Introduction For Prime Factors Binomials

Introduction For Prime Factors Binomials:

      Prime factors: A number written has no divisors and it divisible by itself and as a product of prime factors is said to in the prime   factor form.
     Example for prime factors:
             Prime factor form of 5 = 1*5 thus 1, 5  are prime factors.

     Binomials: An expression with two unlike terms is called a binomials.
     Example for binomials:
             x+y, m-5, mn+4m

Steps for Finding Prime Factors:

Step 1: Finding a common factor
      When terms of an algebraic equations A have a common factor B, we divide each term of A by B and get an expression C. Now, A is factored to be B × C.

Step 2: Grouping the terms
      When the terms of an algebraic equations it does not have a common factor, the terms may be grouped in an appropriate manner and a common factor is determined

Prime Factors Binomials:

Example 1:
Find prime factors for 25m^2 - 16n^2

Solution:
        We have - 25m^2- 16n^2 = (5m)2- (4n)2        where formula, a^2-b2 = (a+b)(a-b)
                                        = (5m+4n) (5m-4n)


Example 2:
 Find prime factors for x^2 – 7x + 12.

Solution :
        Since, a + b = – 7, ab = 12,and negative factors of 12 are – 1, – 2, – 3, – 4, – 6 and – 12, we find that a = – 4 and
b = – 3 (or a = – 3 and b = – 4). Hence,
        x^2 – 7x + 12 = x^2 + {(– 4) + (– 3)}x + (– 4) × (– 3)
                           = (x – 4) (x – 3)

Example  3:
 Find prime factors for x^2 + 3x – 10.

Solution :
Here, we have to find two numbers a and b such that a + b = 3 (the coefficient of x) and ab = – 10 (the constant term).
Now factors of –10 are ± 1, ± 2, ± 5 and ± 10. A little experimentation with these numbers tells us that we may take a and b as 5 and – 2. The sum of 5 and – 2 is 3, and product of 5 and – 2 = – 10. Hence,
              x^2 + 3x – 10 = x^2 + {5+ (– 2)}x + 5(– 2)
                                 = (x + 5) (x – 2)

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Introduction for scale data definition

Introduction for scale data definition:  

                    The scale data is a ratio between the linear dimension of a representation or model and those of the object represented, as on a map or technical drawing. And scale data is a measurement. Scale Matters, develops concepts about scale. Reading scales is significant for students if they are to make use of measure devices to represent calculations using single and double number lines, to interpret locations in co-ordinate systems and to interpret many different forms of data display.

                    Scale can be identified by the concept of number line. A number line is a line inside which real numbers can be located, according to their value. In this article we shall discuss about scale data definition.

Definition and Methods of Scale Data:

Definition:

              The ratio between the linear dimension of a representation or model and those of the object represented, as on a map or technical drawing.

Methods:

             Scale factor.

             Measurement of scale.

             Proportions.

 Scale factor

              The multiplying factor for each linear measurement of an object when it is to be enlarged about a given centre of enlargement. A scale factor can be positive, negative or fractional. If the scale factor is positive, the image is larger than the object and on the same side of centre of enlargement as the object as the object. If the scale factor is fractional positive, the image will be smaller than the object,  but on the same side of the centre of enlargement. If the scale factor is negative, the image will be on the opposite side of the centre of enlargement and will be invented.

              For example, doubling distance corresponds to a scale factor of 2 for distance, while cutting a cake in half results in pieces with a scale factor of ½.

Measurement of scale:

               We do measurements in our routine life in a number of conditions. For example, we calculate the length of a cloth for stitching, the area of a wall for white washing, the perimeter of a land for fencing and the volume of a container for filling. Based upon the measurements, we do further calculations according to our needs. The branch of mathematics which deals with the measure of lengths, angles, areas, perimeters and volumes of plane.

Area and Perimeter:

              Rectangle:

                          Area = l × b sq.units

                          Perimeter = 2 (l + b) units

                         d = `sqrt((l^2)+(b^2))` units

            Parallelogram:

                           Area = b × h sq.units

                          Perimeter = 2(a + b) units.

           Triangle with a given base and height:

                         Area = `1 / 2` (b × h) sq.units

           Quadrilateral:

                        Area = 21 d × (h1 + h2) Sq.units

Proportion for Scale Data Definition:

            A relation giving the equality of two ratios, in the form

                                         `a / b` = `c / d`

            Before it was written as a: b :: c: d, which has become obsolete these days. Here a and b are recognized as extremes, b and c are known as means. If two ratios are in proportion then the product of extremes must be equal to the product of means. ad = bc.

Example 1:
            Jane ran 150 meters in 20 seconds. How long did she take to run 1 meter?

Solution:

Step 1: Think of the word problem as:

              If, 150 then 20, If 1 then, how many?

Step 2: Write the proportional relationship:

             150 ? 20

             1? (1 / 150) x 20 = 0.15

Answer: She took 0.133 seconds

Example 2:

A car travels 150 miles in 4 hours. How far would it travel in 6 hours?

Solution:

Step 1: Think of the word problem as:

              If 4 then 150. If 6 then how many?

Step 2: Write the proportional relationship:

                 4 ? 150

                 6 ? `(6 / 4)` x 150 = 225

Answer: He traveled 225 miles.

Fraction to equivalents percentage

Steps for converting a fraction to equivalents percentage:-

                          The procedure of fraction to percentage translation involve the employ of fundamental regulation of fractions..  The subsequent steps demonstrate how to find equivalents percentage for fraction.
Step: - 1.
Convert the given fraction to decimal.
Step:- 2
Multiply the obtained decimal by 100.
The resulting answer is the percentage equivalents of the given fraction.
Now lets see some solved and practice problems on converting fraction to equivalent percentage.

Solved Problems for Fraction Percent Equivalents:-

Problem 1:-

Find the equivalent percentage for the fraction `1/10` .

Solution:-

The given fraction is `1/10` .

Step 1

Find the decimal equivalent for `1/10` .

The decimal equivalent for `1/ 10` is 0.1.

Step 2

Multiply the decimal equivalent by 100.

=0.1  * 100 = 10 %.

The percentage equivalent for `1/ 10` is 10%.

Problem 2:-

Find the equivalent percentage for the fraction `3/ 10` .

Solution:-

The given fraction is `3/ 10` .

Step 1

Find the decimal equivalent for `3/ 10` .

The decimal equivalent for `3/ 10` is 0.3.

Step 2.

Multiply the decimal equivalent by 100.

= 0.3* 100. = 30 %.

The percentage equivalent for `3/ 10` is 30%.

Problem 3:-

Find the equivalent percentage for the fraction` 25 / 345` .

Solution:-

The given fraction is `25/ 345` .

Step 1

Find the decimal equivalent for `25/ 345` .

The decimal equivalent for `25/ 345` is 0.072.

By rounding it to hundredth place. We get 0.07

Step 2.

Multiply the decimal equivalent by 100.

=0.07.* 100 = 7 %.

The percentage equivalent for `25/ 345` is 7%.

Problem 4:-

Find the equivalent percentage for the fraction `346 / 2000` .

Solution:-

The given fraction is `346 / 2000` .

Step 1

Find the decimal equivalent for `346 / 2000` .

The decimal equivalent for `346 / 2000` is 0.173

By rounding it to hundredth place. We get 0.17

Step 2.

Multiply the decimal equivalent by 100.

=0.17.* 100. = 17 %.

The percentage equivalent for `346 / 2000` is 17%.

Practice Problems for Fraction Percent Equivalents:-

Problem 1:-

Find the equivalent percentage for the fraction `5/10` .

Answer:- 20 percentage.

Problem 2:-

Find the equivalent percentage for the fraction `23/89` .

Answer:- 25 percentage.

Problem 3:-

Find the equivalent percentage for the fraction `189/ 390` .

Answer:-  48 percentage.

Statistics Scatter plot

To understand what is a scatter plot in math, lets look at the following example:
Below is the data for X and Y, where X represents number o f hours of study put in by a particular student the previous night, and Y represents his test score the next day morning.

Name of student X = number of hours of study Y = test score (%)
Ann 5 60
Ben 6 70
Carol 8 90
Dan 9 80
Elene 7 70

We are interested in finding if there is any relation between the number hours of study put in the previous night and the test score.
For that, we take a graph sheet and plot the above data as ordered pairs. So the points we would get would be : (5,60), (6,70), (8,90), (9,80), (7,70). Alternatively we can also use and online scatter plot tool to get the graph. The graph would look like below:

A graph such as above is called a scatter plot.
From the graph we see the general trend that if number of hours of study increases, the test score also increases and vice versa. Though it is not possible to find the exact score that the student will get if he studies for say 10 hours, but we can say that most probably the score would be 90 or more if number of hours of study put in is 10.

Applications of scatter plots:
Scatter plot statistics have various applications. Usually a scatter plot is used when the variables under consideration can be controlled by us. The independent variable is also called the control parameter and that is plotted along the x axis. The dependent variable is usually plotted along the y axis.
A scatter plot helps us to derive some relation between the variables. This relation can be of various types, liner, quadratic, inverse, logarithmic or exponential etc. Based on how the points are flowing, we can predict a relation. For the above example the relation can be linear.
For example, a scatter plot on line of regression would give us the deviation of the data from the proposed regression line or the line of control. A scatter plot is also used in comparing two sets of data. When relation between the variables is not linear, the scatter plot is most useful. By merely plotting the scatter plot of the data we can see what kind of a relation the two variables could have.

Scatter plots could be learned over the net through scatter plot online as well.

Know more about the Statistics help,  Statistics homework Help. This article gives basic information about Scatter plot. Next article will cover more statistics concept and its advantages,problems and many more. Please share your comments.

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Let us know more with Algebra Linear equations

Linear equations in two variables is the equation of the form ax + by = 0 where a and b = 0.
A Linear equation is a first degree algebraic expression with one, two or more variables equated to a constant. Graphically a linear equation with one variable or linear equation in two variable is a straight line whereas linear equation with three variable represents a plane.
A simple linear equation is a statement of equality between two algebraic expressions involving an unknown quantity called the variable. In a linear equation the power of the variable is always equal to 1. The two sides of an equation are called Left-Hand Side (LHS) and Right Hand Side (RHS).They are written on either side of = sign.
The two sides of an equation are like the two pans of a balance.

Basic Equations Concept

The two expressions (LHS and RHS) are equal only for a particular value of the variable (x). These equations are called equations of condition. An equation of condition is generally referred to as an equation.

Solving linear equations in two variables

The process of finding the value of the unknown quantity for which the equation is true, is called solving the equation. The value so found is called the root or solution of the equation.
An equation whose graph is a straight line is called a linear equation. (linear means straight). An equation of degree one is linear.
A linear equation in two variables is of the form ax + by = c,where

Graphing Linear Equations in two Variables

The position of a point in a plane is fixed by selecting two axes of reference which are formed by combining two number lines at right angles so that their zeros coincide.
The horizontal number line is called x-axis and the vertical number line is called y-axis

Algebra Problems

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures.

Lets see some of the problems in algebra:

Example 1:Solve Graphically
x+y=-1; y-2x=-4


Answer: x+y=-1
y=-1-x
At x=-2, y=-1+2=1
At x=-3, y=-1+3=2
At x=0, y=-1-0=-1

y-2x=-4
y=2x-4
At x=1, y=2-4=-2
At x=-1, y=-2-4=-6
At x=0, y=0-4=-4

Solving Trigonometric Functions

This will help you in solving the Trigonometric Functions.

This is how to solve the Trigonometric Functions