How to Study Math: Algebra

There are many methods for solving equations, but the two main methods are algebraic method and graphic method.

Algebraic methods: These methods involve using algebraic manipulation to isolate the variable on one side of the equation and find its value. This can include using operations such as addition, subtraction, multiplication, and division, as well as the use of inverse operations (e.g. undoing addition with subtraction) and properties of equality (e.g. transitive property).

Graphic methods: These methods involve using graphs to represent the equation and find the solution. This can include plotting the equation on a coordinate plane and finding the points of intersection, or using a graphing calculator or software to plot the equation and find the solution.

It's worth noting that the method used to solve an equation will depend on the complexity of the equation and the information available. Some equations can be easily solved using algebraic methods, while others may require a combination of algebraic and graphic methods or an entirely different approach.

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The formula for scale factor is: Scale Factor = New Length / Original Length.

Scale factory the rescue between two corresponding length, area or the volumes of two similar figure it is used to compare the size of one figure to another as well as to the enlarge of reduced to size of a figure the scale factor is expressed as a ratio such as one is to to fit the first number is the original size and the second is the new size.

This is used to determine the factor by which an object has been scaled up or down. For example, if an object was originally 8 inches long and then scaled up to 16 inches long, the scale factor would be 2, as 16 is twice the length of 8.

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Answer:

6x^3 + x^2 - 12x^2 - 18x - 6x - 6 = 6x^3 - 18x^2 - 12x - 6.

Step-by-step explanation:

simplify the expression (2x+3)(3x^2-6x+2)
First, we'll use the distributive property to expand the product of the two binomials:

(2x+3)(3x^2-6x+2) = 2x(3x^2-6x+2) + 3(3x^2-6x+2)

Next, we'll expand the product of each term in the first binomial with each term in the second binomial, using the distributive property again:

= 2x3x^2 + 2x(-6x) + 2x2 + 33x^2 + 3*(-6x) + 3*2

We can now simplify the resulting terms by combining like terms and combining the coefficients:

= 6x^3 -12x^2 + 4x + 9x^2 -18x + 6

we will combine the like terms

= 6x^3 - 18x^2 + 4x + 6

This is our final expression in standard form

Yes, 2x²-√3x+9=0 is a quadratic equation.

A quadratic equation is a type of polynomial equation that can be written in the form of ax² + bx + c = 0, where a, b, and c are constants and x is the variable. In this case, the equation 2x²-√3x+9=0 can be written in the form of ax² + bx + c = 0, where a = 2, b = -√3 and c = 9. Therefore, it is a quadratic equation. Quadratic equations have solutions in the form of x = (-b ± √(b² - 4ac))/2a, which is also known as the quadratic formula. In this case, if we substitute the values of a, b, and c into the quadratic formula, we can find the solutions for x in the equation 2x²-√3x+9=0.

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Complete question:

2x²-√3x+9=0 is it a quadratic equation​?

The equation of the perpendicular bisector of the segment with endpoints G (-2,0) and H(8,-6) would be, y = -(3/4)x + (9/2)

What is Perpendicular bisector of the segment?

A perpendicular bisector is a line that cuts another line segment through the junction point at a straight angle. As a result, a perpendicular bisector always cuts a line segment through its midway. The term bisect means to divide equally or uniformly.

The midpoint of the segment GH is the point (3,-3).

The slope of the line perpendicular to GH is the negative reciprocal of the slope of GH, which is -6/8 = -3/4

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

The point-slope form of the equation of the line is y - y1 = m(x - x1)

So we have

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

y + 3 = (-3/4)x + (9/2)

We can find the equation of the perpendicular bisector of the segment G(x1, y1) and H(x2, y2) by using the midpoint of the segment, (x1 + x2)/2, and (y1 + y2)/2, and the slope of the segment, (y2 - y1)/(x2 - x1)

so our final equation is y = -(3/4)x + (9/2)

Therefore, equation of the perpendicular bisector of the segment with endpoints G (-2,0) and H(8,-6) would be, y = -(3/4)x + (9/2)

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In January, the number of days shown by the equation m = 4w + 3.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

A pattern shown in the image.

Let m is the number of days in a month.

And w represents the number of days in the weeks.

So, algebraic equation,

m = 4w + 3.

Therefore, the equation is m = 4w + 3.

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Answer:

Step-by-step explanation:

the way to determine if two atoms are of elements in the same group in the periodic table is to look at the number of valence electrons in the outermost energy level of the atom. Elements in the same group have the same number of valence electrons. For example, elements in Group 1 have 1 valence electron, elements in Group 2 have 2 valence electrons, and so on.

It's worth mentioning that the group in the periodic table is also known as family or column.

On solving the question, The value of x in Right Angle Triangle is  .The value of x is .[tex]16\sqrt{2}[/tex]

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

In the triangle 2 angles are  respectively.

The third angle is  = 45

The triangle is issosceles triangle

So the side which is not x is 16.

Now by using pythagorus Theorem

The value of x is .[tex]16\sqrt{2}[/tex]

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Step-by-step explanation:

we need Pythagoras for right-angled triangles

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs.

we also need to remember that the sum of all angles in a quadrilateral (4-sided shape) is 360°.

so, as 3 angles in the main quadrilateral are 90°, so is also the 4th angle. and that makes the quadrilateral a regular rectangle.

we know the length of the rectangle (15 ft).

the width is also the second leg of the attached right-angled triangle.

so, we know

13² = 5² + (leg2)²

169 = 25 + (leg2)²

144 = (leg2)²

leg2 = sqrt(144) = 12 ft

the total area is

the area of the rectangle

+

the area of the triangle

the area of the rectangle is

length × width = 15 × 12 = 180 ft²

the area of the right-angled triangle is

leg1 × leg2 / 2 = 5 × 12 / 2 = 5×6 = 30 ft²

the total area is

180 + 30 = 210 ft²

FYI - a different way is to directly calculate the area of the trapezoid :

(base1 + base2)×height/2

height = the width of the rectangle or leg2 of the right-angled triangle.

so, we have

(15 + (15 + 5))×12/2 = (15 + 20)×6 = 35×6 = 210 ft²

Answer:

y = 37x

Step-by-step explanation:

We know

The value of y is 37 times the value of x, so our equation is

y = 37x

An ordered pair is a set of two values, (x,y), that represents a point on a coordinate plane. The x-coordinate represents the horizontal position and the y-coordinate represents the vertical position. The formula for an ordered pair is (x,y). where x and y are the coordinates.

From the given figure, we can say that it is a relation as 0 is input for both -2 and 1.

What is the Onto function ?

Onto function can be defined as the function in which the range is equals to codomain.

We know that relation  can be defined as the relationship between sets of values and it is denoted by R.

And Function can be defined as the it is a relation where with only one output to each input.

From the given figure,

(0,-2) (0,1) (1,2) (2,1) (3,4) are the ordered pairs and here 0 is input for both -2 and 1
Hence , From the given figure, we can say that it is a relation as 0 is input for both -2 and 1.

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No, it is not possible to define all terms in geometry. The point, line, and plane are only a few of the many undefined terms in geometry. All other concepts in geometry may be defined from these three undefined terms.

The father of geometry, Euclid was a brilliant mathematician. Learn more about Euclid and the history of some of the math ideas we use today to see how important they have become.

The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.

The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.

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No, it is practically not possible to define all terms in geometry. Points, lines, and planes are just a few of the many terms not defined in geometry.

The point, line, and plane are only adequately described by examples and descriptions, hence they are regarded as undefined words in geometry. Give the points, lines, and planes a name. Points that are on the same line are known as collinear points.

A legal document's definitions are often located at the outset, or at the start of a standalone portion like a schedule or section.

The study of different mathematical or real-world shapes, sizes, and figures is known as Geometry. You will learn about points, lines, planes, angles, parallel lines, triangles, similarity, quadrilaterals, transformations, circles, and area in geometry.

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The correct answer is C. We can add and subtract terms regardless if they have the same base.

To add polynomials, we add the coefficients of the like terms together. For example, to add 2x^3 + 5x^2 + 6x + 3 and 3x^2 + 7x + 8, we would first identify the like terms, which in this case are x^2 and x. The coefficients of the like terms are then added together, so 2x^3 + (5+3)x^2 + (6+7)x + (3+8). The result is 2x^3 + 8x^2 + 13x + 11.

To  subtract polynomials, we subtract the coefficients of the like terms. For example, to subtract 3x^2 + 7x + 8 from 2x^3 + 5x^2 + 6x + 3, we would identify the like terms, which in this case are x^2 and x. The coefficients of the like terms are then subtracted, so 2x^3 + (5-3)x^2 + (6-7)x + (3-8). The result is 2x^3 + 2x^2 - x - 5.

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No, prime numbers are not divisible by any other number apart from one and number itself.

As given in the question,

Given numbers are prime numbers,

Condition to be asked :

Prime numbers are divisible.

Prime numbers are those numbers which are only divisible by only two numbers one and number itself.

Prime numbers has only two factors one and number itself.

Example of prime numbers are as follow :

2, 3, 5, 7, 11,.....so on.

If the number has more than two factors then the numbers are considered as composite numbers.

One is neither prime nor composite.

Therefore, prime numbers are not divisible by any other number.

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1. steps to find the value of x

The first step is to equalize the form of the equation.

y = 6x-11 = -6x+y= -11

-2x-3y = -7

thus becoming:

-6x+y= -11

-2x-3y = -7

Then eliminate y:

-6x+y= -11 | times -3| becomes 18x-3y=33

18x-3y=33

-2x-3y = -7

y in the equation can be eliminated to become:

20x=40

x=40/20

x=2

steps to find the value of y:

The first step is to equalize the form of the equation.

y = 6x-11 = -6x+y= -11

-2x-3y = -7

thus becoming:

-6x+y= -11

-2x-3y = -7

Then eliminate x:

-2x-3y = -7 | multiplied by 3| becomes -6x-9y=-21

-6x+y= -11

-6x-9y=-21

x in the equation can be eliminated to become:

10y=10

y=-10/10

y=1

2.

1. steps to find the value of x

The first step is to equalize the form of the equation.

2x-3y = -1

y = x-1 becomes -x+y=-1

thus becoming:

-2x-3y = -1

-x+y=-1

Then eliminate y:

-x+y=-1| times -3| to 3x-3y=3

-2x-3y = -1

3x-3y=3

y in the equation can be eliminated to become:

-5x=-4

x=4/5

Steps to find the value of y:

The first step is to equalize the form of the equation.

2x-3y = -1

y = x-1 becomes -x+y=-1

thus becoming:

-2x-3y = -1

-x+y=-1

Then eliminate x:

-x+y=-1| multiplied by 2| becomes -2x+2y=-2

-2x-3y = -1

-2x+2y=-2

x in the equation can be eliminated to become:

-5y=1

y=-1/5

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A aggregate of 360 residers left Planet X in the once three times.

What's Linear Equation?

A direct equation is an algebraic equation of the form y = mx b, where m is the pitch and b is the y- intercept, and only a constant and a first- order( direct) term are included. The variables in the antedating equation are y and x, and it's sometimes appertained to as a" direct equation of two variables."

The point- pitch form, standard form, and pitch- intercept form are the three main types of direct equations.

At a pace of 120 occupants every time, they've been departing earthX.

So, by the formuls;

- 120x 3 = 360

thus, A aggregate of 360 residers left Planet X in the once three times.

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Answer:

9√6

Step-by-step explanation:

3√2 × 3√3

3√2×3 ×3

3√6×3

9√6

Percentage of questions attempt by Desmond's in his math's exam is given by :

a) In his first attempt percentage of question answered by Desmond is 67.74%.

b) In his second attempt percentage of question answered by Desmond is 93.55%.

c) Improvement in the percentage of question answered by Desmond is 25.81%.

As given in the question,

Total number of questions attempted by Desmond = 31

Number of questions fully right in first attempt of Desmond = 21

a ) Correct percentage of questions in the first attempt

= ( 21 / 31 ) × 100

= 67.74%

b) Number of questions fully right in second attempt of Desmond = 29

Correct percentage of questions in the second attempt

= ( 29 / 31 ) × 100

= 93.55%

c ) Improvement in the percentage comparing both the attempts

= ( 93.55 - 67.74 ) %

= 25.81%

Therefore, the percentage of questions attempt by Desmond is given as follow :

a) In his first attempt percentage of question answered by Desmond is 67.74%.

b) In his second attempt percentage of question answered by Desmond is 93.55%.

c) Improvement in the percentage of question answered by Desmond is 25.81%.

The above question is incomplete , the complete question is :

Desmond's GCSE math's exam is next week. As part of his revision he attempted 31 questions on his least favorite topic of percentages. He got 21 questions fully right on the first attempt. Two days later he tried all 31 questions again and this time got 29 correct.

a) What percentage of question did he get correct on his first attempt?

b) What percentage of question did he get correct on his second attempt?

c) What is the percentage improvement in Desmond's results?

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Answer:

67.1

Step-by-step explanation:

Writing the statement '49 is 73% of what number?' where x is the number we are trying to find:

[tex]49 = 73\% \: of \: x[/tex]

To find the percentage of a number, we multiply the number by the decimal equivalent of the percentage, so can be rewritten as:

[tex]49 = \frac{73}{100} \times x[/tex]

[tex]49 = 0.73x[/tex]

[tex] \frac{49}{0.73} = x[/tex]

[tex]x = 67.1 \: rounded \: to \: 3 \: signifiant \: figures[/tex]

the equation 10-2x is plotted below.

What is equation straight line?

Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

The equation of the line y=10−2x

m=-2

intercept = 10

Hence the equation 10-2x is plotted below.

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Answer:

The simple interest is calculated by multiplying the principal amount by the interest rate and the number of years.

Simple Interest = Principal x Interest Rate x Time

The simple interest on Boden's account is:

800 x 3.2% x 4 = 800 x 0.032 x 4 = $256

To find the total amount in the account after 4 years, we add the interest to the principal:

800 + 256 = $1056

So, Boden's account will have $1056 after 4 years.

The slope of the line connecting the points (5,1) and (-1,3) will be - 1/3.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

The points are given below.

(5, 1) and (-1, 3)

The slope of the line is given as,

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

m = 2 / (-6)

m = - 1/3

The slope of the line connecting the points (5,1) and (-1,3) will be - 1/3.

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Triangle ABC and Triangle are congruent, but PF is the corresponding side.

A triangle in geometry is a three-sided polygon with three edges and three vertices.

The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.

This characteristic is known as the triangle's angle sum property.

If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.

In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.

A closed, two-dimensional shape is a triangle. It is a polygon with three sides. Straight lines make up all of the sides.

The vertex is the intersection of two straight lines. The triangle therefore has three vertices. 

According to our question-

The matching parts of two figures that are congruent are identified by their respective vertices in the same order.

The side PF of PDF corresponds to the side AC of ABC (the first and last letters of the name or vertices) (corresponding letters in the name).

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On solving the provided question, we can say that percentage of the days was she late = 14/250 * 100 = 5.6%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

Karrie was late to work = 14 times last year.

she worked = 250 days last year

percentage of the days was she late = 14/250 * 100 = 5.6%

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A perpendicular bisector is a line that passes through the midpoint of two points, and is perpendicular to the line connecting the two points.

An example of a perpendicular bisector is the line between points A(2,4) and B(4,6). The midpoint of A and B is (3,5), and the equation of the line perpendicular to A and B is y= -x+10. To verify that the equation is perpendicular to A and B, we can calculate the slope of the line connecting A and B. The slope of A and B is (6-4)/(4-2) which is equal to 2. The slope of a perpendicular line is the negative reciprocal of 2, which is -1/2. Therefore, the equation of the perpendicular line is y = -(1/2)x + 10. This equation passes through the midpoint (3,5) which verifies that it is a perpendicular bisector of A and B.

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....................

The correct option is C.

A graph is a visual representation of data or a function, typically shown on a coordinate plane. It can be used to display information in a clear and concise way, and can be used to identify patterns, trends, or relationships within the data. Graphs can take many forms, including line graphs, bar graphs, scatter plots, and pie charts. They are used in many different fields, including mathematics, science, engineering, economics, and statistics. A right angled triangle is a type of triangle in which one angle is 90 degrees. The side opposite the right angle is called the hypotenuse and the other two sides are called the legs. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

There are several types of graphs that can be used to represent data and information, including:

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Answer:

6(x+2y) + 3 + 4y + 5

6x+12y+3+4y+5

Simplified: 6x+16y+8

Step-by-step explanation: