3 minutes to consume a doughnut using the formula= 6/2 = 3 minutes

In one minute, the amount of doughnut can be consumed by a student is 1/3 of a doughnut

This method can be used to predict how many doughnuts 8 students can consume in 9 minutes:

X = 8 x 9 x (1/3) = 24 doughnuts

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The velocity of the object dropped from a height of 100 feet is equal to 21.86 m/sec

Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time

Given here: V(x)=0.9×4.4√x

Thus if x=100feet or 30.47 m putting this value in the equation we get

V(30.47)=0.9×4.4√30.47

             = 21.86 m/sec

Hence, the velocity of the object dropped from a height of 100 feet is equal to 21.86 m/sec

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The slope of -6 means that the battery reduces by 6% each hour

What is the linear equation?

Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0.

The slope of -6 means that, the battery reduces by 6% each hour and the equation is B = -6t + 48

The points

The points on the graph are represented using the following ordered pair (1, 42) and (5,18)

The slope

Start by calculating the slope (m) using:

m = (B2 - B1)/(t2 - t1)

So, we have:

m = (18 -42)/5-1

m = -24/4

m = -6

The equation

The equation is then calculated as:

B = m(t - t1) + B1

This gives

B = -6(t - 1) + 42

B = -6t + 6 + 42

B = -6t + 48

Hence, The slope of -6 means that the battery reduces by 6% each hour

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The functions differ from functions that we have used in algebra in the past as the functions can be combined and are more about rotation rather than where they move.

An output variable and one or more input variables are the minimum number of variables in a function.

An equation can have any number of variables and declares that two expressions are equal (none, one, or more). Although not all equations are functions, a function is frequently expressed as an equation.

It should be recalled that a function is merely an equation in which the x inserted produces precisely one from the equation.

In this instance, the functions are different from the ones we have used in algebra in the past since they may be coupled and focus more on rotation than on where they travel.

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Answer:

A. -1

Step-by-step explanation:

imma human calculator and no one can stop me

So on solving the provided question we can say that we know that all angles of  Quadrilateral is 90, 4x - 2 = 90; x = 22

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

we know that all angles of  Quadrilateral is 90

4x - 2 = 90

4x = 88

x = 22

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Answer:

d = 24

Step-by-step explanation:

d/4 - 9 = -3

d/4 - 9 + 9 = -3 + 9

d/4 = 6

d/4 * 4 = 6*4

d = 24

Check:

(24)/4 - 9 = -3

6 - 9 = -3

-3 = -3 (Correct)

Hope this helps!

Answer:

The measure of the third side of a triangle, when the measures of the other two sides are 18 ft and 23 ft, must be greater than the difference between the measures of the other two sides (which is 18 ft - 23 ft = -5 ft) and less than the sum of the measures of the other two sides (which is 18 ft + 23 ft = 41 ft).

This is because according to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So the measure of the third side must be between the difference of the two given sides and the sum of the two given sides.

Therefore the range of the measure of the third side of a triangle with side lengths 18 ft and 23 ft is:

(-5 ft < x < 41 ft)

or

[x > -5 ft and x < 41 ft].

It is also important to note that any value of x within this range will produce a valid triangle, however, any value less than -5 or greater than 41 will not.

Step-by-step explanation:

(1, 1) is not  solution of system of equations.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

We need to check the  point (1, 1) is a solution to the system of equations.

graph of a line 3 times x plus 2 and the absolute value of x minus 1 plus one.

y = 3x + 2

g = |x-1| +1

We obtain the intersection point

(0,2)

The only point of intersection of the graphs is (0, 2).

The point of intersection is the solution to the system of equations. (1, 1) is not the point of intersection

Hence, (1, 1) is not  solution of system of equations.

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The real distance by means of scales used in the map that is described in the statement is approximately equal to 72.11102550928 kilometers.

Scales are a useful resource to represent any system in a size different than real. Maps are usually created from application of scales. Mathematically speaking, scales are described by following mathematical ratio:

r = s / R

Where:

If we know that r = 0.1 centimeters per kilometers and s = 7.211102550928 centimeters, then the real distance derived from the distance shown in the map that is described in the statement is:

R = s / r

R = (7.211102550928 cm) / (0.1 cm / km)

R = 72.11102550928 km

By using scales on the map, the real distance is approximately equal to 72.11102550928 kilometers.

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The grouping symbols commonly used in mathematics are the following:

Now, According to the question:

What are the 4 types of grouping symbols?

The grouping symbols commonly used in mathematics are the following:

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

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The Volume of shape Q is 25,600 cm³.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared.

Let z be the scale factor

x be the surface area of shape Q

and, y be the surface area of shape P

So, z²=x/y

we have,

x = 2880 cm², y= 720 cm²

z² = 2880/720

z² = 4

z = 2

Now, If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

z³ = x/y

We have z= 2 and y = 3200 cm³

So, 2³ = x/3200

x = 8×3200

x = 25,600 cm³

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A corollary is a theorem that connects to an established theorem in mathematics with a brief proof. As opposed to statement or theorem, the term "corollary" is inherently arbitrary.

A corollary may be unquestionably true if the idea or theory it is founded on is correct. Any triangle's internal angles, for instance, add up to 180 degrees in all cases. Each interior angle of an equilateral triangle is 60 degrees, which is a corollary of the aforementioned theorem.

A triangle is equiangular if it is equilateral, which is a corollary to the Base Angles Theorem. Converse of Base Angles Theorem Corollary: If a triangle is equiangular, it is also equilateral.

The sum of the measurements of the two distant interior angles determines how large an exterior angle of a triangle must be. the triangle's angle-sum Corollaries: A right triangle's acute angles are complimentary. A theorem whose proof naturally follows from another theorem is called a corollary.

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The corollary interior angles theorem is a mathematical result that relates to the number of sides in a polygon and the sum of the interior angles of that polygon.

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Answer: The exponential form should be 10⁵=9x+1 instead of 9x+1=10⁵

Step-by-step explanation:

The exponential form of a logarithm should be the other way around.

The mathematical concepts used to calculate insurance premiums include probability, actuarial science, risk assessment, pricing models, financial models, and statistical analysis.

Probability:

To calculate premiums, insurance companies use statistical data to determine the likelihood of a claim occurring. Probability is used to estimate the likelihood of certain events happening, such as accidents, illnesses, or natural disasters, and to determine the likelihood of a claim being made.

Actuarial Science:

Actuarial science is the application of mathematical and statistical methods to assess risk and uncertainty in insurance, finance, and other industries. Actuaries use mathematical models to analyze data and make predictions about future events, which is crucial in determining insurance premiums.

Risk Assessment:

Insurance companies use risk assessment to determine the level of risk associated with insuring a particular individual or group. Factors such as age, health, occupation, and location are considered when assessing risk, and premiums are adjusted accordingly.

Pricing models:

Pricing models are used to determine the cost of insurance based on the perceived level of risk. Pricing models like Loss Ratio, Pure Premium, and Captive pricing are used to arrive at the insurance premium.

Financial Models:

Financial models are used to determine the long-term financial stability of an insurance company and to ensure that the company has enough funds to pay out claims. Actuaries use financial models to calculate the amount of money an insurance company needs to set aside in order to pay claims and to determine the long-term financial health of the company.

Statistical Analysis:

Insurance companies use statistical analysis to evaluate data on claims and losses, and to identify patterns that can be used to predict future claims and losses. This analysis is used to identify trends in claims, to identify high-risk groups, and to set premiums.

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The number of the cans that is produced is 5832.

We know that the term direct proportion has to do with a case in which one of the variables is increasing and the other is also increasing along side. This implies that the two variables can be seen to increase at the same time.

We have that the relationship of the process can be given as shown in question in simple format as; y = 243x where;

x = Number of hours

y = Number of cans

After 24 hours, we have;

y = 243(24)

y = 5832

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The amount of diesel remaining after traveling more than 28 miles will always be greater than or equal to 0.

If a vehicle uses diesel fuel, the amount of diesel remaining after traveling more than 28 miles will depend on the efficiency of the vehicle and the total capacity of the tank. We can express this as an inequality by saying that the diesel remaining will always be greater than or equal to 0.

diesel remaining ≥ 0

The amount of diesel remaining after traveling more than 28 miles will always be greater than or equal to 0.

The amount of diesel remaining after traveling more than 28 miles will depend on the efficiency of the vehicle and the total capacity of the tank. We can express this as an inequality, which states that the diesel remaining will always be greater than or equal to 0. This means that no matter how far the vehicle has traveled, there will always be some diesel left in the tank.

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The correct option is 1/(n+1).The upper bound for the integral is 1/(n+1).

To determine the upper bound, we can use the fact that the integrand is bounded by its maximum value on the interval. The maximum value of the integrand on the interval [0, 1] is:

f(x) = 5x(1 + x)^(0.5)

At x = 1, f(x) = 5(1 + 1)^(0.5) = 5√2.

Therefore, an upper bound for the integral is:

In ≤ 5√2∫x^n dx

             0

Using integration by parts, we obtain:

In ≤ 5√2[x^(n + 1)/(n + 1)]_0^1

= 5√2/ (n + 1)

Therefore, the upper bound for the integral is 1/(n+1).

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To obtain how fast the ball traveling 2 seconds after it is thrown, we differentiate the position equation with respect to time once;

dh(t) =  d  (-16[tex]t^{2}[/tex] + 40t +5 )

dt        dt

dh(t) = -32t  + 40

dt

with t= 2:

h'(2) =-32 (2) +40

h'(2) =-24 ft/s.

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Yes, the triangle can be easily formed for the sides 7 cm, 5 cm and 3 cm.

According to the side side side rule of triangle, if the sum of the any two sides of triangle is more than third side, it will form a triangle. Let us check the same by assuming side a to be 7 cm, side b to be 5 cm and side c to be 3 cm.

Side a + side b > side c

7 + 5 > 3

Add the digits in Left Hand Side of the equation

12 > 3

Side b + side c > side a

5 + 3 > 7

Add the digits in Left Hand Side of the equation

8 > 7

side c + side a > side b

3 + 7 > 5

Add the digits in Left Hand Side of the equation

10 > 5

We see that the two sides of the triangle are greater than third side, hence, it is possible to form the triangle.

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A 3-dimensional vector is a line segment running from a point called head to the point called tail in 3-Dimensional space.

Vectors are mathematical or geometrical quantity that has two independent properties i.e., direction and magnitude. There are many types of vectors like unit vectors, equal vectors, etc.

The magnitude of the vector is the length of the line segment without it the direction has no power, Similarly unit vectors help us to find the direction of vectors and their magnitude is 1.

A 3-dimensional vector has majorly 3 components i.e., it has projections in the x, y, and z axes. For a three-dimensional vector A(a1,a2,a3), the formula for its magnitude is ∥a∥=√a21+a22+a23.

Along with magnitude and directions, the 3-D vectors also have angles and they are formed from the vector directly to each of the 3 positive axes.\ i.e., x, y, z axes. The formula used to calculate angle  is θ = cos-1 [ (a · b) / (|a| |b|) ]

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